Differential Games and Nonlinear ${\Cal H}_\infty$ Control in Infinite Dimensions

Research Report MRR97-020

Differential Games and Nonlinear ${\Cal H}_\infty$ Control in Infinite Dimensions

Maciej Kocan and Pierpaolo Soravia

Abstract: This paper studies the ${\Cal H}_\infty$ control problem for a nonlinear, unbounded, infinite dimensional system with state constraints. We characterize the solvability of the problem by means of a Hamilton-Jacobi-Isaacs equation, proving that the ${\Cal H}_\infty$ problem can be solved if and only if the HJI equation has a nonnegative viscosity supersolution, vanishing at the origin.

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