Optimized input-to-state stabilization of discrete-time nonlinear systems with bounded inputs

In the problem of input-to-state stabilization of nonlinear systems, synthesis of input-to-state stabilizing feedback laws is usually carried out off-line. This results in a constant input-to-state stability (ISS) gain, which is guaranteed for the closed-loop system. As an alternative, we propose a finite dimensional optimization problem that allows for the simultaneous on-line computation of an ISS control action, and minimization of the ISS gain of the closed-loop system. The advantages of the developed controller are: ISS is guaranteed for any (feasible) solution of the optimization problem, constraints can be explicitly accounted for and feedback to disturbances is provided actively, on-line. The control scheme also has favorable computational properties for nonlinear systems affine in control. In this case the optimization problem can be formulated as a single quadratic or linear program.