Enlargement And Application Of The Region Of Attraction Of Nonlinear System Based On Edge Impulsive Control

In recent years,the researches focus of impulsive control system is gradually shift-ing from fixed time impulsive control system to state-dependent impulsive control system.Among them,the stability analysis of the system is the most fundamental problem in non-linear system theory,and when a nonlinear system has a local equilibrium or has multiple equilibria,it is necessary to study the region of attraction of its local stable equilibria.In addition,the actuator saturation phenomenon is widely present in practical engineering systems,which brings difficulties to the design and stability analysis of control systems.Therefore,in this paper,based on the existing research on state-dependent impulse con-trol,a state-dependent edge impulse control mechanism is proposed to realize the expan-sion of the region of attraction of the local stable equilibrium point of a nonlinear system and the expansion of the local synchronous region of attraction of a nonlinear multi-agent system with actuator saturation,respectively.The main contributions of this paper are as follows:(1)The local stability and expansion of region of attraction of a class of nonlinear systems with multiple equilibria is investigated.There are many studies on the estima-tion of the region of attraction in the previous literature,but there are few studies on its enlargment.In this paper,a state-dependent edge impulsive control is proposed,and the estimation and enlargment of the region of attraction of this equilibrium point can be achieved by incorporating the state-dependent edge impulsive control,combined with the sum-of-squares technique and trajectory reversing.This impulse control mechanism can be implemented to design the final desired region of attraction size according to the actual requirements,and the impulsive control makes the estimation of the region of at-traction expand to the desired size.Finally,the effectiveness of the state-dependent edge impulsive control mechanism is illustrated by three examples of nonlinear systems.(2)The local synchronization problem of nonlinear multi-agent systems with actua-tor saturation is studied.There have been numerous studies on global synchronization of linear multi-agent systems,but few on local synchronization of nonlinear multi-agent sys-tems with actuator saturation.This paper proposes a hybrid control of continuous control and impulsive control to achieve local synchronization of the system,where the hybrid control input includes sampled state-dependent impulsive control and piecewise continu-ous control,which realize the local synchronization of nonlinear multi-agent with actuator saturation and obtains its local synchronous region of attraction.The synchronous region of attraction is defined as the set of the maximum difference between the initial state of the agent that can follow the leader to converge to the target trajectory and the initial state of the leader.Finally,paper uses state-dependent edge impulsive control with actuator saturation to enlarge the local synchronous region of attraction.