Adaptive Fuzzy Control For Complex Nonlinear Strict-feedback Interconnected Systems

Because of the improvement of the scientific technology,the actual systems become more and more complicated.The traditional multiple-input multiple-output(MIMO)system models can not truly reflect the dynamic of the systems.Considering that the nonlinear interconnected systems with system uncertainties are ubiquitous,this paper investigates the adaptive fuzzy control for a class of complicated nonlinear interconnected systems.The main chapters of this paper are shown as follows:For a class of large-scale interconnected nonlinear networked control systems with input delays,firstly,a filtered error variable is defined with the integral value of the control signals,which is equivalent to tracking error and compensates the influence the input delay.Then,the analysis of tracking error can be transformed to the filtered error.Secondly,the fuzzy logic systems are used to approximate the unknown nonlinear functions in each subsystem of the large-scale interconnected systems.Then a novel adaptive fuzzy decentralized control strategy is proposed to guarantee the stability of the closed-loop nonlinear system and the boundedness of all the system variables are proved.Finally,a simulation example is given to further demonstrate the effectiveness of the proposed method.For a class of large-scale interconnected nonlinear switched systems with actuator failures,firstly,a piecewise constant function is selected as the system switching signal.Secondly,the actuator stuck failures and failed failures are compensated in the controller design process,so that the system maintains in the previous stable condition before the faults occur.Then,according to the universal approximation theorem,proper fuzzy logic systems are selected to approximate the unknown nonlinear functions in the system.A novel adaptive fuzzy backstepping fault-tolerant decentralized control strategy is proposed and the stability of the system and the boundedness of all the variables are proved according to the Lyapunov theorem.Finally,the effectiveness of the proposed method is verified by a numerical simulation example.For a class of nonlinear high-order multi-agent systems with input quantization,considering the difficulties of high orders of the nonlinear multi-agent systems and the information transmission among the subsystems and the unaccessible of the reference trajectory to some subsystems,firstly,an error variable associated with the relevant adjacency matrix is defined in the backstepping control design process and an additional adaptive parameter is introduced because of the unknown parametersin the system.At the same time,in order to reduce the control signal variation frequency and cut down the communication cost,the quantizer is introduced which is compensated in the adaptive fuzzy backstepping distributed control design process to reduce the decline of system performance.Finally,the proper positive definite Lyapunov function is chosen to prove the stability of the system and all the variables of the closed-loop system are bounded.A simulation example is given to further demonstrate the effectiveness of the proposed method.