Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

This paper investigates the Pareto optimal strategy of discrete-time stochastic systems under H infinity constraint, in which the weighting matrices of the weighted sum cost function can be indefinite. Combining the H infinity control theory with the indefinite LQ control theory, the generalized difference Riccati equations (GDREs) are obtained. By means of the solution of the GDREs, the Pareto optimal strategy with H infinity constraint is derived, and the necessary and sufficient conditions for the existence of the strategy are presented. Then the Pareto optimal solution under the worst-case disturbance is solved. Finally, the efficiency of the obtained results is illustrated by a numerical example.