Optimal switching between controlled subsystems with free mode sequence

The problem of optimal switching and control of nonlinear switching systems with controlled subsystems is investigated in this study where the mode sequence and the switching times between the modes are unspecified. An approximate dynamic programming based method is developed which provides a feedback solution for unspecified initial conditions and different final times. The convergence of the proposed algorithm is proved. Versatility of the method and its performance are illustrated through different numerical examples.