A Reduced-Order Method to Design Incentive Strategy for the Discrete System with Slow and Fast Modes

When the system contains slow and fast modes, the Stackelberg game is numerically stiff and ill-conditioned. It is necessary to find some methods to alleviate this ill-conditioning and to reduce the amount of computation. In this paper, we consider the linear-quadratic infinite-time Stackelberg game for the discrete-time systems with slow and fast modes. A team-near optimal incentive strategy is constructed by solving a series of well-conditioned and reduced-order problems. Well-posedness of this near-optimal incentive strategy is investigated. By using this near-optimal incentive strategy to the full-order Stackelberg game, we can assure that the resulting value of the cost function for the leader has the same limit with the full-order team cost value as a small positive parameter ¿ tends to zero.