ε-Suboptimal Nash Game of Discrete-Time Markov Jump Systems with Generally Bounded Transition Probabilities
This paper investigates the differential game problem for discrete-time Markov jump systems with generally bounded transition probabilities.By using the method of free-connection weighting matrix,the existence conditions of control strat-egy and the expression of the upper bound of performance index are proposed.It is proved that sufficient conditions for the existence of ε-suboptimal control strategy is equivalent to solving a set of optimization problems satisfying a set of linear matrix inequalities.Subsequently,it is deduced that the sufficient conditions for the existence of two-person and multi-person Nash equilibrium strategies are equivalent to solving optimization problem satisfying a set of bilinear matrix inequalities and linear matrix inequalities.A heuristic algorithm is given to solve them.Finally,the validity and practicability of the research results are proved by an example of economic system simulation.
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