Neural-Network-Based Constrained Optimal Control Scheme for Discrete-Time Switched Nonlinear System Using Dual Heuristic Programming

In this paper, a novel iterative two-stage dual heuristic programming (DHP) is proposed to solve the optimal control problems for a class of discrete-time switched nonlinear systems subject to actuators saturation. First, a novel nonquadratic performance functional is introduced to confront control constraints of the saturating actuator. Then, the iterative two-stage DHP algorithm is developed to solve the Hamilton-Jacobi-Bellman (HJB) equation of the switched system with the saturating actuator. Moreover, the convergence and optimality of the two-stage DHP algorithm are strictly proven. To implement this algorithm efficiently, there are two neural networks used as parametric structure to approximate the costate function and the corresponding control law, respectively. Finally, simulation results are given to verify the effectiveness of the proposed algorithm. Note to Practitioners-This paper is motivated by the optimal control problem for a class of switched systems subject to actuators saturation. Actuator saturation is often encountered in practical applications due to the fact that it is usually impossible to implement unlimited control signals, and is frequently one of the main sources of instability, degradation of system performance of a control system. In addition, the traditional dynamic programming technique because of the "curse of dimensionality" cannot handled effectively the optimal control problems for switched systems. Therefore, in this paper, a new iterative two-stage DHP algorithm is proposed to deal with the optimal control problem for a class of switched systems subject to actuators saturation. This study presents the method for practitioners interested in developing optimal controller design for the switched systems subject to actuators saturation.