ON A STATE-SPACE APPROACH TO NONLINEAR H-INFINITY CONTROL

We study the standard H-infinity optimal control problem using state feedback for smooth nonlinear control systems. The main theorem obtained roughly states that the L2-induced norm (from disturbances to inputs and outputs) can be made smaller than a constant gamma > 0 if the corresponding H-infinity norm for the system linearized at the equilibrium can be made smaller than gamma by linear state feedback. Necessary and sufficient conditions for the latter problem are by now well-known, e.g. from the state space approach to linear H-infinity optimal control. Our approach to the nonlinear H-infinity optimal control problem generalizes the state space approach to the linear H-infinity problem by replacing the Hamiltonian matrix and corresponding Riccati equation as used in the linear context by a Hamiltonian vector field together with a Hamilton-Jacobi equation corresponding to its stable invariant manifold.