Designing an optimal control law for nonlinear system by using intelligent algorithm

Abstract

The Purpose of this paper is based on Inverse Optimal Control method. There are two methods for designing optimal control stabilizer In order To minimize the presented cost function for any nonlinear systems, (Direct method and Inverse method). In direct method, in order to solve the optimization problem, HJB equation must be solved, in which there is no exist exact feasible mathematical techniques for solving Hamilton-Jacobi-Bellman equation, while in inverse method, by considering Control Lyapunov Function and an obtained feedback control law, a cost function will be designed so that the presented control law will be optimal for designed cost function. In this paper a new approach is presented so that there will be no need to solve the Hamilton-Jacobi-Bellman equation and the suboptimal controller will be designed without numerical method. In this approach, by using Inverse Optimal Control method and determining cost function for the system, Control Lyapunov Function and suboptimal control law are designed simultaneously in which the Control Lyapunov Function will be designed by intelligent algorithm such as PSO algorithm and GA separately. To analyze the optimal level of designed controller and Control Lyapunov Function, different performance criteria will be used. In this method any structure of Control Lyapunov Function could be considered.