EQUIVALENCE BETWEEN NONLINEAR H-INFINITY CONTROL-PROBLEMS AND EXISTENCE OF VISCOSITY SOLUTIONS OF HAMILTON-JACOBI-ISAACS EQUATIONS

In this paper we extend to completely general nonlinear systems the re sult stating that the H-infinity suboptimal control problem is solved if and only if the corresponding Hamilton-Jacobi-lsaacs (HJI) equation has a nonnegative (super)solution. This is well known for linear syst ems, using the Riccati equation instead of the HJI equation. We do thi s using the theory of differential games and viscosity solutions.