IEEE Trans Cybern. 2016 Nov;46(11):2670-2680. doi: 10.1109/TCYB.2015.2494007. Epub 2016 Feb 23.
In this paper, we propose an optimal control scheme-based adaptive neural network design for a class of unknown nonlinear discrete-time systems. The controlled systems are in a block-triangular multi-input-multi-output pure-feedback structure, i.e., there are both state and input couplings and nonaffine functions to be included in every equation of each subsystem. The design objective is to provide a control scheme, which not only guarantees the stability of the systems, but also achieves optimal control performance. The main contribution of this paper is that it is for the first time to achieve the optimal performance for such a class of systems. Owing to the interactions among subsystems, making an optimal control signal is a difficult task. The design ideas are that: 1) the systems are transformed into an output predictor form; 2) for the output predictor, the ideal control signal and the strategic utility function can be approximated by using an action network and a critic network, respectively; and 3) an optimal control signal is constructed with the weight update rules to be designed based on a gradient descent method. The stability of the systems can be proved based on the difference Lyapunov method. Finally, a numerical simulation is given to illustrate the performance of the proposed scheme.
在本文中，我们提出了一种基于最优控制方案的自适应神经网络设计，用于一类未知的非线性离散时间系统。被控系统具有块三角式多输入多输出纯反馈结构，即每个子系统的每个方程中都存在状态和输入耦合以及非仿射函数。设计目标是提供一种控制方案，不仅保证系统的稳定性，而且实现最优的控制性能。本文的主要贡献在于首次为这类系统实现了最优性能。由于子系统之间的相互作用，使得最优控制信号成为一项困难的任务。设计思路如下：1）将系统转换为输出预测器形式；2）对于输出预测器，可以分别使用作用网络和评价网络来逼近理想控制信号和策略效用函数；3）使用基于梯度下降法设计的权重更新规则构建最优控制信号。可以基于差分 Lyapunov 方法证明系统的稳定性。最后，给出了一个数值仿真示例来说明所提出方案的性能。
