Tang Li, Liu Yan-Jun, Chen C L Philip
IEEE Trans Neural Netw Learn Syst. 2018 Nov;29(11):5681-5690. doi: 10.1109/TNNLS.2018.2805689. Epub 2018 Mar 23.
This paper concentrates on the adaptive critic design (ACD) issue for a class of uncertain multi-input multioutput (MIMO) nonlinear discrete-time systems preceded by unknown backlashlike hysteresis. The considered systems are in a block-triangular pure-feedback form, in which there exist nonaffine functions and couplings between states and inputs. This makes that the ACD-based optimal control becomes very difficult and complicated. To this end, the mean value theorem is employed to transform the original systems into input-output models. Based on the reinforcement learning algorithm, the optimal control strategy is established with an actor-critic structure. Not only the stability of the systems is ensured but also the performance index is minimized. In contrast to the previous results, the main contributions are: 1) it is the first time to build an ACD framework for such MIMO systems with unknown hysteresis and 2) an adaptive auxiliary signal is developed to compensate the influence of hysteresis. In the end, a numerical study is provided to demonstrate the effectiveness of the present method.
本文聚焦于一类具有未知类反冲滞后的不确定多输入多输出（MIMO）非线性离散时间系统的自适应评判设计（ACD）问题。所考虑的系统呈块三角纯反馈形式，其中存在非仿射函数以及状态与输入之间的耦合。这使得基于ACD的最优控制变得非常困难和复杂。为此，利用均值定理将原始系统转换为输入 - 输出模型。基于强化学习算法，建立了具有演员 - 评判结构的最优控制策略。不仅确保了系统的稳定性，还使性能指标最小化。与先前的结果相比，主要贡献在于：1）首次为具有未知滞后的此类MIMO系统构建了ACD框架；2）开发了一种自适应辅助信号来补偿滞后的影响。最后，通过数值研究证明了本方法的有效性。
