In this paper, a data-based scheme is proposed to solve the optimal tracking problem of autonomous nonlinear switching systems. The system state is forced to track the reference signal by minimizing the performance function. First, the problem is transformed to solve the corresponding Bellman optimality equation in terms of the Q-function ( also named as action value function ) . Then, an iterative algorithm based on adaptive dynamic programming ( ADP ) is developed to find the optimal solution which is totally based on sampled data. The linear-in-parameter ( LIP ) neural network is taken as the value function approximator. Considering the presence of approximation error at each iteration step, the generated approximated value function sequence is proved to be boundedness around the exact optimal solution under some verifiable assumptions. Moreover, the effect that the learning process will be terminated after a finite number of iterations is investigated in this paper. A sufficient condition for asymptotically stability of the tracking error is derived. Finally, the effectiveness of the algorithm is demonstrated with three simulation examples.

中文翻译：

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基于数据的自主非线性开关系统的最优跟踪

本文提出了一种基于数据的方案来解决自主非线性切换系统的最优跟踪问题。通过最小化性能函数，系统状态被迫跟踪参考信号。首先，将问题转换为根据Q函数（也称为动作值函数）求解相应的Bellman最优性方程。然后，开发了一种基于自适应动态规划（ADP）的迭代算法，以找到完全基于采样数据的最优解决方案。参数线性（LIP）神经网络被用作值函数近似器。考虑到每个迭代步骤都存在近似误差，在某些可验证的假设下，证明所生成的近似值函数序列在精确的最优解周围是有界的。此外，本文研究了在有限次数的迭代后终止学习过程的效果。得出了跟踪误差渐近稳定的充分条件。最后，通过三个仿真实例证明了该算法的有效性。