Optimal nonlinear-nonquadratic feedback control for systems with L 2 disturbances

We develop an optimality-based framework to address the problem of nonlinear-nonquadratic control for disturbance rejection of nonlinear systems with bounded exogenous disturbances. Specifically, using nonlinear dissipation theory with appropriate storage functions and supply rates we transform the nonlinear disturbance rejection problem into a optimal control problem by modifying a nonlinear-nonquadratic cost functional to account for the exogenous disturbances. As a consequence, the resulting solution to the modified optimal control problem guarantees disturbance reflection for nonlinear systems with bounded input disturbances. Furthermore, it is shown that the Lyapunov function guaranteeing closed-loop stability is a solution to the steady-state Hamilton-Jacobi-Bellman equation for the controlled system