Reinforcement Learning of Structured Control for Linear Systems with Unknown State Matrix
This work addresses the challenge of structured control design for large-scale cyber-physical systems where the state matrix is unknown, offering a method that could enhance distributed learning control, though it appears incremental as it builds on existing LQR and RL techniques.
The paper tackles the problem of designing stabilizing feedback control gains for continuous linear systems with unknown state matrices under structural constraints, by developing a reinforcement learning framework that integrates dynamic programming and policy iteration to compute these gains from trajectory data, with theoretical guarantees and validation on a multi-agent networked system.
This paper delves into designing stabilizing feedback control gains for continuous linear systems with unknown state matrix, in which the control is subject to a general structural constraint. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. We first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the Linear Quadratic Regulator (LQR) gain computation in the continuous-time setting. Subsequently, we transform this LQR formulation into a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. Theoretical guarantees are provided for stability and convergence of the structured RL (SRL) algorithm. The introduced RL framework is general and can be applied to any control structure. A special control structure enabled by this RL framework is distributed learning control which is necessary for many large-scale cyber-physical systems. As such, we validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.