发表机构
Technische Universität Chemnitz（开姆尼茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种结合李雅普诺夫函数约束的自适应动态规划方法，采用无海森矩阵优化，可保证闭环稳定性，其评价网络方法在多初始条件下性能优于标称稳定控制器。
AI 中文摘要
本研究关注一种用于近似求解给定无限时域最优控制问题的稳定自适应动态规划（ADP）方法。由于这类问题通常无法精确求解，ADP中引入了用于近似无限时域代价函数的参数化函数近似器（即所谓的“评价网络”），该评价网络用于调整函数近似器的参数；而所谓的“动作网络”则推导系统的最优输入。由于控制方案中使用了近似结构，保证ADP的闭环稳定性是一个公认的难题。鉴于ADP分析中始终至少假设系统可稳定，因此可调用相应的李雅普诺夫函数。所提出的ADP方案明确利用该李雅普诺夫函数同时优化评价网络并保证闭环稳定性，采用无海森矩阵的优化程序求解动作网络和评价网络的优化问题，证明了其收敛至最优解的指定邻域。计算研究表明，在一系列初始条件下，与标称稳定控制器相比，基于评价网络的方法性能有显著提升。
英文摘要
This work is concerned with a stabilizing adaptive dynamic programming (ADP) approach to approximate solution of a given infinite-horizon optimal control problem. Since the latter problem cannot, in general, be solved exactly, a parametrized function approximator for the infinite-horizon cost function is introduced in ADP (so called ``critic''). This critic is used to adapt the parameters of the function approximator. The so called ``actor'' in turn derives the optimal input of the system. It is a notoriously hard problem to guarantee closed-loop stability of ADP due to the use of approximation structures in the control scheme. Since at least stabilizability is always assumed in the analyses of ADP, it is justified to invoke a respective Lyapunov function. The proposed ADP scheme explicitly uses the said Lyapunov function to simultaneously optimize the critic and guarantee closed-loop stability. A Hessian-free optimization routine is utilized for the actor and critic optimization problems. Convergence to prescribed vicinities of the optima is shown. A computational study showed significant performance improvement for the critic-based approach compared a nominal stabilizing controller for a range of initial conditions.
Journal refIEEE Control Systems Letters, vol. 3, no. 4, pp. 901-906, Oct. 2019
DOI：10.1109/LCSYS.2019.2919439
