Adaptive Neural Network Control For Several Types Of Constrained Uncertain Nonsmooth Nonlinear System

In practical engineering fields and applied sciences,the nonsmooth nonlinear system(e.g.the stick-slip vibration system,the collision vibration system and electrical power system)which described by the nonsmooth function with right-hand discontinuity as a part of the nonlinear system has witnessed growing attention.In order to ensure the normal operation of the system,system output or system states are subject to different constraints in many industrial processes.Output constraint or state constraints can reduce the damage of industrial equipment and affect control system’s performance.Therefore,it is necessary to consider the nonlinear system with constraints during the control design process.In conclusion,how to deal with the nonlinear system with constraints is a hot topic which motivates us to the present study.In this paper,we consider the problems of uncertain nonsmooth nonlinear systems with state constraints,output constraint,adaptive funnel control and event-triggered mechanism control.The main research results are as follows:1.Output feedback adaptive neural network control for uncertain nonsmooth nonlinear systems with input deadzone and saturationThis paper considers the output feedback adaptive neural network control problem for nonsmooth nonlinear systems with input deadzone and saturation.First,the nonsmooth input deadzone and saturation is converted to a smooth function of affine form with bounded estimation error by means of the mean-value theorem.Second,with the help of approximation theorem and the Filippov’s differential inclusion theory,the given nonsmooth system is converted to an equivalent smooth system model.Then,by introducing a proper logarithmic barrier Lyapunov function,an output feedback adaptive neural network controller is set up by constructing an appropriate observer and adopting the adaptive backstepping technique.New stability criterion is established to guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded.Finally,the circuit system model is offered to verify the effectiveness of the proposed control algorithm.2.Command filter based adaptive neural network tracking control for uncertain nonsmooth nonlinear systems with output constraintThis paper investigates the command filter based adaptive neural network tracking control problem for uncertain nonsmooth nonlinear systems.First,an integral barrier Lyapunov function is introduced to deal with the symmetric output constraint and make the output comply with prescribed restrictions.Second,by the Filippov’s differential inclusion theory and approximation theorem,the considered nonsmooth nonlinear system is converted to an equivalent smooth nonlinear system.Third,the Levant’s differentiator is used to deal with the “explosion of complexity”problem.An error compensation mechanism is established to attenuate the effect of the filtering error on control performance.Then,an adaptive neural network controller is set up by resorting to the backstepping technique.It is strictly mathematically proved that the tracking error can converge to an arbitrarily small neighborhood of the origin and all the signals in the closed-loop system are semi-globally uniformly ultimately bounded.Finally,a numerical example and an application example of the robotic manipulator system are provided to demonstrate the availability of the proposed control strategy.3.Adaptive neural network output feedback control for uncertain nonsmooth nonlinear systems with network communication constraintsThis paper investigates adaptive funnel output feedback event-triggered control problem for uncertain nonsmooth nonlinear systems.First,adaptive funnel function is designed to ensure that the tracking error converges to the predefined funnel boundary,which improves the transient and steady-state performance.Second,by the Filippov’s differential inclusion theory and approximation theorem,the considered nonsmooth nonlinear system is converted to an equivalent smooth nonlinear system.Third,the observer is used to handle the unmeasurable system states,the neural network is utilized to approximate the unknown nonlinear function,and a novel event-triggered mechanism is designed to alleviate the computational burden.The proposed adaptive neural network output feedback controller ensures that all the signals of the closed-loop system are bounded.Finally,a example of the circuit system is used to verify the effectiveness of the proposed control strategy.