Optimizing shifted stabilizers with asymmetric input saturation

We develop a controller design for linear systems subject to asymmetric actuator saturation that maximizes the estimate of the region of attraction of the corresponding closed-loop system. Stabilization is achieved by stabilizing shifted equilibria selected via the solution of an optimization problem enjoying desirable asymptotic properties. To enable the computational time required by these optimizers, we impose sampled-data updates of these equilibria and cast our description within a hybrid dynamical systems formulation. We provide two feedback solutions using exact and inexact optimization algorithms, thus establishing interesting interplays between continuous-time dynamics and iterative discrete-time parametric optimization schemes. Enlarged estimates of the region of attraction and the real-time applicability of the control law are illustrated on numerical examples