Using a co-operative co-evolutionary genetic algorithm to solve optimal control problems in a hysteresis system

This paper presents the use of a co-operative co-evolutionary genetic algorithm (CCGA) for solving optimal control problems in a hysteresis system. The hysteresis system is a hybrid control system which can be described by a continuous multivalued state-space representation that can switch between two possible discrete modes. The problems investigated cover the optimal control of the hysteresis system with fixed and free final state/time requirements. With the use of the Pontryagin maximum principle, the optimal control problems can be formulated as optimisation problems. In this case, the decision variables consist of the value of control signal when a switch between discrete modes occurs while the objective value is calculated from an energy cost function. The simulation results indicate that the use of the CCGA is proven to be highly efficient in terms of the minimal energy cost obtained in comparison to the results given by the searches using a standard genetic algorithm and a dynamic programming technique. This helps to confirm that the CCGA can handle complex optimal control problems by exploiting a co-evolutionary effect in an efficient manner.