Saturated Impulsive Control For Several Classes Of Nonlinear Systems

In the practical engineering,the controlled system is often subject to nonlinear input,which can cause a lot of trouble for the system's controller design and stability analysis.Saturation is a common constraint phenomenon.In practical engineering,state variables are often affected by the control system itself or the external environment.This control system of the state or input of the system state itself is generally referred to as the state saturation control system.The impulsive model is a typical hybrid system,it is the mathematical modeling of the widespread mutation phenomenon.Meanwhile,the impulsive control system has gained the attention of researchers,because it solves some problems that cannot be solved by continuous control system.In this paper,we study the saturated input problem of nonlinear hybrid dynamical systems.The main research is divided into the following aspects:Firstly,we consider the stability of a class of saturated state dependent impulsive differential equations.The impulsive behavior is limited to a range,not the linear hypothesis in some existing literature,but a bounded impulsive dynamic behavior.First of all,the existence of solution for the system and some sufficient conditions which can be guaranteed every solution intersecting each impulsive surface exactly once are derived.Some sufficient conditions for the dynamic network exponential synchronization are given.Meanwhile,several examples with simulations are given to validate the effectiveness of the proposed criteria.Secondly,the stability of a class of boundary constraint impulsive systems is considered,where the state of the system is limited to a reasonable region,and the impulse occurs at the boundary of the region,which means that the impulse is triggered when the state reaches the boundary.Through the method of constructing the appropriate barrier Lyapunov function,the sufficient condition which guarantees the robust stability of the closed system is given.Thirdly,we propose the problem of impulsive input saturation for the delayed systems.The problem of exponential stability via the constrained impulsive control is studied.Different from the traditional impulsive feedback control,the saturation phenomenon of impulsive control actuator is considered in this paper.By using the convex analysis,matrix measure theory,inequality and so on,the criteria of exponential stability for the autonomous systems with time delays are given by introducing the auxiliary matrix.Fourthly,the exponential stabilization problem of the dynamic system with time delays is studied by using state constraint impulsive control.The two types of constraint impulsive controller are designed: the full state constraint and the partial state constraint controller.Combined with the technique of convex analysis,mathematical induction,matrix measure theory and so on,some rules of exponential stabilization are given to guarantee the dynamical system of the variable structure dynamical systems.Fifthly,the problem of delayed-impulsive input saturation of discrete time systems is studied.Different from the general impulsive control design,the delay is considered in the design of saturated impulsive controller.The theoretical model is more in line with the practical system modeling.Through Lyapunov theory,the problem of delayed impulsive control with actuator saturation and the synchronization application of coupled system are studied.