Adaptive Neural Network Control For Non-strict Feedback Switching Systems

A switching system is a hybrid system consisting of a series of continuous or discrete subsystems and a rule that coordinates the switching between these subsystems.In recent years,especially in the field of adaptation,switching between different controllers has been widely used.In the mechanical control,automation industry,aerospace control,power switching systems and other areas,switching systems are increasingly widely used.In this paper,we study the problem of a class of single-input single-output nonlinear switching systems,and the control system has a non-strictly feedback form.To control non-linear systems with non-strict feedback systems has always been a challenging task,and such systems have high coupling.Because of the special properties of such system,the general control method is difficult to apply directly to this class system,resulting in difficult to obtain accurate system equations,exacerbated the difficulty of system analysis and control.The adaptive neural network control method is used to approximate the nonlinear function of the system.Under the condition of not knowing the exact function of the system,it can be analyzed by designing the adaptive feedback controller so that the output signal of the system can track the given reference signal.The second chapter of this paper gives some basic knowledge of the research,in section 2.1 introduced the characteristic of the neural network system,and what kind of tasks that can apply neural network system.In Section 2.2,the concept of switching system stability under the Lyapunov theory is introduced.Compared with the general non-switching system,the analysis and control of the switching system has more possibilities and higher complexity.Therefore,the switching system's control and analysis also has a higher degree of difficulty.In this paper,we introduce a basic characteristic of neural network system.In this paper,we use this characteristic to extend the unknown nonlinear system from strict feedback to non-strict feedback system.In the third chapter,we study a nonlinear switching system with a single input single output form.The model is described in 3.1,the neural network system is used to replace the unknown nonlinear function.The adaptive feedback controller is designed to keep the unknown uncertain system to track the given reference signal.In section 3.2,the appropriate parameters and center points are selected,applying neural network system to approximate the target model described in 3.1.In Section 3.3,based on the Lyapunov theory,the appropriate Lyapunov equation is chosen to analyze the system,and the adaptive feedback controller is designed to stabilize the system.Since the switching system has multiple subsystems,when the switching signal is switched between multiple subsystems,the stability of the system is uncertain.In this section,a common Lyapunov equation is chosen to ensure the stability when switching between the different subsystems.Section 3.4 analyzes the stability of the designed observer,it shows that under the controller's effect,all the signals converge to a small origin.In section 3.5,the example simulation shows the effectiveness of the designed controller.In the practical project,most of the system state can not be measured directly,so the designed controller in Chapter 3 can not be directly applied to the practical project.In the fourth chapter of this paper,we design a fuzzy observer system on the foundation of the third chapter,and use the observed state to design the controller,aiming at tracking the given target.In section 4.2,compared to linear controllers,the designed non-linear observer has a wider applicability.In this section,the stability of the observer is determined using the properties of the convex combination.Section 4.3 is mainly talking about the control and design of the system.Unlike the approach in Chapter 3,we choose a common Lyapunov function.In this section,different subsystems select different Lyapunov functions and reduce the common Lyapunov function restraints.The stability of the switching system under any switching signal is analyzed by the average time method.In section 4.3-4.4,the stability of the system under designed controller is analyzed.In 4.5,the simulation results show that the designed adaptive controller can track the given signal well and has good performance.The fifth chapter of this paper,briefly introduces the contribution of this work,the second part of this chapter discuss the limitations of this study and the problems to be solved in the future.