Research On Stability Of Nonlinear Systems Based On Event Triggering And Quantization

In a non-linear sampling data system,the components in the system are connected through a wired or wireless network,and the sampling value and feedback gain are also transmitted in the network.In order to ensure the stability of the controlled system,periodic sampling is widely used because of its simple design.However,in sampling data systems,periodic data sampling control will cause data redundancy,and in wireless network control systems,the network load is low means less energy consumption.The application of the event trigger mechanism makes periodic data transmission into aperiodic data transmission,which greatly reduces the amount of network data transmission.Therefore,for the non-linear data sampling system,designing an event-triggering condition that can ensure the stability of the system,a controller with better performance,and improving the operating performance of the non-linear sampling system in complex environments are urgent issues to be solved.In order to solve the above problems,we do the following research:(1)Since the signal is transmitted as a digital signal in the network,a quantizer is required to convert the sampled value to a digital signal,so that the discrete digital sampled signal can be transmitted downward through the network broadband.Due to the introduction of the quantizer,the sampled value is there must be errors in the signal before and after quantization by the quantizer.It will definitely affect the non-linear sampling system.According to the selected non-linear system model,the article selects the rule of pair quantization,and uses the sector-bounded algorithm to mathematically model the pair quantizer.The inverted pendulum system is simulated.Based on the quantization error,the system finally stabilizes.(2)Aiming at the stability of the non-linear sampling data system and considering the event-trigger mechanism,a neural network controller is designed.First,based on the selected nonlinear system model,an event-trigger mechanism was introduced,and a four-layer fullyconnected feedforward neural network controller was designed.Its weights and bias were optimized by genetic algorithms.At the same time,a cost function was introduced to determine the controller's advantages for the transmission delay in the network,a timevarying delay function model is introduced.Considering the analysis between time-delay zones,the time-delay analysis method is used to transform the analysis of the stability conditions of the neural network controller into a corresponding time-delay system analysis method.Then,by using the second stability theorem of Lyapunov-Krasovskii,the integral inequality is introduced,and the stability conditions of the nonlinear sampling data system are given.Sampling values are transmitted only when the event-trigger threshold conditions are met,reducing network information redundancy.(3)Aiming at the problem of quantization control of non-linear sampling data systems,considering the event-trigger mechanism and network data quantization mechanism,a neural network controller is designed.Considering the quantization mechanism in the signal network transmission process,the sampler monitors the non-linear system at all times.The sampled signal is detected by the event-trigger mechanism.After the threshold is met,the quantizer is quantized and passed to the controller.In order to reduce the system's conservativeness,a new piecewise Lyapunov-Krasovskii functional is selected.For the transmission delays contained in the system,a delay analysis method is used to make the transition.In combination with Jensen's inequality,the stability conditions of the nonlinear system are given.Finally,the validity of the proposed method is verified by simulation of an inverted pendulum.