Multimodel prey-predator LQ differential games

A two person prey-predator (evader-pursuit) dynamic linear quadratic game is considered. In general, this problem belongs to the class of non-zero sum dynamic games. An original dynamic linear time varying system with additive disturbances or uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external bounded disturbances. Each model from a given finite set is characterized by a quadratic performance index. The developed minimax LG control strategy provides a Nash equilibrium in the given mini-max differential game. This problem is shown to be reduced to finding of a Nash equilibrium point in a finite dimensional simplex.