A Performance-Based Model Recovery Anti-Windup Design for Linear Systems Subject to Actuator Saturation

In this paper, we investigate the problem of reference tracking for a class of linear systems subject to actuator saturation and propose a performance-based model recovery anti-windup strategy. We adopt the classic model recovery anti-windup framework and regard the states or one of the outputs of the anti-windup compensator as the tracking error, by which the difference between the unconstrained system and the saturated system is quantified. Then, instead of employing the commonly used
$\mathcal{L}_{2}$
gain, we present the prescribed performance functions (PPFs) to characterize the real-time tracking error such that the system performance can be captured more specifically. In particular, to avoid singular issues arising from the occurrence of saturation, we modify the existing PPFs with an auxiliary system when saturation occurs. Based on these modified performance functions, we follow a modified prescribed performance control approach and design the remaining output of the anti-windup compensator. Such a design procedure is constructive, making it more promising for extension to nonlinear systems. Theoretical results establish the boundedness of all signals in the closed-loop system. Simulation results verify the effectiveness of our design strategy.