Control And Anti-Windup Design For Linear Systems Subject To Actuator Saturation

Due to factors such as safety requirements and physical structure limitations,actuator saturation is unavoidable in many practical systems.Actuator saturation causes that output signals of a controller are inconsistent with the input signal of the plant,which may cause performance degradation and even instability of the closed-loop systems.The saturated close-loop system is essentially a nonlinear system,which makes the stabilization problem much more complicated.At the same time,time delay introduced by the system itself or the control device,naturally appears in various practical situations,and large delays may also cause instability of the closed-loop systems.Recently,scholars in the field of control research are mainly focused on the actuator saturation in a single system.However,in the study of linear multi-agent systems with actuator saturation,the output feedback control and anti-windup compensator design are still conservative.This thesis mainly studies the gain-scheduling control design for linear time-delay systems and the anti-windup design for linear multi-agent systems.The main contents of this thesis are given as follows:We firstly focus on the problem of robust control of linear differential systems subject to actuator saturation.A novel continuous set of nonlinear controllers is constructed by a parameterdependent composite Lyapunov function.Compared with methods based on the quadratic Lyapunov function,a set of robustness conditions with less conservativeness are obtained.The control gain is selected according to the system state,to ensure that the closed-loop system is input to the state stable(ISS),and to reduce the system peak-to-peak(PP)performance.In addition,the parameter-dependent controller gain is solved by combining the linear spline method and the path-following method.As for state-delay linear sy stems with actuator saturation,we construct a family of continuous controllers based on a parameter-dependent Lyapunov-Krasovskii functional.The controller with the best performance is selected,at each time,based on the closed-loop state vector,while complying with the saturation bound,and the resulting closed-loop system is locally ISS with reduced PP performance.Subsequently,we consider a stabilization problem for linear systems subject to saturation and time-varying delay in the control input.Based on the delay values,the considered system is described by a switched system including a stabilizable subsystem and an unstabilizable subsystem.A time-dependent switching rule orchestrating the proposed controllers is established to guarantee the regional stability of the closed-loop system.Compared with the existing results on time-delay systems with constrained inputs,the benefit of the proposed methods obtains a larger delay size and a larger estimate of the domain of attraction.It should be mentioned that the above controller designs have been considering the effect of actuator saturation from beginning to end,which is mainly focused on designing controllers to avoid saturation,or representing the saturated function as a convex hull of linear functions via auxiliary matrices.Another effective approach to deal with saturation is the so-called antiwindup design.An anti-windup protection loop relies on a high performance nominal controller and is activated to guarantee stability and performance only when saturation appears.In multiagent systems(MASs),dynamic output control and even anti-windup designs are more complicated than a single system due to the communication exchange among followers.Finally,we investigate the leader-follower tracking problem and containment problem of linear MASs with input saturation.The problems are solved by designing distributed general output feedback controls and anti-windup compensation.For the case that the control inputs of the leaders are non-zero and time-varying,we treat the leaders' inputs as external disturbances.The containment problem is solved by minimizing the PP gain,from the leaders' inputs to the tracking error.Next,a static anti-windup loop is applied to each follower's compensator to ensure stability and performance in the presence of actuator saturation.The control gains and anti-windup gains are given by linear matrix inequalities.