Stability Analysis And Adaptive Control Of Double Switching System

The dual switching system is a class of switching systems consisting of deterministic switching subsystems,stochastic switching subsystems,and a switching signal that specifies the active subsystem.The switching signal has two types in the dual switching system.One is the deterministic switching signal,specifying the operation of the deterministic switching subsystem,and it can be designed and controlled.The other one is stochastic switching signal,which is affected by the characteristics of the stochastic subsystems and is usually undesignable.In this paper,the Markov stochastic process is used to describe the stochastic switching subsystem,and then the stochastic switching signal is determined by its transfer rate and is randomly uncontrollable.Since its introduction,the dual switching system has been applied to systems with complex switching mechanisms,such as wind turbine systems,network control systems,and epidemic infection models.With the development of the fourth-generation industrial revolution,society has become more control demanding for complex systems,so new control methods are needed for the dual switching nonlinear system containing uncertainty,time delay and other problems.After summarizing the domestic and foreign research on dual switching systems,we study the stability theory of switching control systems in depth.Combining Backstepping technology,neural network algorithm,adaptive control theory,preset performance control theory,and other theories,we try to apply the control theory of switching system innovatively to the dual switching nonlinear system,broaden the control stability theory of dual switching system,and bring new graphical ideas and methods for the modeling and control of the actual complex application system.The research results of this paper for dual-switching nonlinear systems are summarized as follows.1.The stability problem of a class of dual switching continuous-time nonlinear systems is studied.Firstly,its stochastic subsystems are described by a Markov stochastic jump process.The different transfer rates between different subsystems will lead to the loss of the ergodicity of the modes,which makes the analysis very difficult.We first use the probabilistic analysis method and the large number law to solve the problem of modal ergodicity no longer.Then two types of deterministic switching signals are designed by using the energy expectation minimum switching method and the energy expectation error maximum speed method,respectively.Finally,the globally asymptotic stability almost everywhere and exponential stability almost everywhere of the dual switching continuous-time nonlinear system under the two types of signals are investigated by using stochastic multiple Lyapunov functions and sufficient conditions for the stability of the system are given.Finally,the validity of the proposed method is verified by three numerical examples.The global asymptotic stability almost surely(GAS a.s.)and the almost surely exponential stability(ES a.s.)are compared,and the system convergence rates at different switching signals are analyzed.2.Dual switching system is a special hybrid system that contains both deterministic and stochastic switching subsystems.Due to its complex switching mechanism,few studies have been conducted for dual switching systems,especially for systems with uncertainty.Usually,the stochastic subsystems are described as Markov jump systems.Based upon the upstanding identity of RBF neural network on approaching nonlinear data,the tracking models for uncertain subsystems are constructed and the neural network adaptive controller is designed.The global asymptotic stability almost surely(GAS a.s.)and almost surely exponential stability(ES a.s.)of dual switching nonlinear error systems are investigated by using the energy attenuation theory and Lyapunov function method.An uncertain dual switching system with two subsystems,each with two modes,is studied.The uncertain functions of the subsystems are approximated well,and the approximation error is controlled to be below 0.05.Under the control of the designed adaptive controller and switching rules,the error system can obtain a good convergence rate.The tracking error is quite small compared with the original uncertain dual switching system.3.Considering a class of dual switching continuous-time nonlinear systems with both uncertainty and time delay,we study its adaptive neural network preconditioned performance control problem.First,the error function is constructed based on the prescribed performance control theory,and a formal transformation is performed by homogeneous mapping to convert the error space from the constrained space to the unconstrained space.Then the Backstepping technique and neural network algorithm are combined to design the controller and adaptive law.Finally,a sufficient condition for the semi-globally uniformly bounded of the system is given using the stochastic multi-Lyapunov stability method.Under the joint action of the designed switching signals and the controller,all signals in the closed-loop system are bounded,and the system states satisfy both steady-state and transient performance at the switching moments.Finally,the validity of the scheme is verified by numerical algorithm simulation,and the experimental data show that the error of the system is always within the performance boundary function and achieves the prescribed performance.4.The modeling method,stability analysis theory and the adaptive control method of the dual switching continuous-time nonlinear system are applied to the multi-loop network control systems.Consider a class of multi-loop network control systems with packet loss in communication networks and uncertain functions in the system equations;model them using the theory of dual switching nonlinear systems.Then,use the RBF neural network algorithm to approximate the unknown functions in the system,construct the error dynamic equations,and design the switching strategy according to the expected error minimization criterion,so as to ensure that the controller of NCS selects the appropriate device to operate to realize the adaptive control of the system.Finally,the effectiveness of the method is verified through application case experiments to ensure that the multi-loop network control system has a good performance.