Nash games and mixed H2/H∞ control
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The established theory of non-zero sum games is used to solve a mixed H 2/H ∞ control problem. Our idea is to use the two pay-off functions associated with a two player Nash game to represent the H 2 and H ∞ criteria separately. We treat the state feedback problem, and we find necessary and sufficient conditions for the existence of a solution. A full stability analysis is available in the infinite horizon case , and the resulting controller is a constant state feedback law which is characterised by the solution to a pair of cross-coupled Riccati differential equations.
KeywordsNash Equilibrium Riccati Equation Nash Equilibrium Strategy Nash Solution Nash Game
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