Approximate Dynamic Programming for Trajectory Tracking of Switched Systems

This article develops a technique for online approximate optimization of tracking control policies for a family of switched nonlinear dynamical systems. Optimization is realized via approximate dynamic programming, and integral concurrent learning is used for robustness to parametric uncertainties. The family of switched systems is composed of finitely many subsystems, which may have differing characteristics, such as dynamics and cost functions. This article develops a new result on the analysis of switched systems comprised of locally practically stable subsystems using multiple Lyapunov-like functions. Local practical stability of the overall switched system and convergence of the applied tracking control policies to a neighborhood of the optimal tracking control policies is then proven for an arbitrary switching sequence provided that a set of sufficient gain conditions and a minimum dwell-time condition are satisfied. Simulation results are presented for the optimal control of an autonomous underwater vehicle in the presence of a set of discretely varying irrotational currents to show the efficacy of the developed technique.