An Improved Particle Swarm Optimization Algorithm for Solving Impulsive Control Problem

The particle swarm optimization (PSO), a newly developed method to the optimal impulse control, is an optimized algorithm with collective intelligence. The impulsive control problem has abrupt change of system states that make the problem of finding the global optimum difficult using any usual mathematical approaches. In this paper, an improved PSO algorithm is applied to obtain optimal numerical solutions to impulsive control problem. The operation strategy of ordered variables and Boolean variables is devised in such a way that the dynamic process inherent in the basic PSO is preserved. To demonstrate its efficiency and versatility, the proposed algorithm is applied and tested in two numerical experiments. Our results indicate that PSO algorithms can effectively find good enough solutions approximate to global optimum, although the solution algorithm is a population-based search one and is not suitable for the on-line implementation in real-time problems.