Signal saturation is a common phenomenon in engineering applications and biotechnology.It often occurs when the signal input or external signal stimulus exceeds the receiver's physical limit.In recent years,as one of the important constraint problems in practical control systems,actuator saturation has attracted more and more attention.At present,the control systems considered in the papers on actuator saturation are mainly linear and mostly without time-delay.However,they are generally nonlinear and inevitably exist time-delay in signal transmission.Therefore,considering time-delay and actuator saturation in the nonlinear model has important theoretical significance and practical application valueThis paper mainly discusses the control of a class of nonlinear time-delay systems with actuator saturation.The research contents are as follows:In the first chapter,the time-delay system's and actuator saturation's research background and research situation at home and abroad are described.Then the problems that this paper studies and main innovation points are providedIn the second chapter,the relevant definitions and lemmas are introduced to provide necessary preparation for the proof of the main results.In the third chapter,the control of nonlinear discrete time-delay system with actuator saturation is studied.First of all,the saturation nonlinearity is treated by using the improved convex combination method,and a new form of discrete time invariant set related to the initial value is proposed.Secondly,with the aid of Lyapunov function and discrete Halanay-type inequality,the exponential stability of the closed-loop system are investigated,thus the set invariance conditions are obtained.Thirdly,combining with given conditions and shape reference sets,it provides an optimization method of the invariant set to estimate the domain of attraction.What's more,the mechanism of the state feedback controller is designed.In the end,two numerical simulations illustrate the validity of the relevant results.In the forth chapter,the control of nonlinear discrete time-delay system with actuator saturation and noise disturbance is further investigated.Firstly,the domain of attraction of the invariant set is defined through generalizing the relevant concept in the system without noise disturbance.Secondly,in order to deal with the control problem,the discrete Halanay-type inequality is generalized.Via utilizing some new analysis techniques,the construction of state feedback controller is proposed.It guarantees the existence of two nested invariant sets and satisfies that the larger invariant set is inside the attractive domain of the smaller invariant set.What's more,The smaller invariant set is minimized by an optimization method to better disturbance rejection.Finally,the validity of the relevant results is illustrated by a numerical simulation.In the fifth chapter,in order to save control cost and improve the efficiency of the system,the intermittent control strategy in the construction of state feedback controller is introduced.Therefore,the control of nonlinear continuous time-delay systems with actuator saturation under intermittent control is mainly studied.Firstly,by representing the saturation nonlinearity as the improved convex combination,the corresponding piecewise closed-loop system is obtained,and a new form of continuous time invariant set related to the initial value is also proposed.Secondly,on the basis of the Lyapunov function and some differential inequality techniques,the exponential stability of the system is studied,then criterions for invariant set are derived.Furthermore,by using given shape reference sets and optimizing the invariant set,an estimate of the domain of attraction is obtained.Finally,the intermittent controller is designed.It also provides a numerical simulation to verify the effectiveness of the relevant results. |