H∞控制理论在纳什均衡动态对策问题中的应用研究

在l2范数有界不确定性扰动影响情况下，把N人线性二次纳什对策问题归结为由非合作、非零和线性二次动态对策及二人零和动态对策组成的复合对策问题；基于纳什均衡对策理论的H∞控制理论方法，给出并证明了不确定环境下纳什对策问题状态反馈解存在的条件及其求解方法；通过一个政府债务稳定问题简例，说明了算法的有效性。

Application Research of H

The N-person linear quadratic Nash dynamic game with l２ normbounded uncertainty is considered as a compound dynamic game, which is composed of non-cooperative non-zero sum linear quadratic dynamic game and two-person zero sum dynamic games. Based on Nash dynamic game theory and H∞ control theory approach, the existence conditions and designing method of state feedback solution are presented and proved. Finally, an example about government debt stabling problem illustrated the validation of this algorithm.