Construction of Approximate Saddle-Point Strategies for Differential Games in a Hilbert Space

Two-person zero-sum infinite-dimensional differential games with strategies and payoff as in Berkovitz (SIAM J. Control Optim. 23: 173–196, 1985) are studied. Using Yosida type approximations of the infinitesimal generator (of the unbounded dynamics) by bounded linear operators, we prove convergence theorems for the approximate value functions. This is used to construct approximate saddle-point strategies in feedback form. A.J. Shaiju: NBHM Postdoctoral Fellow and the financial support from NBHM is gratefully acknowledged.