Optimal Regulation of Multi-Objective Continuous-Time Nonlinear Switching Systems

This paper investigates the optimal control problem of multi-objective continuous-time nonlinear switching systems. To address this challenge, we utilize the embedding-transformation method to convert the switching system into a traditional dynamic system. The optimal control is proven to be of the bang-bang type by demonstrating that the Hessian matrix of the Hamiltonian concerning the switching input is negative semidefinite. Subsequently, we obtain the optimal value function using approximate dynamic programming (ADP). Finally, we validate the proposed algorithm through simulations.