Liu Yan-Jun, Li Shu, Tong Shaocheng, Chen C L Philip
IEEE Trans Neural Netw Learn Syst. 2019 Jan;30(1):295-305. doi: 10.1109/TNNLS.2018.2844165. Epub 2018 Jun 28.
In this paper, an optimal control algorithm is designed for uncertain nonlinear systems in discrete-time, which are in nonaffine form and with unknown dead-zone. The main contributions of this paper are that an optimal control algorithm is for the first time framed in this paper for nonlinear systems with nonaffine dead-zone, and the adaptive parameter law for dead-zone is calculated by using the gradient rules. The mean value theory is employed to deal with the nonaffine dead-zone input and the implicit function theory based on reinforcement learning is appropriately introduced to find an unknown ideal controller which is approximated by using the action network. Other neural networks are taken as the critic networks to approximate the strategic utility functions. Based on the Lyapunov stability analysis theory, we can prove the stability of systems, i.e., the optimal control laws can guarantee that all the signals in the closed-loop system are bounded and the tracking errors are converged to a small compact set. Finally, two simulation examples demonstrate the effectiveness of the design algorithm.
本文针对离散时间下的不确定非线性系统设计了一种最优控制算法，该系统为非仿射形式且带有未知死区。本文的主要贡献在于首次针对具有非仿射死区的非线性系统构建了最优控制算法，并且利用梯度规则计算了死区的自适应参数律。采用均值理论处理非仿射死区输入，并适当引入基于强化学习的隐函数理论来寻找未知理想控制器，该控制器通过动作网络进行近似。将其他神经网络作为评判网络来近似策略效用函数。基于李雅普诺夫稳定性分析理论，我们可以证明系统的稳定性，即最优控制律能够保证闭环系统中的所有信号都是有界的，并且跟踪误差收敛到一个小的紧致集。最后，两个仿真例子证明了设计算法的有效性。
