Finite Horizon Robust Optimal Tracking Control Based on Approximate Dynamic Programming for Switched Systems with Uncertainties

In this paper, an approximate dynamic programming (ADP)-based approach is developed to handle the robust optimal tracking control problem for switched systems with uncertainties in the finite horizon. The switched systems with unknown matched uncertainties are formulated by virtue of system dynamics and reference trajectory, where the complicated tracking problem is converted to a stabilizing robust optimal control problem. To avoid the requirement of system dynamics knowledge, a neural network (NN)-based identifier is utilized to estimate the unknown switched systems dynamics. The actor-critic NNs are constructed to approximate the optimal control input and the corresponding performance index, where the weights are trained backward-in-time in an off-line manner. Benefiting from the Lipschitz continuous condition, the convergence of the proposed approach is proved, which illustrates the iteration approach will converge to the unique solution under a small enough sampling time interval. Finally, two numerical simulation cases are employed to verify the effectiveness of the proposed approach.