针对未知扰动的连续时间LQR控制，提出兼具稳定性保证与简单性的离线学习方法。
On the System Theoretic Offline Learning of Continuous-Time LQR with Exogenous Disturbances
- 基于自适应动态规划与李雅普诺夫分析，设计可离线学习的LQR控制策略
- 在样本近似下证明了控制增益的稳定性和收敛性，适用于不可测扰动场景
- 适合控制理论研究者及需要鲁棒控制方案的工程应用人员
我们分析了带有不确定扰动的线性二次调节器（LQR）的离线设计。首先考虑外生变量可在受控环境中估计的情形，随后处理更实际且更具挑战性的随机环境下扰动未知的情况。方法基于自适应动态规划（ADP）的学习框架，并结合李雅普诺夫分析，构建算法并推导出源自马尔可夫决策过程（MDP）的样本逼近方法。对于不可测扰动情形，进一步建立了在样本近似下的控制增益稳定性与收敛性保证。整体方法强调简洁性的同时提供严格的理论保障。最后的数值实验聚焦于离线连续时间LQR设计中的复杂性与有效性验证。
原文摘要 · Abstract (English)
We analyze offline designs of linear quadratic regulator (LQR) strategies with uncertain disturbances. First, we consider the scenario where the exogenous variable can be estimated in a controlled environment, and subsequently, consider a more practical and challenging scenario where it is unknown in a stochastic setting. Our approach builds on the fundamental learning-based framework of adaptive dynamic programming (ADP), combined with a Lyapunov-based analytical methodology to design the algorithms and derive sample-based approximations motivated from the Markov decision process (MDP)-based approaches. For the scenario involving non-measurable disturbances, we further establish stability and convergence guarantees for the learned control gains under sample-based approximations. The overall methodology emphasizes simplicity while providing rigorous guarantees. Finally, numerical experiments focus on the intricacies and validations for the design of offline continuous-time LQR with exogenous disturbances.
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