Data-based optimal tracking of autonomous nonlinear switching systems

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.