School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China; Department of Electrical, Computer and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA.
Department of Electrical, Computer and Biomedical Engineering, University of Rhode Island, Kingston, RI 02881, USA.
Neural Netw. 2018 Sep;105:142-153. doi: 10.1016/j.neunet.2018.05.005. Epub 2018 May 26.
In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme.
在本文中，我们为一类具有不匹配互联的不确定非线性系统开发了一种新颖的最优控制策略。首先，我们通过修改辅助子系统的最优控制律的一个集合，为互联非线性系统提出了一个稳定的反馈控制器。我们还证明，该反馈控制器确保了指定的成本函数达到最优。然后，在自适应评论家设计的框架下，我们使用评论家网络来求解与辅助子系统最优控制律相关的哈密顿-雅可比-贝尔曼方程。评论家网络的权重通过梯度下降法与附加的稳定项相结合进行调整。通过使用新建立的权重调整规则，我们不再需要初始的可接受控制条件。此外，我们还使用经典的 Lyapunov 技术证明了闭环辅助子系统中所有信号的一致有界稳定性。最后，我们提供了一个互联非线性 plant 来验证所提出的控制方案。
