Fixed-time Fuzzy Adaptive Tracking Control For A Class Of Nonlinear Systems

With the rapid development of the system control theory,the actual controlled system becomes complex.The system parameters brought by measuring instruments are difficult to obtain accurately,which results in uncertainties and nonlinear features of the system.Recently,the control problem of nonlinear systems has attracted scholars' attention because of its widespread application in practice.Unlike the asymptotic stability,the finite-time stability has higher tracking performance.One defect is that the convergrnce time of the system needs to know the value of the initial state in advance.However,the initial states of many systems are difficult to obtain ahead of time in real-world,which makes it hard to obtain the approximate value of the settling time.The fixed-time control scheme has a remarkable characteristic that the settling time is unrelated to the initial conditions and depends on the design parameters.As a consequence,the fixed-time tracking control of nonlinear systems has important research value.In this paper,the fixed-time fuzzy adaptive tracking control problem is further researched for a category of uncertain strict-feedback nonlinear systems.The main work is summarized as follows:Firstly,for strict feedback systems subject to the unmeasurable states,external disturbances as well as unknown nonlinear functions,the tracking control issue is investigated.The fuzzy state observer and the disturbance observer are co-designed to estimate the unavailable states and the compounded disturbances.Moreover,the first-order filter is introduced into the backstepping design,and the complex differential operation is transformed into a simple algebraic operation.The model of the output feedback controller is developed,which can insure the fixed-time stability of the closed-loop system,and make the trajectory of the tracking error fluctuate in a particularly small neighborhood of the origin.In the end,the numerical example as well as the simulation example of the pendulum system are utilized to verify the feasibility of the devised controller.Secondly,for strict feedback systems subject to the unknown nonlinear functions,full-state constraints,external disturbances and unknown virtual control coefficients,the tracking control issue is considered.Furthermore,the issue of the unknown virtual control coefficient is solved through the barrier Lyapunov function with the reciprocal of the lower bound of the unknown virtual control coefficient,and the requirement of the full-state constraints is satisfied.Base on the criterion of the practically fixed-time stable,the fuzzy adaptive controller is devised,and the ideal tracking effect is obtained.Lastly,the simulation example of the single-link robot manipulator system as well as the numerical example are utilized to confirm the effectiveness of the developed control scheme.