Research On Fixed Time Convergence Adaptive Control Based On Backstepping Control

With the development of modern technology,problems such as disturbance,time delay,and output constraints in the controlled system have become difficult points in analyzing nonlinear systems.Compared with the finite time,the upper bound of the convergence time of the fixed time is only related to the parameter design of the controller and not depend on the initial conditions,and the convergence time is known in advance.However,the design of fixedtime controllers is often complicated and difficult.Therefore,this paper is studied the control problems of nonlinear systems with disturbances,time delays and output constraints.The main contributions of this thesis are given as follows:(1)Based on back-stepping control strategy and Lyapunov stability theory,a composite simplified fixed-time controller is developed using a nonlinear disturbance observer-based control approach.It is worth mentioning that the fixed-time back-stepping control algorithms often suffer from singular problem caused by repeating differential of the virtual control laws.To address this problem,a smooth fixed-time back-stepping controller is constructed without using the fractional power items.By compensating the disturbance estimation into the each step of backstepping control scheme,a composite practical fixed-time controller is built,which achieve highly precise control in fixed-time convergence settings.Finally,the effectiveness of the proposed control scheme is theoretically.(2)A dynamic surface fixed-time controller based on RBF(Radial basis function)neural network is proposed for a class of strict-feedback nonlinear systems.In order to avoid the "differential explosion" of the backstepping method and the slow convergence of the tracking error of the traditional dynamic surface filter near the origin,a fixed-time controller,new filter and parameter adaptive law are designed and the stability of the system is analyzed by Lyapunov stability theory.Finally,the effectiveness of the algorithm is verified by comparative simulation.(3)A fixed-time controller based on RBF neural network is proposed for a class of adaptive tracking problems of nonlinear systems with time delays and output constraints.To deal with the time delay and output constraints,the pade and Lyapunov barrier function are used,respectively,and the design method of the virtual controller and the controller is given based on the adaptive law and fixed-time filter.It is proved that all signals of the closed-loop system are bounded and the tracking error of the system converges to a small neighborhood by using the Lyapunov stability theorem and the fixed-time control theories.Finally,simulation results are presented to verify the effectiveness of the control scheme.