A gradient flow on a continuous-time Bellman error parametrized by feedback gain converges to the optimal LQR controller and stays inside the stabilizing region.
On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
In this paper, we discuss various topological and metrical aspects of the set of stabilizing static feedback gains for multiple-input-multiple-output (MIMO) linear-time-invariant (LTI) systems, in both continuous and discrete-time. Recently, connectivity properties of this set (for continuous time) have been reported in the literature, along with a discussion on how this connectivity is affected by restricting the feedback gain to linear subspaces. We show that analogous to the continuous-time case, one can construct instances where the set of stabilizing feedback gains for discrete time LTI systems has exponentially many connected components.
verdicts
UNVERDICTED 4representative citing papers
An indirect optimization method inner-approximates the set of passivating state-feedback gains for continuous-time LTI systems by a convex polytope and uses projected gradient flow to minimize the LQR cost inside that polytope.
A convex data-driven formulation yields the optimal LQI feedback gain for continuous-time systems directly from measured data without system matrices.
The authors adapt closed-loop and IRL parameterizations to continuous time, deriving policy iteration schemes, a data-driven CARE, convex reformulations, and a policy gradient flow while unifying the two approaches.
citing papers explorer
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Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error
A gradient flow on a continuous-time Bellman error parametrized by feedback gain converges to the optimal LQR controller and stays inside the stabilizing region.
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Towards Optimal Passive Feedback Control of LTI Systems under LQR Performance
An indirect optimization method inner-approximates the set of passivating state-feedback gains for continuous-time LTI systems by a convex polytope and uses projected gradient flow to minimize the LQR cost inside that polytope.
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Data-driven Linear Quadratic Integral Control: A Convex Formulation and Policy Gradient Approach
A convex data-driven formulation yields the optimal LQI feedback gain for continuous-time systems directly from measured data without system matrices.
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Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations
The authors adapt closed-loop and IRL parameterizations to continuous time, deriving policy iteration schemes, a data-driven CARE, convex reformulations, and a policy gradient flow while unifying the two approaches.