A uniqueness result for the Isaacs equation corresponding to nonlinear H infinity control

The dynamic programming equation (DPE) corresponding to nonlinear H-infinit y control is considered. When the cost grows quadratically in the state,,it is well known that there may be an infinite number of viscosity solutions to the DPE. In fact, there may be more than one classical solution when a c lassical solution exists. For the case of fixed feedback control, it is sho wn that there exists a unique viscosity solution in the class of solutions meeting a certain growth condition, and a representation in terms of availa ble storage is obtained. For the active control case, where the H-infinity problem is represented by a differential game, a similar representation res ult is obtained under the assumption of existence of a suboptimal feedback control.