Adaptive optimal controllers based on Generalized Policy Iteration in a continuous-time framework

D. Vrabie, K. Vamvoudakis, F. Lewis
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引用次数: 51

Abstract

In this paper we present two adaptive algorithms which offer solution to the continuous-time optimal control problem for nonlinear, affine in the inputs, time-invariant systems. Both algorithms were developed based on the Generalized Policy Iteration technique and involve adaptation of two neural network structures namely Actor, providing the control signal, and Critic, performing evaluation of the control performance. Despite the similarities, the two adaptive algorithms differ in the manner in which the adaptation takes place, required knowledge on the system dynamics, and formulation of the persistence of excitation requirement. The main difference is that one algorithm uses sequential adaptation of the actor and critic structures, i.e. while one is trained the other one is kept constant, while for the second algorithm the two neural networks are trained synchronously in a continuous-time fashion. The two algorithms are described in detail and proof of convergence is provided. Simulation results of applying the two algorithms for finding the optimal state feedback controller of a nonlinear system are also presented.
连续时间框架下基于广义策略迭代的自适应最优控制器
本文提出了两种自适应算法,解决了输入为非线性仿射的时不变系统的连续时间最优控制问题。这两种算法都是基于广义策略迭代技术开发的,并涉及两个神经网络结构的自适应,即提供控制信号的Actor和对控制性能进行评估的Critic。尽管有相似之处,但这两种自适应算法在自适应发生的方式、所需的系统动力学知识以及激励持久性要求的表述方面存在差异。主要区别在于,一种算法使用演员和评论家结构的顺序适应,即,当一个被训练时,另一个保持不变,而对于第二种算法,两个神经网络以连续时间的方式同步训练。详细描述了这两种算法,并给出了收敛性证明。最后给出了应用这两种算法求解非线性系统最优状态反馈控制器的仿真结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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