Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

Abstract

This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti-windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous L2 bounded input. The system is presumed to have locally Lipschitz nonlinearities, time-varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm-bounded inputs both in the state and the output equations. Several bilinear matrix inequality-based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter-varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and L2 gain minimization. The proposed multiobjective AWC-based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time-varying parametric norm-bounded uncertainties, the asymptotic stability of the closed-loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC-based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.