Particle swarm optimization for time-optimal control design

Abstract

In this paper, a particle swarm optimization (PSO) based method is proposed to obtain the time-optimal bang-bang control law for both linear and nonlinear systems. By introducing a penalty function, the method can be modified to deal with systems with constraints. Compared with existing computational methods, the proposed method can be implemented in a straightforward manner. The convergent solutions can be achieved by selecting suitable PSO parameters regardless of the initial guess of the switching times. A double integrator and a third-order nonlinear system are used to demonstrate the effectiveness and robustness of the proposed method. The method is applied to obtain the time-optimal control law for a high performance linear motion positioning system. The results show the practicality of the proposed algorithm.