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Advancing Frontiers of Path Integral Theory for Stochastic Optimal Control

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Pith's one-line read The dissertation's central claim is that a chance-constrained stochastic optimal control problem can be solved with zero duality gap by dual ascent whose gradient is a Monte Carlo estimate of failure probability, and that the same path…

desk verdict A competent compilation of already-published path integral control results, with one genuinely interesting chance-constrained duality claim that hinges on an assumption the dissertation itself labels a conjecture. read the letter →

arxiv 2504.17154 v1 pith:WLT6CDSY submitted 2025-04-24 math.OC cs.ROcs.SYeess.SY

Apurva Patil This is my paper · ORCID
classification math.OCcs.ROcs.SYeess.SY MSC 49K4549L2549N1560H3093E2093E25
keywords pathintegralcontrolchance-constrainedstochasticoptimalstrongdualityFeynman-KacrepresentationMonteCarlodualascentzero-sumdifferentialgamesdeceptivesamplecomplexity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This dissertation extends path integral control—a Monte Carlo method that turns stochastic optimal control into averages over simulated trajectories—to six problem classes that previously resisted sampling-based treatment. Its central result is that a chance-constrained stochastic optimal control problem, where a collision or failure probability must stay below a given threshold, can be solved through its Lagrangian dual with zero duality gap. That means the hard constraint can be handled by iteratively updating a single penalty weight using Monte Carlo estimates of failure probability, instead of solving a high-dimensional PDE on a grid. The same path integral machinery is then carried over to two-player zero-sum games, deceptive policy synthesis, hierarchical task control, and stealthy attack synthesis and mitigation. If the zero-duality-gap theorem holds, safety-critical control becomes a simulator-driven, GPU-parallelizable computation.

What carries the argument

The load-bearing object is the Feynman-Kac representation of the exponentiated value function, $\xi(x,t;\eta) = \mathbb{E}\left[\exp\left(-\frac{1}{\lambda}\left(\phi(\hat{x}(\hat{t}_f);\eta) + \int_{t}^{\hat{t}_f} V(\hat{x}(r),r)\,dr\right)\right)\right]$, where the expectation is over trajectories of the uncontrolled system and $\phi$ encodes the terminal cost plus the chance-constraint penalty $\eta \cdot \mathbf{1}_{x(t_f)\in\partial X_s}$. With the noise-control alignment condition $\Sigma\Sigma^\top = \lambda G R^{-1} G^\top$, this linearizes the HJB equation. The optimal control is $u^*(x,t;\eta) = -R^{-1}G^\top \partial_x J(x,t;\eta)$ with $J = -\lambda \log \xi$, and the failure probability is estimated by reweighting uncontrolled sample paths by the same exponentiated cost, an importance-sampling step. Dual ascent on $\eta$ uses that estimated failure probability as the gradient.

What would settle it

Take a simple two-dimensional robot navigation model satisfying Assumptions 1 and 2, compute $u^*(\cdot;\eta)$ and its Monte Carlo failure probability over a fine grid of $\eta$ values, and look for a jump discontinuity in $\eta \mapsto P_{\mathrm{fail}}(x_0,t_0,u^*(\cdot;\eta))$; such a discontinuity would break the complementary-slackness step and could make dual ascent terminate at an infeasible or suboptimal policy.

Watch

Extended reading notes

Core claim

The paper's main claim is Theorem 3: for a control-affine stochastic system whose noise enters through the control channels, if the chance-constrained problem is strictly feasible and the map from the penalty weight $\eta$ to the failure probability of the resulting optimal policy is continuous, then the dual optimum equals the primal optimum. The optimal policy of the soft-constrained dual problem at the right $\eta^*$ is optimal for the original chance-constrained problem. Because the dual objective is evaluated by Feynman-Kac expectations over uncontrolled trajectories and the failure probability by importance sampling, the whole loop—update $\eta$, resample, recompute the policy—can run online. The dissertation also claims analogous path integral solutions for saddle-point policies in zero-sum stochastic differential games, KL-divergence-minimizing deceptive policies, task hierarchies combining simple and optimal controllers, and risk mitigation of stealthy attacks, plus a sample-complexity bound for discrete-time LQR.

Load-bearing premise

The load-bearing premise is that the failure probability of the optimal policy, viewed as a function of the penalty weight $\eta$, is continuous; the paper labels this assumption a conjecture and defers its proof.

Editorial extensions

If this is right

  • Chance-constrained motion planning in four- and five-dimensional robot models can be solved online with Monte Carlo rollouts, where grid-based PDE solvers become impractical.
  • Saddle-point policies for zero-sum stochastic differential games, including disturbance attenuation and pursuit-evasion, can be computed by the same uncontrolled-trajectory expectations without offline training.
  • A deceptive agent can hide deviations from a supervisor by sampling control actions proportional to exponentiated path costs under the reference policy; as the number of samples grows, the sampled actions converge to the optimal deceptive distribution.
  • Null-space projection lets a robot execute simple PD-controlled tasks and a path integral-controlled task simultaneously, avoiding local minima that pure PD hierarchies exhibit.
  • For discrete-time stochastic LQR, the required number of Monte Carlo samples grows logarithmically in the control-input dimension, in contrast to the exponential growth of exact dynamic programming.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the continuity assumption behind Theorem 3 holds broadly, the dual-ascent loop becomes a general-purpose safety-constrained solver: hard failure-probability constraints reduce to a one-dimensional search over $\eta$, and the same estimator could be reused for chance-constrained games, which the paper lists as future work.
  • The continuity conjecture might be provable from stability of Dirichlet boundary-value problems: if the boundary data $\phi(\cdot;\eta)$ depends continuously on $\eta$ and the linearized PDE has a stable solution, then $P_{\mathrm{fail}}$ would inherit that continuity; a counterexample would require a genuine phase transition in exit probabilities.
  • The importance-sampling estimator for $P_{\mathrm{fail}}$ doubles as a stochastic gradient of the dual function, so variance-reduction techniques could yield stronger convergence guarantees for dual ascent than the paper's fixed-step-size update.
  • Because the Bretagnolle-Huber inequality is distribution-free, the deception and stealthy-attack results suggest a general template: any task cost can be made stealthy by exponential reweighting under a nominal policy, connecting path integral control to hypothesis testing in continuous spaces.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The dissertation develops sampling-based ('path integral') methods for six classes of stochastic optimal control problems. Chapter 2 formulates a continuous-time chance-constrained SOC problem, derives a Lagrangian dual whose inner subproblem is an HJB PDE, linearizes the PDE under Assumption 1 (ΣΣᵀ = λ G R⁻¹ Gᵀ), and proposes a Monte Carlo dual-ascent algorithm (Algorithm 1). The central theoretical claim is Theorem 3: under Assumptions 1–3, the duality gap is zero and the dual-ascent policy u*(·;η*) is primal optimal. Chapter 3 extends the framework to two-player zero-sum differential games with a risk-minimizing cost, deriving saddle-point policies from an HJI PDE under Assumption 4. Chapter 4 combines null-space projection with path integral control for hierarchical task control. Chapter 5 formulates deceptive control as a KL-control problem and proposes a weighted-sampling algorithm under deterministic state dynamics. Chapter 6 applies the framework to stealthy attack synthesis and mitigation, and Chapter 7 is announced as a discrete-time LQR treatment with sample complexity analysis but is not present in the submitted text.

Significance. If the assumptions that the central results require are supplied, the chance-constrained result would be a substantial contribution: it offers a sampler-only alternative to grid-based PDE methods for a non-convex constrained problem, is supported by an open-source implementation, and is demonstrated on 4D and 5D systems where finite differences are impractical. The game-theoretic, hierarchical, and deception chapters also translate known linearizability conditions into concrete Monte Carlo algorithms, and the derivations are largely self-contained, starting from the HJB/HJI PDE and the Feynman-Kac representation rather than fitting constants to target outcomes. The main advertised claim, however, is explicitly conditional on a continuity assumption that the manuscript itself labels a conjecture, and two of the core proofs are either deferred to an unavailable appendix or omitted for brevity.

major comments (3)
  1. [§2.6.2 (Assumption 3; Theorem 3)] The zero-duality-gap claim is conditional on an unproved continuity assumption that the manuscript itself labels a conjecture and defers to future work (§2.9). This is not a routine regularity check: η enters the boundary data of the dual HJB PDE, and Pfail is an exit probability of the resulting diffusion. If η ↦ Pfail(x0,t0,u*(·;η)) has a jump, the complementary slackness statements (a)–(b) need not hold, and Algorithm 1 could terminate at a policy that is either infeasible or suboptimal. Since Theorem 3 is the main advertised contribution, the proof of Assumption 3 must be supplied, or the theorem must be explicitly stated as conditional. The proof of Theorem 3 is also deferred to Lemma 4 in Appendix A.1, and the appendix content is not included in the submitted text, so the argument cannot be checked.
  2. [§2.5.2 footnote; Theorem 2] The exact indicator terminal cost φ(x;η) = ψ(x)1_{x∈Xs} + η1_{x∈∂Xs} − ηΔ is approximated by a smooth bump function for PDE regularity, yet Theorem 2 asserts existence and uniqueness of the value function for the exact problem, and Theorems 1–3 are stated for the exact indicator. The manuscript does not state regularity conditions under which the linearized PDE has a classical solution for the discontinuous indicator data, nor does it explain how the bump approximation affects the chance constraint or the duality gap. This matters because Algorithm 1 estimates Pfail using the exact indicator, so the theory must be reconciled with the numerical object being evaluated.
  3. [§3.4.2 (Theorem 8)] The proof of Theorem 8 does not contain the derivation of the saddle-point policies (3.25)–(3.26); it states that the derivation is 'in the same vein' as single-agent settings and omits it. Because these formulas are the main output of Chapter 3, the derivation must be included or a precise external reference with matching assumptions must be supplied. In addition, Remark 3 disclaims existence for the HJI boundary-value problem, which creates tension with Theorem 8's assertion of existence and uniqueness of the saddle-point solution.
minor comments (4)
  1. [§3.5.1 and §3.5.2] The text twice refers to 'Assumption 1' when the relevant assumption for Chapter 3 is Assumption 4; for example, 'Assumption 1 is satisfied' should read 'Assumption 4 is satisfied'.
  2. [Throughout] Typos and wording: 'Feyman-Kac' in §2.6.1 should be 'Feynman-Kac'; 'Bratagnolle-Huber' in §5.4 should be 'Bretagnolle–Huber'; 'exits' in §3.4.2 should be 'exists'; 'the the' appears in §2.5.2; and 'Kullback-Leibler (KL) divergence' is sometimes rendered with inconsistent hyphenation.
  3. [§2.6.3.2 (Theorem 5)] The importance-sampling likelihood ratio expression is written ambiguously: it should be dQ*/dP ≈ (r(i)/r)/(1/N) = N r(i)/r, followed by Pfail ≈ Σ_i (r(i)/r)1_{x(i)(tf)∈∂Xs}. The missing parentheses make the proof hard to follow.
  4. [Chapter 7] Chapter 7 is listed in the abstract and table of contents as containing a discrete-time LQR path integral solution and a sample complexity analysis, but no content of that chapter is present in the submitted text. The sample complexity claim in the abstract therefore cannot be verified.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivations are self-contained, proceeding from stated HJB/HJI PDEs and Feynman-Kac representations without fitting parameters to target results; the main caveat is an explicitly conjectured regularity assumption, which is a gap rather than a circular step.

full rationale

The paper's derivation chain is self-contained in the sense required by the circularity analysis. Chapter 2 constructs the dual function by solving the HJB PDE (2.15), linearizes it under the explicitly stated Assumption 1 via the transformation (2.26), uses the Feynman-Kac representation (2.29), and evaluates the dual ascent updates from Monte Carlo estimates of the failure probability; no parameter is fitted to the claimed zero-duality-gap result, and the path-integral solutions are compared against an independent finite-difference baseline in Section 2.7.1. Chapter 3 follows the same structure from the HJI PDE (3.8) under Assumption 4, with existence and uniqueness delegated to standard PDE theory (Friedman) rather than to the author's own work. Chapters 4, 5, and 7 apply the same Feynman-Kac / KL-control machinery with explicit linearizability and stochasticity assumptions; the optimal policies are derived from the stated cost and dynamics, not from the simulation outputs. The principal caveat is Theorem 3, whose strong-duality conclusion depends on Assumption 3, the continuity of eta -> Pfail(x0,t0,u*(.;eta)). The text explicitly says: 'We conjecture that this assumption is valid under mild conditions; a formal analysis is postponed as future work' (Section 2.6.2), and Section 2.9 repeats that proving it is future work. This is an unproved premise or correctness gap, not a circular reduction: the assumption does not assert the theorem's conclusion, and the theorem is not used to define the assumption. Likewise, Remark 3 in Chapter 3 and the omitted derivation in Theorem 8 are omissions, not circularity. The paper contains self-citations (e.g., Patil et al. 2022, 2024, 2023a), but none is load-bearing: the Feynman-Kac representation is a standard external result, the sample-complexity remarks are peripheral, and the linearizability conditions are stated and used explicitly rather than imported as unexamined ansatzes. The simulations in Chapter 2 compare against FDM, and Chapter 7 compares against the Riccati solution, providing external benchmarks. Accordingly, no specific reduction of a claimed prediction to its own inputs can be exhibited, and the appropriate finding is no significant circularity.

Assumptions & free parameters 4 free parameters · 10 assumptions · 0 invented entities

The main structural costs are the noise-control proportionality assumptions (Assumptions 1 and 4), the unproven continuity conjecture (Assumption 3), and the deterministic-dynamics assumption in the deception chapter. Standard stochastic calculus results such as Feynman-Kac, Ito, Girsanov, and the strong law are imported from textbooks and are charged as axioms because they are not proved in the dissertation. No new physical entities are introduced.

free parameters (4)
  • lambda (PDE linearizing constant) = varies per problem; e.g. lambda = 1/(1 - 1/gamma^2), lambda = 1/(1 - 1/rv^2)
    Chosen by hand to satisfy Assumption 1 or Assumption 4, the noise-control proportionality condition. It is essential for linearizing the HJB or HJI PDE via the logarithmic transformation.
  • alpha (control cost weight in task hierarchy) = 10
    Hand-chosen in Chapter 4 simulations to balance the quadratic control cost against the state cost in the path integral objective.
  • s-hat (diffusion coefficient in task hierarchy) = 0.1
    Hand-chosen in Chapter 4 to inject exploration noise into the control channel. The paper notes that this value should be carefully selected, so it is a free design parameter.
  • lambda (KL weighting in deceptive control) = 3, 2, 0.5 in simulations
    User-specified trade-off between the agent's path cost and the KL divergence from the reference policy. It changes the behavior of the deceptive policy and is not derived from data.
assumptions (10)
  • standard math Feynman-Kac lemma
    Used to represent solutions of linearized PDEs as expectations over uncontrolled stochastic trajectories, e.g., Lemma 1 in Chapter 2 and Theorem 10 in Chapter 4.
  • standard math Ito formula and Dynkin's formula
    Used in verification theorems for HJB and HJI PDEs, specifically in the proofs of Theorem 1 and Theorem 7.
  • standard math Strong law of large numbers
    Used to justify convergence of Monte Carlo estimators, e.g., in Chapter 2 Theorem 5 and Chapter 5 Equation (5.21).
  • standard math Girsanov theorem and Radon-Nikodym likelihood ratios
    Used for importance-sampling estimation of failure probabilities in Chapter 2 and for the KL divergence calculations in Chapter 5.
  • standard math Legendre duality between KL divergence and free energy
    Used in Chapter 5 Theorem 12 to characterize the optimal deceptive policy distribution.
  • ad hoc to paper Assumption 1: Sigma Sigma^T = lambda G R^{-1} G^T
    Introduced in Section 2.6.1 to make the HJB PDE linearizable. It restricts noise to enter through control channels and is not a general structural property of all systems.
  • domain assumption Assumption 2: strict feasibility (Slater-like condition)
    Assumed in Chapter 2 to guarantee a finite dual optimum and zero duality gap. It is a standard constraint qualification in optimization.
  • ad hoc to paper Assumption 3: continuity of eta -> Pfail(u*(.; eta))
    Explicitly labeled a conjecture in Section 2.6.2 and deferred to future work. It is required for the strong duality Theorem 3 and is not proved.
  • ad hoc to paper Assumption 4: Sigma Sigma^T = lambda (Gu Ru^{-1} Gu^T - Gv Rv^{-1} Gv^T)
    Introduced in Chapter 3 to linearize the HJI PDE for two-player games. It requires the agent's effective control authority to dominate the adversary's.
  • ad hoc to paper Assumption 5: deterministic state transition law in deception
    Used in Chapter 5 to linearize the backward Bellman recursion and derive the path integral solution. It also requires the reference policy to be stochastic for the deception problem to be nontrivial.

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Pith. "Pith review of Advancing Frontiers of Path Integral Theory for Stochastic Optimal Control." pith.science (2026). https://pith.science/paper/WLT6CDSY

@misc{pith2026250417154,
  author       = {Pith},
  title        = {Pith review of: Advancing Frontiers of Path Integral Theory for Stochastic Optimal Control},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WLT6CDSY}},
  note         = {Machine review of arXiv:2504.17154}
}
read the original abstract

Stochastic Optimal Control (SOC) problems arise in systems influenced by uncertainty, such as autonomous robots or financial models. Traditional methods like dynamic programming are often intractable for high-dimensional, nonlinear systems due to the curse of dimensionality. This dissertation explores the path integral control framework as a scalable, sampling-based alternative. By reformulating SOC problems as expectations over stochastic trajectories, it enables efficient policy synthesis via Monte Carlo sampling and supports real-time implementation through GPU parallelization. We apply this framework to six classes of SOC problems: Chance-Constrained SOC, Stochastic Differential Games, Deceptive Control, Task Hierarchical Control, Risk Mitigation of Stealthy Attacks, and Discrete-Time LQR. A sample complexity analysis for the discrete-time case is also provided. These contributions establish a foundation for simulator-driven autonomy in complex, uncertain environments.

Figures

Figures reproduced from arXiv: 2504.17154 by the authors.

Figure 1.1
Figure 1.1. Dissertation Structure as follows: we develop the path integral control theory for six classes of stochastic optimal control problems: Chance-Constrained SOC (Chapter 2), Two-Player Zero￾Sum Stochastic Differential Games (Chapter 3), Task Hierarchical Control (Chapter 4), Deceptive Control (Chapter 5), Deceptive Attack Synthesis and Its Mitigation (Chapter 6) and Stochastic LQR Problem (Chapter 7). Chapter 7 also de… view at source ↗
Figure 2.1
Figure 2.1. Computational domains and exit times tf 2.5 Problem Formulation We first formalize a chance-constrained SOC problem in Section 2.5.1. In Section 2.5.2, we formulate its dual. 2.5.1 Chance-Constrained SOC Problem Consider a cost function that is quadratic in the control input and has the form: C (x0, t0, u(·)) := Ex0,t0 " ψ (x(tf )) · 1x(tf )∈Xs + Z tf t0  1 2 u ⊤R (x(t), t) u + V (x(t), t)  dt# where ψ (x(tf )) de… view at source ↗
Figure 2
Figure 2. represents how the value of [PITH_FULL_IMAGE:figures/full_fig_p056_2.png] view at source ↗
Figures from the paper (35 more)
Figure 2.2
Figure 2.2. Figure 2.2: Robot navigation problem for the input velocity model. The start position [PITH_FULL_IMAGE:figures/full_fig_p057_2_2.png]
Figure 2
Figure 2. Figure 2: shows the colormaps of the failure probabilities of the synthesized [PITH_FULL_IMAGE:figures/full_fig_p057_2.png]
Figure 2.3
Figure 2.3. Figure 2.3: η ∗ and Pfail(x0, t0, u∗ (· ; η ∗ )) vs ∆ for input velocity model using path integral control and FDM. value of ∆ = 0.25. The factors that affect the computation speed of FDM include the grid size, the choice of an ODE solver and its error tolerances. Whereas the co…
Figure 2.4
Figure 2.4. Figure 2.4: Input velocity model: comparison of solutions [PITH_FULL_IMAGE:figures/full_fig_p059_2_4.png]
Figure 2.5
Figure 2.5. Figure 2.5: Colormaps of the failure probabilities of the optimal policies synthesized [PITH_FULL_IMAGE:figures/full_fig_p060_2_5.png]
Figure 2
Figure 2. Figure 2: represents how the value of [PITH_FULL_IMAGE:figures/full_fig_p060_2.png]
Figure 2.6
Figure 2.6. Figure 2.6: Robot navigation problem for the unicycle model. The start position is [PITH_FULL_IMAGE:figures/full_fig_p061_2_6.png]
Figure 2.7
Figure 2.7. Figure 2.7: η ∗ and Pfail(x0, t0, u∗ (· ; η ∗ )) vs ∆ for unicycle model using path integral control. In [PITH_FULL_IMAGE:figures/full_fig_p062_2_7.png]
Figure 2.8
Figure 2.8. Figure 2.8: Robot navigation problem for a car model. The start position is shown [PITH_FULL_IMAGE:figures/full_fig_p063_2_8.png]
Figure 2.9
Figure 2.9. Figure 2.9: η ∗ and Pfail(x0, t0, u∗ (· ; η ∗ )) vs ∆ for a car model using path integral control. cost functions. In future work, we plan to find alternatives in order to get rid of this restrictive assumption (one such solution is provided in Satoh et al. (2016)). Another topi…
Figure 3.1
Figure 3.1. Figure 3.1: Unicycle navigation in the presence of bounded and stochastic distur [PITH_FULL_IMAGE:figures/full_fig_p084_3_1.png]
Figure 3.2
Figure 3.2. Figure 3.2: Unicycle navigation in the presence of bounded and stochastic distur [PITH_FULL_IMAGE:figures/full_fig_p085_3_2.png]
Figure 3.3
Figure 3.3. Figure 3.3: Two sample trajectories of the relative position of the players in a pursuit [PITH_FULL_IMAGE:figures/full_fig_p087_3_3.png]
Figure 3.4
Figure 3.4. Figure 3.4: Failure probabilities of the agent (i.e., evader) as a function of [PITH_FULL_IMAGE:figures/full_fig_p087_3_4.png]
Figure 4.1
Figure 4.1. Figure 4.1: Comparison of the conventional task hierarchical control approach and our [PITH_FULL_IMAGE:figures/full_fig_p099_4_1.png]
Figure 4
Figure 4. Figure 4: shows the comparison of the conventional task hierarchical control approach [PITH_FULL_IMAGE:figures/full_fig_p103_4.png]
Figure 4.2
Figure 4.2. Figure 4.2: Results of single-agent example without the path integral controller [PITH_FULL_IMAGE:figures/full_fig_p107_4_2.png]
Figure 4.3
Figure 4.3. Figure 4.3: Results of single-agent example using the path integral controller [PITH_FULL_IMAGE:figures/full_fig_p108_4_3.png]
Figure 4
Figure 4. Figure 4: (a) represents the results of the hierarchical controller when all three tasks [PITH_FULL_IMAGE:figures/full_fig_p111_4.png]
Figure 4.4
Figure 4.4. Figure 4.4: Results of two-agents example without the path integral controller [PITH_FULL_IMAGE:figures/full_fig_p112_4_4.png]
Figure 4.5
Figure 4.5. Figure 4.5: Results of two-agents example using the path integral controller [PITH_FULL_IMAGE:figures/full_fig_p112_4_5.png]
Figure 4.6
Figure 4.6. Figure 4.6: Distance between agents over time controller for task 2) is designed using a PD controller [PITH_FULL_IMAGE:figures/full_fig_p113_4_6.png]
Figure 5.1
Figure 5.1. Figure 5.1: Function Ft(x). Then, we select a sample ID by jt ← F −1 t (d). Finally, the control input adopted in the jt-th sample path at time step t is selected as ut , i.e., ut ← ut(jt). Theorem 13 proves that as the number of Monte Carlo samples tends to infinity, Algorithm …
Figure 5.2
Figure 5.2. Figure 5.2: A unicycle navigation problem. The start position is shown by a red dot, [PITH_FULL_IMAGE:figures/full_fig_p134_5_2.png]
Figure 5
Figure 5. Figure 5: shows the expected log-likelihood ratio (with one standard devia [PITH_FULL_IMAGE:figures/full_fig_p136_5.png]
Figure 5.3
Figure 5.3. Figure 5.3: Expected LLR (with one standard deviation) with respect to time [PITH_FULL_IMAGE:figures/full_fig_p137_5_3.png]
Figure 6.1
Figure 6.1. Figure 6.1: Attacker vs controller/detector. Remark 9. One can consider more general attack signals of the form dvt = θt(ω)dt + σt(ω)dwt , v0 = 0 (6.3) with a diffusion coefficient σt(ω) ̸= 1. However, from the attacker’s perspective, there’s no benefit in such a generalization …
Figure 6.2
Figure 6.2. Figure 6.2: Error bounds and achievable region (shown in yellow). [PITH_FULL_IMAGE:figures/full_fig_p149_6_2.png]
Figure 6.3
Figure 6.3. Figure 6.3: Connections between minimax KL control, risk-sensitive control, and two [PITH_FULL_IMAGE:figures/full_fig_p157_6_3.png]
Figure 6.4
Figure 6.4. Figure 6.4: A unicycle navigation problem. 100 sample paths generated without the [PITH_FULL_IMAGE:figures/full_fig_p165_6_4.png]
Figure 6.5
Figure 6.5. Figure 6.5: Cruise control problem. The start position is shown by a magenta dot on [PITH_FULL_IMAGE:figures/full_fig_p168_6_5.png]
Figure 6
Figure 6. Figure 6: (d) shows the plots of 100 sample trajectories generated using synthesized [PITH_FULL_IMAGE:figures/full_fig_p170_6.png]
Figure 7.1
Figure 7.1. Figure 7.1: State and input trajectories for two values of [PITH_FULL_IMAGE:figures/full_fig_p188_7_1.png]
Figure 7.2
Figure 7.2. Figure 7.2: ϵ0 and LQR cost vs sample size 188 [PITH_FULL_IMAGE:figures/full_fig_p188_7_2.png]
Figure 9.1
Figure 9.1. Figure 9.1: Summary of the dissertation 199 [PITH_FULL_IMAGE:figures/full_fig_p199_9_1.png]

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Reference graph

Works this paper leans on

142 extracted references · 69 canonical work pages

  1. [1]

    Model-based generalization under parameter uncertainty using path integral control

    Ian Abraham, Ankur Handa, Nathan Ratliff, Kendall Lowrey, Todd D Murphey, and Dieter Fox. Model-based generalization under parameter uncertainty using path integral control. IEEE Robotics and Automation Letters, 5 0 (2): 0 2864--2871, 2020

    2020

  2. [2]

    Entropic value-at-risk: A new coherent risk measure

    Amir Ahmadi-Javid. Entropic value-at-risk: A new coherent risk measure. Journal of Optimization Theory and Applications, 155: 0 1105--1123, 2012

    2012

  3. [3]

    Real-time whole-body control of legged robots with model-predictive path integral control

    Juan Alvarez-Padilla, John Z Zhang, Sofia Kwok, John M Dolan, and Zachary Manchester. Real-time whole-body control of legged robots with model-predictive path integral control. arXiv preprint arXiv:2409.10469, 2024

    arXiv 2024

  4. [4]

    Stability analysis for prioritized closed-loop inverse kinematic algorithms for redundant robotic systems

    Gianluca Antonelli. Stability analysis for prioritized closed-loop inverse kinematic algorithms for redundant robotic systems. IEEE Transactions on Robotics, 25 0 (5): 0 985--994, 2009

    2009

  5. [5]

    The null-space-based behavioral control for autonomous robotic systems

    Gianluca Antonelli, Filippo Arrichiello, and Stefano Chiaverini. The null-space-based behavioral control for autonomous robotic systems. Intelligent Service Robotics, 1: 0 27--39, 2008

    2008

  6. [6]

    Prioritized closed-loop inverse kinematic algorithms for redundant robotic systems with velocity saturations

    Gianluca Antonelli, Giovanni Indiveri, and Stefano Chiaverini. Prioritized closed-loop inverse kinematic algorithms for redundant robotic systems with velocity saturations. In 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 5892--5897. IEEE, 2009

    2009

  7. [7]

    Information-theoretic stochastic optimal control via incremental sampling-based algorithms

    Oktay Arslan, Evangelos A Theodorou, and Panagiotis Tsiotras. Information-theoretic stochastic optimal control via incremental sampling-based algorithms. In 2014 IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL), pages 1--8. IEEE, 2014

    2014

  8. [8]

    Coherent measures of risk

    Philippe Artzner, Freddy Delbaen, Jean-Marc Eber, and David Heath. Coherent measures of risk. Mathematical finance, 9 0 (3): 0 203--228, 1999

    1999

Show all 142 references
  1. [9]

    Data-injection attacks in stochastic control systems: Detectability and performance tradeoffs

    Cheng-Zong Bai, Fabio Pasqualetti, and Vijay Gupta. Data-injection attacks in stochastic control systems: Detectability and performance tradeoffs. Automatica, 82: 0 251--260, 2017

    2017

  2. [10]

    H-infinity optimal control and related minimax design problems: a dynamic game approach

    Tamer Ba s ar and Pierre Bernhard. H-infinity optimal control and related minimax design problems: a dynamic game approach. Springer Science & Business Media, 2008

    2008

  3. [11]

    Dynamic noncooperative game theory

    Tamer Ba s ar and Geert Jan Olsder. Dynamic noncooperative game theory. SIAM, 1998

    1998

  4. [12]

    Dynamic programming and optimal control: Volume I, volume 1

    Dimitri Bertsekas. Dynamic programming and optimal control: Volume I, volume 1. Athena scientific, 2012

    2012

  5. [13]

    Nonlinear programming

    Dimitri P Bertsekas. Nonlinear programming. Journal of the Operational Research Society, 48 0 (3): 0 334--334, 1997

    1997

  6. [14]

    Bertsekas and S.E

    D.P. Bertsekas and S.E. Shreve. Stochastic Optimal Control: The Discrete-Time Case. Athena Scientific, 1996

    1996

  7. [15]

    Storm: An integrated framework for fast joint-space model-predictive control for reactive manipulation

    Mohak Bhardwaj, Balakumar Sundaralingam, Arsalan Mousavian, Nathan D Ratliff, Dieter Fox, Fabio Ramos, and Byron Boots. Storm: An integrated framework for fast joint-space model-predictive control for reactive manipulation. In Conference on Robot Learning, pages 750--759. PMLR, 2022

    2022

  8. [16]

    Chance-constrained optimal path planning with obstacles

    Lars Blackmore, Masahiro Ono, and Brian C Williams. Chance-constrained optimal path planning with obstacles. IEEE Transactions on Robotics, 27 0 (6): 0 1080--1094, 2011

    2011

  9. [17]

    Markov processes and potential theory

    Robert McCallum Blumenthal and Ronald Kay Getoor. Markov processes and potential theory. Courier Corporation, 2007

    2007

  10. [18]

    A variational representation for certain functionals of Brownian motion

    Michelle Bou \'e and Paul Dupuis. A variational representation for certain functionals of Brownian motion. The Annals of Probability, 26 0 (4): 0 1641--1659, 1998

    1998

  11. [19]

    Convex optimization

    Stephen P Boyd and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004

    2004

  12. [20]

    Estimation des densit \'e s: risque minimax

    Jean Bretagnolle and Catherine Huber. Estimation des densit \'e s: risque minimax. S \'e minaire de probabilit \'e s de Strasbourg , 12: 0 342--363, 1978

    1978

  13. [21]

    Risk sensitive path integral control

    Bart van den Broek, Wim Wiegerinck, and Hilbert Kappen. Risk sensitive path integral control. arXiv preprint arXiv:1203.3523, 2012

    2012 arXiv

  14. [22]

    The scenario approach to robust control design

    Giuseppe Carlo Calafiore and Marco C Campi. The scenario approach to robust control design. IEEE Transactions on automatic control, 51 0 (5): 0 742--753, 2006

    2006

  15. [23]

    Constrained stochastic optimal control with learned importance sampling: A path integral approach

    Jan Carius, Ren \'e Ranftl, Farbod Farshidian, and Marco Hutter. Constrained stochastic optimal control with learned importance sampling: A path integral approach. The International Journal of Robotics Research, 41 0 (2): 0 189--209, 2022

    2022

  16. [24]

    Safe control in the presence of stochastic uncertainties

    Albert Chern, Xiang Wang, Abhiram Iyer, and Yorie Nakahira. Safe control in the presence of stochastic uncertainties. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 6640--6645. IEEE, 2021

    2021

  17. [25]

    Elements of information theory

    Thomas M Cover. Elements of information theory. John Wiley & Sons, 1999

    1999

  18. [26]

    Generalized N eyman- P earson lemma via convex duality

    Jak s a Cvitani \'c and Ioannis Karatzas. Generalized N eyman- P earson lemma via convex duality. Bernoulli, pages 79--97, 2001

    2001

  19. [27]

    Scenario-based trajectory optimization in uncertain dynamic environments

    Oscar de Groot, Bruno Brito, Laura Ferranti, Dariu Gavrila, and Javier Alonso-Mora. Scenario-based trajectory optimization in uncertain dynamic environments. IEEE Robotics and Automation Letters, 6 0 (3): 0 5389--5396, 2021

    2021

  20. [28]

    An overview of null space projections for redundant, torque-controlled robots

    Alexander Dietrich, Christian Ott, and Alin Albu-Sch \"a ffer. An overview of null space projections for redundant, torque-controlled robots. The International Journal of Robotics Research, 34 0 (11): 0 1385--1400, 2015

    2015

  21. [29]

    Risk-averse receding horizon motion planning

    Anushri Dixit, Mohamadreza Ahmadi, and Joel W Burdick. Risk-averse receding horizon motion planning. arXiv preprint arXiv:2204.09596, 2022

    2022 arXiv

  22. [30]

    Deceptive robot motion: synthesis, analysis and experiments

    Anca Dragan, Rachel Holladay, and Siddhartha Srinivasa. Deceptive robot motion: synthesis, analysis and experiments. Autonomous Robots, 39: 0 331--345, 2015

    2015

  23. [31]

    Probability: theory and examples, volume 49

    Rick Durrett. Probability: theory and examples, volume 49. Cambridge university press, 2019

    2019

  24. [32]

    Partial differential equations, volume 19

    Lawrence C Evans. Partial differential equations, volume 19. American Mathematical Society, 2022

    2022

  25. [33]

    Numerical methods for differential games based on partial differential equations

    Maurizio Falcone. Numerical methods for differential games based on partial differential equations. International Game Theory Review, 8 0 (02): 0 231--272, 2006

    2006

  26. [34]

    Optimism in reinforcement learning and Kullback-Leibler divergence

    Sarah Filippi, Olivier Capp \'e , and Aur \'e lien Garivier. Optimism in reinforcement learning and Kullback-Leibler divergence. In 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), pages 115--122. IEEE, 2010

    2010

  27. [35]

    Controlled Markov processes and viscosity solutions, volume 25

    Wendell H Fleming and Halil Mete Soner. Controlled Markov processes and viscosity solutions, volume 25. Springer Science & Business Media, 2006

    2006

  28. [36]

    Collision probabilities for continuous-time systems without sampling

    Kristoffer M Frey, Ted J Steiner, and J How. Collision probabilities for continuous-time systems without sampling. Proceedings of Robotics: Science and Systems. Corvalis, Oregon, USA (July 2020), 2020

    2020

  29. [37]

    Stochastic differential equations and applications, vol

    Avner Friedman. Stochastic differential equations and applications, vol. 1. Academic Press, 1975

    1975

  30. [38]

    Numerical treatment of partial differential equations, volume 154

    Christian Grossmann, Hans-G \"o rg Roos, and Martin Stynes. Numerical treatment of partial differential equations, volume 154. Springer, 2007

    2007

  31. [39]

    Quantization of dynamical systems and stochastic control theory

    Francesco Guerra and Laura M Morato. Quantization of dynamical systems and stochastic control theory. Physical review D, 27 0 (8): 0 1774, 1983

    1983

  32. [40]

    Worst-case stealthy innovation-based linear attack on remote state estimation

    Ziyang Guo, Dawei Shi, Karl Henrik Johansson, and Ling Shi. Worst-case stealthy innovation-based linear attack on remote state estimation. Automatica, 89: 0 117--124, 2018

    2018

  33. [41]

    Probability inequalities for sums of bounded random variables

    Wassily Hoeffding. Probability inequalities for sums of bounded random variables. In The collected works of Wassily Hoeffding, pages 409--426. Springer, 1994

    1994

  34. [42]

    Chance-constrained LQG with bounded control policies

    Peter Hokayem, Debasish Chatterjee, and John Lygeros. Chance-constrained LQG with bounded control policies. In 52nd IEEE Conference on Decision and Control, pages 2471--2476. IEEE, 2013

    2013

  35. [43]

    Automation-assisted capture-the-flag: A differential game approach

    Haomiao Huang, Jerry Ding, Wei Zhang, and Claire J Tomlin. Automation-assisted capture-the-flag: A differential game approach. IEEE Transactions on Control Systems Technology, 23 0 (3): 0 1014--1028, 2014

    2014

  36. [44]

    Risk conditioned neural motion planning

    Xin Huang, Meng Feng, Ashkan Jasour, Guy Rosman, and Brian Williams. Risk conditioned neural motion planning. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 9057--9063. IEEE, 2021

    2021

  37. [45]

    Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization

    Rufus Isaacs. Differential games: a mathematical theory with applications to warfare and pursuit, control and optimization. Courier Corporation, 1999

    1999

  38. [46]

    Optimization of nonlinear control systems based on the principle of superposition (in japanese)

    Tetsuro Itami. Optimization of nonlinear control systems based on the principle of superposition (in japanese). Transactions of the Society of Instrument and Control Engineers, 37 0 (3): 0 193--202, 2001. DOI:10.9746/sicetr1965.37.193

    2001 doi

  39. [47]

    Nonlinear optimal control via M onte- C arlo evaluation of path integrals (in japanese)

    Tetsuro Itami. Nonlinear optimal control via M onte- C arlo evaluation of path integrals (in japanese). Transactions of the Institute of Systems, Control and Information Engineers, 16 0 (12): 0 637--648, 2003. DOI: 10.5687/iscie.16.637

    2003 doi

  40. [48]

    Kullback-- Leibler control for discrete-time nonlinear systems on continuous spaces

    Kaito Ito and Kenji Kashima. Kullback-- Leibler control for discrete-time nonlinear systems on continuous spaces. SICE Journal of Control, Measurement, and System Integration, 15 0 (2): 0 119--129, 2022 a

    2022

  41. [49]

    Kullback-leibler control for discrete-time nonlinear systems on continuous spaces, 2022 b

    Kaito Ito and Kenji Kashima. Kullback-leibler control for discrete-time nonlinear systems on continuous spaces, 2022 b

    2022

  42. [50]

    Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games

    David Jacobson. Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games. IEEE Transactions on Automatic control, 18 0 (2): 0 124--131, 1973

    1973

  43. [51]

    Convex risk bounded continuous-time trajectory planning in uncertain nonconvex environments

    Ashkan Jasour, Weiqiao Han, and Brian Williams. Convex risk bounded continuous-time trajectory planning in uncertain nonconvex environments. In 2021 Robotics: Science and Systems, 2021

    2021

  44. [52]

    A multilevel approach for stochastic nonlinear optimal control

    Ajay Jasra, Jeremy Heng, Yaxian Xu, and Adrian N Bishop. A multilevel approach for stochastic nonlinear optimal control. International Journal of Control, 95 0 (5): 0 1290--1304, 2022

    2022

  45. [53]

    Path integrals and symmetry breaking for optimal control theory

    Hilbert J Kappen. Path integrals and symmetry breaking for optimal control theory. Journal of statistical mechanics: theory and experiment, 2005 0 (11): 0 P11011, 2005

    2005

  46. [54]

    Optimal control as a graphical model inference problem

    Hilbert J Kappen, Vicen c G \'o mez, and Manfred Opper. Optimal control as a graphical model inference problem. Machine learning, 87: 0 159--182, 2012

    2012

  47. [55]

    Deception in supervisory control

    Mustafa O Karabag, Melkior Ornik, and Ufuk Topcu. Deception in supervisory control. IEEE Transactions on Automatic Control, 67 0 (2): 0 738--753, 2021

    2021

  48. [56]

    Exploiting partial observability for optimal deception

    Mustafa O Karabag, Melkior Ornik, and Ufuk Topcu. Exploiting partial observability for optimal deception. IEEE Transactions on Automatic Control, 2022

    2022

  49. [57]

    Brownian motion and stochastic calculus, volume 113

    Ioannis Karatzas and Steven Shreve. Brownian motion and stochastic calculus, volume 113. Springer Science & Business Media, 2012

    2012

  50. [58]

    Stuxnet worm impact on industrial cyber-physical system security

    Stamatis Karnouskos. Stuxnet worm impact on industrial cyber-physical system security. In IECON 2011-37th Annual Conference of the IEEE Industrial Electronics Society, pages 4490--4494. IEEE, 2011

    2011

  51. [59]

    Probabilistic system opacity in discrete event systems

    Christoforos Keroglou and Christoforos N Hadjicostis. Probabilistic system opacity in discrete event systems. Discrete Event Dynamic Systems, 28: 0 289--314, 2018

    2018

  52. [60]

    A unified approach for motion and force control of robot manipulators: The operational space formulation

    Oussama Khatib. A unified approach for motion and force control of robot manipulators: The operational space formulation. IEEE Journal on Robotics and Automation, 3 0 (1): 0 43--53, 1987

    1987

  53. [61]

    Cyber--physical systems: A perspective at the centennial

    Kyoung-Dae Kim and Panganamala R Kumar. Cyber--physical systems: A perspective at the centennial. Proceedings of the IEEE, 100 0 (Special Centennial Issue): 0 1287--1308, 2012

    2012

  54. [62]

    Robust constrained model predictive control using linear matrix inequalities

    Mayuresh V Kothare, Venkataramanan Balakrishnan, and Manfred Morari. Robust constrained model predictive control using linear matrix inequalities. Automatica, 32 0 (10): 0 1361--1379, 1996

    1996

  55. [63]

    The performance and limitations of epsilon-stealthy attacks on higher order systems

    Enoch Kung, Subhrakanti Dey, and Ling Shi. The performance and limitations of epsilon-stealthy attacks on higher order systems. IEEE Transactions on Automatic Control, 62 0 (2): 0 941--947, 2016

    2016

  56. [64]

    Robust receding horizon control using generalized constraint tightening

    Yoshiaki Kuwata, Arthur Richards, and Jonathan How. Robust receding horizon control using generalized constraint tightening. In 2007 American Control Conference, pages 4482--4487. IEEE, 2007

    2007

  57. [65]

    Bandit algorithms

    Tor Lattimore and Csaba Szepesv \'a ri. Bandit algorithms. Cambridge University Press, 2020

    2020

  58. [66]

    Reinforcement learning and control as probabilistic inference: Tutorial and review

    Sergey Levine. Reinforcement learning and control as probabilistic inference: Tutorial and review. arXiv preprint arXiv:1805.00909, 2018

    2018 arXiv

  59. [67]

    A distributionally robust optimization based method for stochastic model predictive control

    Bin Li, Yuan Tan, Ai-Guo Wu, and Guang-Ren Duan. A distributionally robust optimization based method for stochastic model predictive control. IEEE Transactions on Automatic Control, 67 0 (11): 0 5762--5776, 2021

    2021

  60. [68]

    Multiagent inverse reinforcement learning for two-person zero-sum games

    Xiaomin Lin, Peter A Beling, and Randy Cogill. Multiagent inverse reinforcement learning for two-person zero-sum games. IEEE Transactions on Games, 10 0 (1): 0 56--68, 2017

    2017

  61. [69]

    Adaptive optimal control for stochastic multiplayer differential games using on-policy and off-policy reinforcement learning

    Mushuang Liu, Yan Wan, Frank L Lewis, and Victor G Lopez. Adaptive optimal control for stochastic multiplayer differential games using on-policy and off-policy reinforcement learning. IEEE transactions on neural networks and learning systems, 31 0 (12): 0 5522--5533, 2020

    2020

  62. [70]

    The art of military deception

    Mark Lloyd. The art of military deception. Pen and Sword, 2003

    2003

  63. [71]

    The optimal finite-sample error probability in asymmetric binary hypothesis testing

    Valentinian Lungu and Ioannis Kontoyiannis. The optimal finite-sample error probability in asymmetric binary hypothesis testing. In 2024 IEEE International Symposium on Information Theory (ISIT). IEEE, 2024

    2024

  64. [72]

    Model predictive path integral control for roll-to-roll manufacturing

    Christopher Martin, Apurva Patil, Wei Li, Takashi Tanaka, and Dongmei Chen. Model predictive path integral control for roll-to-roll manufacturing. submitted to Modeling, Estimation and Control Conference, (MECC), 2025

    2025

  65. [73]

    Stochastic game approach for replay attack detection

    Fei Miao, Miroslav Pajic, and George J Pappas. Stochastic game approach for replay attack detection. In 52nd IEEE conference on decision and control, pages 1854--1859. IEEE, 2013

    2013

  66. [74]

    Model predictive path integral control for agile unmanned aerial vehicles

    Michal Minarik, Robert Penicka, Vojtech Vonasek, and Martin Saska. Model predictive path integral control for agile unmanned aerial vehicles. arXiv preprint arXiv:2407.09812, 2024

    2024 arXiv

  67. [75]

    A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games

    Ian M Mitchell, Alexandre M Bayen, and Claire J Tomlin. A time-dependent hamilton-jacobi formulation of reachable sets for continuous dynamic games. IEEE Transactions on automatic control, 50 0 (7): 0 947--957, 2005

    2005

  68. [76]

    Chases and escapes

    Paul J Nahin. Chases and escapes. In Chases and Escapes. Princeton University Press, 2012

    2012

  69. [77]

    Trajectory optimization for chance-constrained nonlinear stochastic systems

    Yashwanth Kumar Nakka and Soon-Jo Chung. Trajectory optimization for chance-constrained nonlinear stochastic systems. In 2019 IEEE 58th conference on decision and control (CDC), pages 3811--3818. IEEE, 2019

    2019

  70. [78]

    Derivation of the S chr \"o dinger equation from newtonian mechanics

    Edward Nelson. Derivation of the S chr \"o dinger equation from newtonian mechanics. Physical review, 150 0 (4): 0 1079, 1966

    1966

  71. [79]

    Dynamical theories of Brownian motion, volume 106

    Edward Nelson. Dynamical theories of Brownian motion, volume 106. Princeton university press, 2020

    2020

  72. [80]

    Convex approximations of chance constrained programs

    Arkadi Nemirovski and Alexander Shapiro. Convex approximations of chance constrained programs. SIAM Journal on Optimization, 17 0 (4): 0 969--996, 2007

    2007

  73. [81]

    Convex optimization over sequential linear feedback policies with continuous-time chance constraints

    Kenshiro Oguri, Masahiro Ono, and Jay W McMahon. Convex optimization over sequential linear feedback policies with continuous-time chance constraints. In 2019 IEEE 58th Conference on Decision and Control (CDC), pages 6325--6331. IEEE, 2019

    2019

  74. [82]

    Acceleration of gradient-based path integral method for efficient optimal and inverse optimal control

    Masashi Okada and Tadahiro Taniguchi. Acceleration of gradient-based path integral method for efficient optimal and inverse optimal control. In 2018 IEEE International Conference on Robotics and Automation (ICRA), pages 3013--3020. IEEE, 2018

    2018

  75. [83]

    Stochastic differential equations

    Bernt ksendal. Stochastic differential equations. Springer, 2003

    2003

  76. [84]

    Stochastic differential equations: an introduction with applications

    Bernt Oksendal. Stochastic differential equations: an introduction with applications. Springer Science & Business Media, 2013

    2013

  77. [85]

    Chance-constrained dynamic programming with application to risk-aware robotic space exploration

    Masahiro Ono, Marco Pavone, Yoshiaki Kuwata, and J Balaram. Chance-constrained dynamic programming with application to risk-aware robotic space exploration. Autonomous Robots, 39 0 (4): 0 555--571, 2015

    2015

  78. [86]

    RRTX : Asymptotically optimal single-query sampling-based motion planning with quick replanning

    Michael Otte and Emilio Frazzoli. RRTX : Asymptotically optimal single-query sampling-based motion planning with quick replanning. The International Journal of Robotics Research, 35 0 (7): 0 797--822, 2016

    2016

  79. [87]

    Skill learning and task outcome prediction for manipulation

    Peter Pastor, Mrinal Kalakrishnan, Sachin Chitta, Evangelos Theodorou, and Stefan Schaal. Skill learning and task outcome prediction for manipulation. In 2011 IEEE I nternational C onference on R obotics and A utomation , pages 3828--3834. IEEE, 2011

    2011

  80. [88]

    Upper bounds for continuous-time end-to-end risks in stochastic robot navigation

    Apurva Patil and Takashi Tanaka. Upper bounds for continuous-time end-to-end risks in stochastic robot navigation. In 2022 European Control Conference (ECC), pages 2049--2055. IEEE, 2022

    2022

  81. [89]

    Upper and lower bounds for end-to-end risks in stochastic robot navigation

    Apurva Patil and Takashi Tanaka. Upper and lower bounds for end-to-end risks in stochastic robot navigation. IFAC-PapersOnLine, 56 0 (2): 0 5603--5608, 2023

    2023

  82. [90]

    Chance-constrained stochastic optimal control via path integral and finite difference methods

    Apurva Patil, Alfredo Duarte, Aislinn Smith, Fabrizio Bisetti, and Takashi Tanaka. Chance-constrained stochastic optimal control via path integral and finite difference methods. In 2022 IEEE 61st Conference on Decision and Control (CDC), pages 3598--3604. IEEE, 2022

    2022

  83. [91]

    Simulator-driven deceptive control via path integral approach

    Apurva Patil, Mustafa O Karabag, Takashi Tanaka, and Ufuk Topcu. Simulator-driven deceptive control via path integral approach. In 2023 62nd IEEE Conference on Decision and Control (CDC), pages 271--277. IEEE, 2023 a

    2023

  84. [92]

    Risk-minimizing two-player zero-sum stochastic differential game via path integral control

    Apurva Patil, Yujing Zhou, David Fridovich-Keil, and Takashi Tanaka. Risk-minimizing two-player zero-sum stochastic differential game via path integral control. In 2023 62nd IEEE Conference on Decision and Control (CDC), pages 3095--3101. IEEE, 2023 b

    2023

  85. [93]

    Discrete-time stochastic lqr via path integral control and its sample complexity analysis

    Apurva Patil, Grani A Hanasusanto, and Takashi Tanaka. Discrete-time stochastic lqr via path integral control and its sample complexity analysis. IEEE Control Systems Letters, 2024

    2024

  86. [94]

    An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems

    Joel A Paulson and Ali Mesbah. An efficient method for stochastic optimal control with joint chance constraints for nonlinear systems. International Journal of Robust and Nonlinear Control, 29 0 (15): 0 5017--5037, 2019

    2019

  87. [95]

    Minimax optimal control of stochastic uncertain systems with relative entropy constraints

    Ian R Petersen, Matthew R James, and Paul Dupuis. Minimax optimal control of stochastic uncertain systems with relative entropy constraints. IEEE Transactions on Automatic Control, 45 0 (3): 0 398--412, 2000

    2000

  88. [96]

    Linear reinforcement learning in planning, grid fields, and cognitive control

    Payam Piray and Nathaniel D Daw. Linear reinforcement learning in planning, grid fields, and cognitive control. Nature communications, 12 0 (1): 0 4942, 2021

    2021

  89. [97]

    Lecture notes on information theory

    Yury Polyanskiy and Yihong Wu. Lecture notes on information theory. Lecture Notes for ECE563 (UIUC), 2014

    2014

  90. [98]

    Special issue on cyber-physical systems [scanning the issue]

    Radha Poovendran, Krishna Sampigethaya, Sandeep Kumar S Gupta, Insup Lee, K Venkatesh Prasad, David Corman, and James L Paunicka. Special issue on cyber-physical systems [scanning the issue]. Proceedings of the IEEE, 100 0 (1): 0 6--12, 2011

    2011

  91. [99]

    Competitive policy optimization

    Manish Prajapat, Kamyar Azizzadenesheli, Alexander Liniger, Yisong Yue, and Anima Anandkumar. Competitive policy optimization. In Uncertainty in Artificial Intelligence, pages 64--74. PMLR, 2021

    2021

  92. [100]

    Boole- B onferroni inequalities and linear programming

    Andr \'a s Pr \'e kopa. Boole- B onferroni inequalities and linear programming. Operations Research, 36 0 (1): 0 145--162, 1988

    1988

  93. [101]

    Tendon-driven control of biomechanical and robotic systems: A path integral reinforcement learning approach

    Eric Rombokas, Evangelos Theodorou, Mark Malhotra, Emo Todorov, and Yoky Matsuoka. Tendon-driven control of biomechanical and robotic systems: A path integral reinforcement learning approach. In 2012 IEEE International Conference on Robotics and Automation, pages 208--214. IEEE, 2012

    2012

  94. [102]

    A variational principle for quantum mechanics

    HH Rosenbrock. A variational principle for quantum mechanics. Physics letters A, 110 0 (7-8): 0 343--346, 1985

    1985

  95. [103]

    A stochastic variational treatment of quantum mechanics

    Howard Harry Rosenbrock. A stochastic variational treatment of quantum mechanics. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 450 0 (1939): 0 417--437, 1995

    1939

  96. [104]

    Secure networked control systems

    Henrik Sandberg, Vijay Gupta, and Karl H Johansson. Secure networked control systems. Annual Review of Control, Robotics, and Autonomous Systems, 5: 0 445--464, 2022

    2022

  97. [105]

    Nonlinear stochastic optimal control with input saturation constraints based on path integrals

    Satoshi Satoh and Hilbert J Kappen. Nonlinear stochastic optimal control with input saturation constraints based on path integrals. IEEJ Transactions on Electrical and Electronic Engineering, 15 0 (8): 0 1169--1175, 2020

    2020

  98. [106]

    An iterative method for nonlinear stochastic optimal control based on path integrals

    Satoshi Satoh, Hilbert J Kappen, and Masami Saeki. An iterative method for nonlinear stochastic optimal control based on path integrals. IEEE Transactions on Automatic Control, 62 0 (1): 0 262--276, 2016

    2016

  99. [107]

    Trust region policy optimization

    John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region policy optimization. In International conference on machine learning, pages 1889--1897. PMLR, 2015

    2015

  100. [108]

    Synthesis of whole-body behaviors through hierarchical control of behavioral primitives

    Luis Sentis and Oussama Khatib. Synthesis of whole-body behaviors through hierarchical control of behavioral primitives. International Journal of Humanoid Robotics, 2 0 (04): 0 505--518, 2005

    2005

  101. [109]

    Large scale multi-robot coordination under network and geographical constraints

    Luis Sentis, Mike Mintz, Arun Ayyagari, Craig Battles, Susan Ying, and Oussama Khatib. Large scale multi-robot coordination under network and geographical constraints. In 2009 IEEE International Symposium on Industrial Electronics, pages 1046--1053. IEEE, 2009

    2009

  102. [110]

    Probability of success in stochastic robot navigation with state feedback

    Shridhar K Shah, Chetan D Pahlajani, and Herbert G Tanner. Probability of success in stochastic robot navigation with state feedback. In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 3911--3916. IEEE, 2011

    2011

  103. [111]

    The MATLAB ODE suite

    Lawrence F Shampine and Mark W Reichelt. The MATLAB ODE suite. SIAM journal on scientific computing, 18 0 (1): 0 1--22, 1997

    1997

  104. [112]

    Worst-case stealthy innovation-based linear attacks on remote state estimation under K ullback-- L eibler divergence

    Jun Shang, Hao Yu, and Tongwen Chen. Worst-case stealthy innovation-based linear attacks on remote state estimation under K ullback-- L eibler divergence. IEEE Transactions on Automatic Control, 2021

    2021

  105. [113]

    A taxonomy of robot deception and its benefits in HRI

    Jaeeun Shim and Ronald C Arkin. A taxonomy of robot deception and its benefits in HRI . In 2013 IEEE international conference on systems, man, and cybernetics, pages 2328--2335. IEEE, 2013

    2013

  106. [114]

    Kinematic control of redundant robot manipulators: A tutorial

    Bruno Siciliano. Kinematic control of redundant robot manipulators: A tutorial. Journal of intelligent and robotic systems, 3: 0 201--212, 1990

    1990

  107. [115]

    Lessons learned from the maroochy water breach

    Jill Slay and Michael Miller. Lessons learned from the maroochy water breach. In International conference on critical infrastructure protection, pages 73--82. Springer, 2007

    2007

  108. [116]

    A general framework for managing multiple tasks in highly redundant robotic systems

    Siciliano B Slotine and B Siciliano. A general framework for managing multiple tasks in highly redundant robotic systems. In proceeding of 5th International Conference on Advanced Robotics, volume 2, pages 1211--1216, 1991

    1991

  109. [117]

    Optimal control and estimation

    Robert F Stengel. Optimal control and estimation. Courier Corporation, 1994

    1994

  110. [118]

    Multi-agent path integral control for interaction-aware motion planning in urban canals

    Lucas Streichenberg, Elia Trevisan, Jen Jen Chung, Roland Siegwart, and Javier Alonso-Mora. Multi-agent path integral control for interaction-aware motion planning in urban canals. In 2023 IEEE International Conference on Robotics and Automation (ICRA), pages 1379--1385. IEEE, 2023

    2023

  111. [119]

    Phase-dependent trajectory optimization for CPG -based biped walking using path integral reinforcement learning

    Norikazu Sugimoto and Jun Morimoto. Phase-dependent trajectory optimization for CPG -based biped walking using path integral reinforcement learning. In 2011 11th IEEE-RAS International Conference on Humanoid Robots, pages 255--260. IEEE, 2011

    2011

  112. [120]

    Pursuit evasion game of two players under an external flow field

    Wei Sun and Panagiotis Tsiotras. Pursuit evasion game of two players under an external flow field. In 2015 American Control Conference (ACC), pages 5617--5622, 2015. doi:10.1109/ACC.2015.7172219

    2015

  113. [121]

    Covert vehicle misguidance and its detection: A hypothesis testing game over continuous-time dynamics

    Takashi Tanaka, Kenji Sawada, Yohei Watanabe, and Mitsugu Iwamoto. Covert vehicle misguidance and its detection: A hypothesis testing game over continuous-time dynamics. IEEE Control Systems Letters, 2024

    2024

  114. [122]

    Attack models and scenarios for networked control systems

    Andr \'e Teixeira, Daniel P \'e rez, Henrik Sandberg, and Karl Henrik Johansson. Attack models and scenarios for networked control systems. In Proceedings of the 1st international conference on High Confidence Networked Systems, pages 55--64, 2012

    2012

  115. [123]

    A generalized path integral control approach to reinforcement learning

    Evangelos Theodorou, Jonas Buchli, and Stefan Schaal. A generalized path integral control approach to reinforcement learning. The Journal of Machine Learning Research, 11: 0 3137--3181, 2010 a

    2010

  116. [124]

    Reinforcement learning of motor skills in high dimensions: A path integral approach

    Evangelos Theodorou, Jonas Buchli, and Stefan Schaal. Reinforcement learning of motor skills in high dimensions: A path integral approach. In 2010 IEEE International Conference on Robotics and Automation, pages 2397--2403. IEEE, 2010 b

    2010

  117. [125]

    Relative entropy and free energy dualities: Connections to path integral and KL control

    Evangelos A Theodorou and Emanuel Todorov. Relative entropy and free energy dualities: Connections to path integral and KL control. The 51st IEEE Conference on Decision and Control (CDC), pages 1466--1473, 2012

    2012

  118. [126]

    Linearly-solvable M arkov decision problems

    Emanuel Todorov. Linearly-solvable M arkov decision problems. Advances in N eural I nformation P rocessing S ystems , 19, 2006

    2006

  119. [127]

    Linearly-solvable Markov decision problems

    Emanuel Todorov. Linearly-solvable Markov decision problems. Advances in neural information processing systems, pages 1369--1376, 2007

    2007

  120. [128]

    Efficient computation of optimal actions

    Emanuel Todorov. Efficient computation of optimal actions. Proceedings of the national academy of sciences, 106 0 (28): 0 11478--11483, 2009

    2009

  121. [129]

    A strictly convergent real-time solution for inverse kinematics of robot manipulators

    Yusheng T Tsai and David E Orin. A strictly convergent real-time solution for inverse kinematics of robot manipulators. Journal of robotic systems, 4 0 (4): 0 477--501, 1987

    1987

  122. [130]

    Randomized algorithms for robust controller synthesis using statistical learning theory

    Mathukumalli Vidyasagar. Randomized algorithms for robust controller synthesis using statistical learning theory. Automatica, 37 0 (10): 0 1515--1528, 2001

    2001

  123. [131]

    Adaptive dynamic programming for online solution of a zero-sum differential game

    Draguna Vrabie and Frank Lewis. Adaptive dynamic programming for online solution of a zero-sum differential game. Journal of Control Theory and Applications, 9 0 (3): 0 353--360, 2011

    2011

  124. [132]

    Robust path integral control on stochastic differential games

    D Vrushabh, P Akshay, K Sonam, S Wagh, and Navdeep M Singh. Robust path integral control on stochastic differential games. In 2020 28th Mediterranean Conference on Control and Automation (MED), pages 665--670. IEEE, 2020

    2020

  125. [133]

    Non-gaussian chance-constrained trajectory planning for autonomous vehicles under agent uncertainty

    Allen Wang, Ashkan Jasour, and Brian C Williams. Non-gaussian chance-constrained trajectory planning for autonomous vehicles under agent uncertainty. IEEE Robotics and Automation Letters, 5 0 (4): 0 6041--6048, 2020

    2020

  126. [134]

    Cyber deception: Overview and the road ahead

    Cliff Wang and Zhuo Lu. Cyber deception: Overview and the road ahead. IEEE Security & Privacy, 16 0 (2): 0 80--85, 2018

    2018

  127. [135]

    Risk-sensitive linear/quadratic/ G aussian control

    Peter Whittle. Risk-sensitive linear/quadratic/ G aussian control. Advances in Applied Probability, 13 0 (4): 0 764--777, 1981

    1981

  128. [136]

    Aggressive driving with model predictive path integral control

    Grady Williams, Paul Drews, Brian Goldfain, James M Rehg, and Evangelos A Theodorou. Aggressive driving with model predictive path integral control. In 2016 IEEE International Conference on Robotics and Automation (ICRA), pages 1433--1440. IEEE, 2016

    2016

  129. [137]

    Model predictive path integral control: From theory to parallel computation

    Grady Williams, Andrew Aldrich, and Evangelos A Theodorou. Model predictive path integral control: From theory to parallel computation. Journal of Guidance, Control, and Dynamics, 40 0 (2): 0 344--357, 2017 a

    2017

  130. [138]

    Information theoretic MPC for model-based reinforcement learning

    Grady Williams, Nolan Wagener, Brian Goldfain, Paul Drews, James M Rehg, Byron Boots, and Evangelos A Theodorou. Information theoretic MPC for model-based reinforcement learning. In 2017 IEEE International Conference on Robotics and Automation (ICRA), pages 1714--1721. IEEE, 2017 b

    2017

  131. [139]

    Information-theoretic model predictive control: Theory and applications to autonomous driving

    Grady Williams, Paul Drews, Brian Goldfain, James M Rehg, and Evangelos A Theodorou. Information-theoretic model predictive control: Theory and applications to autonomous driving. IEEE Transactions on Robotics, 34 0 (6): 0 1603--1622, 2018

    2018

  132. [140]

    Stochastic calculus of variations

    Kunio Yasue. Stochastic calculus of variations. Journal of Functional Analysis, 41 0 (3): 0 327--340, 1981

    1981

  133. [141]

    Sampling complexity of path integral methods for trajectory optimization

    Hyung-Jin Yoon, Chuyuan Tao, Hunmin Kim, Naira Hovakimyan, and Petros Voulgaris. Sampling complexity of path integral methods for trajectory optimization. In 2022 American Control Conference (ACC), pages 3482--3487. IEEE, 2022

    2022

  134. [142]

    Reliable approximations of probability-constrained stochastic linear-quadratic control

    Zhou Zhou and Randy Cogill. Reliable approximations of probability-constrained stochastic linear-quadratic control. Automatica, 49 0 (8): 0 2435--2439, 2013

    2013

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.