chapter  7
30 Pages

Adaptive Reliable Control with Actuator Saturation

Control systems with actuator saturation are often encountered in practice. When actuator saturation occurs, in general global stability of an otherwise stable linear closed-loop system cannot be ensured. And the problem of estimating the domain of attraction for a system with a saturated linear feedback has been studied by many researchers in the last few years and various methods have appeared (see, [24, 140]). Model predictive control (MPC) is an effective control algorithm for dealing with actuator saturation. Many formulations have been developed for the stability of MPC (see, [18, 96]). Enlargement of the domain of attraction is achieved in [20, 28, 85, 90]. Anti-windup has been largely discussed and many constructive design algorithms have been formally proved to induce suitable stability properties (see, [25, 26, 27, 48, 68, 143]). Many of these constructive approaches rely on sector condition and S-procedure techniques and provide LMIs for the anti-windup compensator design. In some papers, notion of invariant set and LMI-based optimization approaches were proposed to estimate the stability regions by using quadratic Lyapunov functions and the Lur’e-type Lyapunov functions. In [17] and [142], the modeling of the nonlinear behavior of the system under saturation is made by using a polytopic differential inclusion and quadratic Lyapunov functions. For determining if a given ellipsoid is contractively invariant, [66] described a condition which is based on the circle criterion or the vertex analysis.