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arXiv 2011.01128eess.SYcs.LGcs.SY

状态矩阵未知的线性系统结构化控制的强化学习

Reinforcement Learning of Structured Control for Linear Systems with Unknown State Matrix

Pacific Northwest National Laboratory(太平洋西北国家实验室)

Sayak Mukherjee, Thanh Long Vu

AI总结:

本文针对状态矩阵未知且控制受结构约束的连续线性系统,提出将结构约束嵌入LQR的强化学习策略迭代算法,并给出稳定性与收敛性保证,可应用于分布式学习控制等场景。

摘要:

本文深入研究为状态矩阵未知的连续线性系统设计稳定反馈控制增益的问题,其中控制受到一般结构性约束。我们引入强化学习(RL)的思想,并结合充分的稳定性与性能保证,利用状态和控制的轨迹测量来设计这些结构化增益。我们首先利用动态规划(DP)构建一个基于模型的框架,将结构性约束嵌入连续时间设定下的线性二次调节器(LQR)增益计算中。随后,我们将该LQR公式转化为策略迭代强化学习算法,在保持反馈增益结构的同时,缓解对已知状态矩阵的要求。我们为结构化强化学习(SRL)算法的稳定性和收敛性提供了理论保证。所引入的强化学习框架具有通用性,可应用于任何控制结构。该强化学习框架支持的一种特殊控制结构是分布式学习控制,这对于许多大规模信息物理系统是必需的。因此,我们通过多智能体网络化线性时不变(LTI)动态系统上的数值仿真验证了理论结果。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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