Optimal Control of Switched Linear Systems by Particle Swarm Optimization

AbstractThis paper deals with Optimal Control problems of Dynamical Switched Linear Systems (OCPDSLS). This special class of hybrid systems combines the standard control, where dynamic subsystems are described by differential linear equations with a switching law which activates, alternatively, these subsystems. For a pre-specified modal sequence, we demonstrate that switching time instants and continuous input can be solved simultaneously by using an evolutionary computation technique, namely Particle Swarm Optimization (PSO). Some structural and numerical difficulties encountered in solving such problems by conventional approaches are discussed. The mapping between PSO and OCPDSLS is established via a generic procedure to synthesize optimal control laws. An illustrative numerical non-convex example is solved showing the effectiveness of the proposed technique in overcoming difficulties of this problem known to be NP-hard, non-linear and constrained one.