Switched system optimal control based on dynamical programming principle and evolutional computation

The optimal control problem of the switched system which subsystem is discrete linear system is investigated. At the condition of the given switched number and the quadratic performance function, the multi-periods decision-making problem can be transformed into single decision-making problem, then the analytic solution of the switched discrete system optimal control problem can be obtained globally. The searching procedure for the switched instant and sequence to minimise the performance function by genetic algorithm is presented. A numerical example illustrates the effectiveness of the design approach. The simulation shows that the approach can resolve a kind of switched discrete optimal control problem.