Pith. sign in

REVIEW 3 minor 23 references

Adaptive MPC for Constrained Trajectory Tracking of Uncertain LTI System with Input-Rate Limits

T0 review · 0 major / 3 minor · reviewed 2026-05-08 · grok-4.3

Challenge this review Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read An adaptive MPC framework guarantees recursive feasibility and stability for trajectory tracking of uncertain LTI systems with input-rate limits.

desk verdict This paper claims a new adaptive MPC reformulation that restores recursive feasibility for rate-constrained tracking under full parametric uncertainty, but the proofs and simulations stay at the claim level in the abstract. read the letter →

arxiv 2605.04656 v1 submitted 2026-05-06 eess.SY cs.SY

Bishal Dey , Abhishek Dhar , Sumit kr. Pandey , Anindita Sengupta This is my paper · ORCID
classification eess.SYcs.SY
keywords adaptiveMPCtrajectorytrackingparametricuncertaintyinput-rateconstraintsrecursivefeasibilityLyapunovstabilityLTIsystemsconstrainedcontrol
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

The paper addresses the challenge of tracking trajectories in discrete-time linear time-invariant systems that have unknown but bounded parameters and must respect hard limits on states, inputs, and how fast inputs can change. It shows that by feeding online estimates of the parameters into a specially reformulated model predictive controller and pairing it with an adaptive learning scheme, the optimization problem stays feasible from one step to the next even though the allowed control values change over time because of the rate limits. This setup also lets the authors prove that the tracking error goes to zero and the states stay bounded using a Lyapunov function. Readers should care because many practical systems, from autonomous vehicles to industrial robots, face exactly these uncertainties and actuator speed limits, yet most prior control designs either assume perfect knowledge or drop some of the constraints.

What carries the argument

The reformulated MPC optimization routine that uses estimated parameters together with an adaptive learning process to handle the time-varying admissible control set induced by input-rate constraints.

What would settle it

A case where the adaptive estimates cause the MPC optimization to become infeasible or the tracking error to grow unbounded despite the uncertainty bounds being respected would disprove the feasibility and stability results.

Watch

Extended reading notes

Core claim

This paper claims that an adaptive model predictive control framework, which systematically incorporates estimated system parameters and a suitably designed adaptive learning process, overcomes the challenges of achieving zero tracking error under unknown parameters and the temporal coupling from input-rate constraints. The reformulated MPC ensures recursive feasibility of the optimization routine despite the time-varying admissible control set, and Lyapunov-based analysis guarantees closed-loop stability with convergence of the tracking error and boundedness of system states.

Load-bearing premise

The discrete-time LTI system has bounded parametric uncertainty and a suitably designed adaptive learning process can restore recursive feasibility for the time-varying admissible control set from input-rate constraints.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 3 minor

Summary. The paper proposes an adaptive MPC framework for discrete-time LTI systems with bounded parametric uncertainty, addressing constrained trajectory tracking under hard state, input, and input-rate constraints. It reformulates the MPC optimization using online parameter estimates and a tailored adaptive learning process to handle the time-varying admissible control set induced by rate limits, claims rigorous recursive feasibility despite this coupling, and establishes closed-loop stability via Lyapunov analysis, with simulations validating tracking error convergence and state boundedness.

Significance. If the feasibility and stability results hold as claimed, the work would meaningfully extend adaptive MPC literature by systematically addressing full parametric uncertainty in tracking (rather than regulation) problems that include input-rate constraints, which create temporal dependencies absent from many standard formulations. The combination of online adaptation with a reformulated optimization to restore feasibility could enable safer application in domains like robotics or vehicle control where rate limits and uncertainty coexist.

minor comments (3)
  1. The abstract is truncated mid-sentence ('the pr'); ensure the concluding sentence on simulation validation is completed in the final manuscript.
  2. In the simulation section, the specific system matrices, uncertainty bounds, and comparison baselines (e.g., non-adaptive MPC or other adaptive schemes) are not detailed enough to allow reproduction or assessment of the claimed performance gains.
  3. Notation for the time-varying admissible set and the adaptive update law should be introduced with explicit definitions early in the problem formulation to improve readability of the subsequent feasibility argument.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary of our work and the recommendation for minor revision. The referee's assessment correctly identifies the key contributions regarding adaptive MPC for constrained trajectory tracking under full parametric uncertainty and input-rate limits. No specific major comments were provided in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity identified

full rationale

The paper's derivation chain relies on standard adaptive MPC reformulation to handle time-varying admissible sets from input-rate constraints, followed by recursive feasibility arguments and Lyapunov-based closed-loop stability proofs. These steps are presented as rigorous extensions of existing methods without reducing to self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations. The abstract and description indicate that feasibility and stability follow from the constructed adaptive learning process and MPC optimization, which remain independent of the target results. No quoted equations or steps exhibit the enumerated circular patterns, making the central claims self-contained against external benchmarks.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The paper rests on standard domain assumptions for adaptive MPC; no free parameters, invented entities, or ad-hoc axioms are visible in the abstract.

assumptions (2)
  • domain assumption The plant is a discrete-time LTI system with bounded parametric uncertainty
    Explicitly stated as the problem setting in the abstract.
  • domain assumption An adaptive learning process can be designed to restore recursive feasibility for the time-varying admissible control set
    Invoked to overcome the challenge of input-rate constraints.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Adaptive MPC for Constrained Trajectory Tracking of Uncertain LTI System with Input-Rate Limits." pith.science (2026). https://pith.science/paper/2605.04656

@misc{pith2026260504656,
  author       = {Pith},
  title        = {Pith review of: Adaptive MPC for Constrained Trajectory Tracking of Uncertain LTI System with Input-Rate Limits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2605.04656}},
  note         = {Machine review of arXiv:2605.04656}
}
read the original abstract

This paper addresses the trajectory-tracking problem for discrete-time linear time-invariant systems with bounded parametric uncertainty, subject to hard constraints on system states, control inputs, and input rates. Unlike existing methods, which often consider only partial uncertainty, omit input-rate or state constraints, or focus on regulation problems, this work provides a systematic adaptive model predictive control (MPC) solution for constrained trajectory tracking under full parametric uncertainty. Determining the control input required to achieve zero tracking error under unknown parameters is challenging. Simultaneously, trajectory tracking under uncertainty with input-rate constraints induces temporal coupling in the control sequence, resulting in a time-varying admissible control set and rendering standard recursive feasibility arguments inapplicable. These challenges are overcome by systematically utilizing the estimated system parameters, coupled with a suitably designed adaptive learning process within a reformulated MPC framework. The recursive feasibility of the proposed MPC optimization routine is then rigorously established despite the time-varying admissible control set induced by input-rate constraints. Closed-loop stability is guaranteed via Lyapunov-based analysis, ensuring convergence of the tracking error and boundedness of system states. Simulation results validate the effectiveness of the pr

Figures

Figures reproduced from arXiv: 2605.04656 by the authors.

Figure 1
Figure 1. System States 0 5 10 15 20 25 30 35 40 45 Time (s) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 s e k view at source ↗
Figure 2
Figure 2. Error States 0 5 10 15 20 25 30 35 40 45 Time (s) -3 -2 -1 0 1 2 3 u k view at source ↗
Figure 3
Figure 3. Control Input 0 5 10 15 20 25 30 35 40 45 Time (s) -3 -2 -1 0 1 2 3 u k view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Rate of Change of Control Input [−0.4, 0.15; 0.35, −0.5] and Bˆ 0 = [1, 0.1; 0.1, 0.8]. The prediction horizon length N is set to 5. To assess the performance of the proposed control framework under various conditions, simulations are performed with 10 different initia…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages

  1. [1]

    G. Tian, B. Li, Q. Zhao, and G. Duan. High-precision trajectory tracking control for free-flying space manipula tors 9 with multiple constraints and system uncertainties. IEEE Transactions on Aerospace and Electronic Systems , 60(1):789–801, 2023

    work page 2023

  2. [2]

    C. Hu, Z. W ang, X. Bu, J. Zhao, J. Na, and H. Gao. Optimal tracking control for autonomous vehicle with prescribed performance via adaptive dynamic programming. IEEE Transactions on Intelligent Transportation Systems , 25(9):12437–12449, 2024

    work page 2024

  3. [3]

    B. Dey, A. Dhar, S. K. Pandey, and A. Sengupta. Tlbo integrated mpc for autonomous vehicles with guaranteed safety and passenger comfort. In Proc. Indian Control Conference (ICC), pages 576–581, Bangalore, India, 2025

    work page 2025

  4. [4]

    Z. Liu, O. Zhang, Y. Gao, Y. Zhao, Y. Sun, and J. Liu. Adaptive neural network-based fixed-time control fo r trajectory tracking of robotic systems. IEEE Transactions on Circuits and Systems II: Express Briefs , 70(1):241–245, 2022

    work page 2022

  5. [5]

    Ghosh and S

    P. Ghosh and S. Bhasin. State and input constrained model reference adaptive control with robustness and feasibilit y analysis. IEEE Transactions on Automatic Control , pages 1–7, 2026

    work page 2026

  6. [6]

    Dhar and S

    A. Dhar and S. Bhasin. Indirect adaptive mpc for discrete - time lti systems with parametric uncertainties. IEEE Transactions on Automatic Control, 66(11):5498–5505, 2021

    work page 2021

  7. [7]

    Z. Yang, J. Huang, H. Yin, D. Yang, and Z. Zhong. Path tracking control for underactuated vehicles with matched- mismatched uncertainties. IEEE Transactions on Intelligent Transportation Systems, 23(8):12894–12907, 2021

    work page 2021

  8. [8]

    K¨ ohler

    J. K¨ ohler. Certainty-equivalent adaptive mpc for unce rtain nonlinear systems, 2026. arXiv:2603.17843

    work page Pith review arXiv 2026

Show all 23 references
  1. [9]

    Kouvaritakis and M

    B. Kouvaritakis and M. Cannon. Model Predictive Control . Springer, Cham, Switzerland, 2016

    2016

  2. [10]

    S. V. Rakovi´ c, B. Kouvaritakis, R. Findeisen, and M. Cannon. Homothetic tube model predictive control. Automatica, 48(8):1631–1638, 2012

    2012

  3. [11]

    Langson, I

    W. Langson, I. Chryssochoos, S. V. Rakovi´ c, and D. Q. Mayne. Robust model predictive control using tubes. Automatica, 40(1):125–133, 2003

    2003

  4. [12]

    S. Yao, Q. Kang, M. Zhou, M. J. Rawa, and A. Albeshri. Discriminative manifold distribution alignment for domai n adaptation. IEEE Transactions on Systems, Man, and Cybernetics: Systems , 53(2):1183–1197, February 2023

    2023

  5. [13]

    J. Hu, B. Zhang, H. W ang, L. Zhao, and P. Jiang. Coordinated control and torque distribution of differentia l steering and anti-skid driving of distributed drive electr ic vehicle considering stability. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of...

    2023

  6. [14]

    Rosolia and F

    U. Rosolia and F. Borrelli. Learning how to autonomousl y race a car: A predictive control approach. IEEE Transactions on Control Systems Technology , 28(6):2713–2719, November 2020

    2020

  7. [15]

    Tanaskovic, L

    M. Tanaskovic, L. Fagiano, R. Smith, and M. Morari. Adaptive receding horizon control for constrained mimo systems. Automatica, 50(12):3019–3029, 2014

    2014

  8. [16]

    Fan and S

    D. Fan and S. Di Cairano. Further results and properties of indirect adaptive model predictive control for linear syst ems with polytopic uncertainty. In Proceedings of the American Control Conference (ACC) , pages 2948–2953, 2016

    2016

  9. [17]

    Lorenzen, F

    M. Lorenzen, F. Allg¨ ower, and M. Cannon. Adaptive mode l predictive control with robust constraint satisfaction. IF AC- PapersOnLine, 50(1):3313–3318, 2017

    2017

  10. [18]

    A. Dhar, A. Dey, and S. Bhasin. Homothetic tube-based adaptive mpc. International Journal of Robust and Nonlinear Control, 35(13):5705–5716, 2025

    2025

  11. [19]

    Zhu and X

    B. Zhu and X. Xia. Adaptive model predictive control for unconstrained discrete-time linear systems with parametr ic uncertainties. IEEE Transactions on Automatic Control , 61(10):3171–3176, December 2015

    2015

  12. [20]

    A. D. Ames, J. W. Grizzle, and P. Tabuada. Control barrier function based quadratic programs with applicatio n to adaptive cruise control. In IEEE Conference on Decision and Control , pages 6271–6278, 2014

    2014

  13. [21]

    Bemporad, A

    A. Bemporad, A. Casavola, and E. Mosca. Nonlinear control of constrained linear systems via predictive refer ence management. IEEE Transactions on Automatic Control , 42(3):340–349, 1997

    1997

  14. [22]

    Lavretsky and N

    E. Lavretsky and N. Hovakimyan. Stable adaptation in th e presence of input constraints. Systems & Control Letters , 56(11-12):722–729, 2007

    2007

  15. [23]

    Niu and C

    G. Niu and C. Qu. Global asymptotic nonlinear pid contro l with a new generalized saturation function. IEEE Access , 8:210513–210531, 2020. 10

    2020

Pith tools

Reviewed May 8, 2026 · model on record in the stance chip above.