Adaptive Event-triggered Control Of Nonlinear Discrete Systems

With the development of science and technology,more and more practical engineering systems are characterized by complexity,accuracy,large scale and strong nonlinearity.In addition,many industrial systems are often affected by irresistible uncertainties such as various environmental factors,measurement errors,component aging and external interference.Therefore,for developing modern control theory,it is necessary to study nonlinear systems with uncertainties,and there exist very important theoretical and practical significance.In addition,with the increasing dependence of human society on computer systems,digital computing has penetrated into every corner of social life,in-depth study of discrete-time systems are urgently needed.In this paper,by utilizing Backstepping method,optimization theory and other methods,considering the simultaneous existence of input dead-zone and saturation,and the unavailability of system states,two adaptive control algorithms based on event-triggered mechanism are designed for a class of single-input single-output strict-feedback nonlinear discrete-time systems,and the results are extended to a class of multiple-input multiple-output strict-feedback nonlinear discrete-time systems.The main contents are listed as follows:(1)An adaptive neural network controller based on event-triggered mechanism is designed for nonlinear discrete-time systems with input saturation and dead-zone.A function with affine structure is introduced to represent the dead-zone and saturation characteristics.The event-triggered mechanism is considered between the controller and the actuator,and between the controller and the sensor.The RBFNNs are used to approximate the unknown nonlinear functions.The Lyapunov stability theorem is used to analyze the stability of the system.The effectiveness of the algorithm is verified by a simulation example.(2)For the strict-feedback nonlinear discrete-time system,the coordinate transformation is introduced to solve the problem that the system state is not available.The action neural network and the critic neural network are used to obtain the optimal control signal and the long-term cost function,respectively.In addition,a more concise event-triggered condition is designed,and two adaptive laws of neural network weight parameters are designed based on gradient descent method and event-triggered mechanism.Finally,Lyapunov analysis theory is used to prove the stability and tracking performance of the closed-loop system,and the effectiveness of the strategy is verified by a simulation example.(3)Based on the previous two chapters,a new recursive design framework is introduced for strict-feedback nonlinear discrete-time systems with multiple-inputs and multiple-outputs,which avoids the dependence on virtual control signals in the process of controller design,and reduces the numbers of adaptive weight parameters and event-triggered conditions of each subsystem to one,thus greatly reducing the computational burden and simplifying the algorithm.RBFNNs are used to approximate the unknown nonlinear function,Lyapunov stability theorem is used to analyze the stability of the system,and the effectiveness of the algorithm is verified by simulation.