Evolutionary Strategies for Automatic Selection of Stabilization Parameters in the Differential Game Theory

In the differential game theory, problems of minimax and maximin are resolved. In these types of approaches, the minimization or maximization of a functional is carried out, which is provided by means of the criterion of a quadratic integral whose parameters are: the coordinates of the dynamic system, the control information and the defined, positive, pondering matrices. These defined, positive matrices are obtained based on the engineer’s experience on one dynamic system in particular. It is clear that the good choice of matrices, in an enclosed set, should improve the criterion’s objective. In order to automate the choice of defined positive matrices, we propose an algorithm that uses evolutionary strategies. The important result is obtained by means of two propositions which show that the operations of crossover and mutation preserve the defined, positive properties of the matrices, thereby improving the computational complexity of said algorithm. Key-Words: Control, differential game, evolutionary strategies, crossover operation, mutation operation, stabilization.