Adaptive learning: robust stabilization of two-player games with unmodeled dynamics

Consider the inherent existence of unmodeled dynamics when identifying system models, it is worth investigating control to guarantee the robust stability of the systems. This paper focuses on robust control for two-player time-invariant difference game with uncertain unmodeled dynamics by using adaptive learning way. To this end, the optimization control problem for two-player linear difference games with bounded unmodeled dynamics is formulated first. Then, dynamic programming combined with game theory and adaptive critic learning are employed for the purpose of finding the stabilizing control polices, such that an adaptive learning method is developed for stabilizing the closed-loop two-player dynamics with unmodeled dynamics. The robust stabilization of the uncertain two-player game systems is rigorously proved. Simulations are given to show the effectiveness of the proposed method.