Output Feedback Control For A Class Of Nonlinear Systems With Unknown Growth Rate

In actual engineering systems,there often exist disturbance factors such as unknown parameters and time-varying delays.These factors inevitably affect the control effect of the system.How to design an output feedback controller for such systems is worth studying.Based on the homogeneous system theory,Lyapunov stability theory,the dynamic scaling gain method and adding a power integrator technique,the aim of this paper is to investigate the output feedback control problem for the nonlinear systems with unknown homogeneous growth rate.The main research work of this paper is summarized as follows1.For the nonlinear systems with time-varying delay,the global output feedback control problem is studied.Because the nonlinear terms satisfy the upper triangular homogeneous growth condition with its growth rate unknown,two dynamic gains are introduced into the system.By using adding a power integrator technique,an adaptive output feedback controller is constructed.Based on the homogeneous system theory,the appropriate update rates are selected for the dynamic gain.By using the Lyapunov-Krasovskii functional and Barbalat lemma,it is proved that all signals of the closed-loop system are bounded and the state of the system converges to the origin asymptotically.The result is further extended to the lower-triangular nonlinear systems with time-varying delay.The simulation experiment of the cascade reactor validates the effectiveness of the designed controller.2.For the nonlinear time-delay systems with unknown output functions,the global adaptive output feedback control problem is studied.Based on the dynamic gain technique,a fullorder observer which is not directly related to the output signal is designed to estimate the unknown states of the system.Based on adding a power integrator technique,an output feedback controller with dynamic gain is constructed.And a proper update rate is selected for the dynamic gain by the homogeneous system theory.At last,combined with the Lyapunov-Krasovskii functional,it can be proved that all states of the closed-loop system can converge to the origin under the designed controller.Numerical simulation experiments verify the effectiveness of the proposed control method.3.For the nonlinear systems with unknown growth rate,the global stabilization problem is studied.Based on adding a power integrator technique and the dynamic gain method,an adaptive state feedback controller is designed.Since the nonlinearities of the system have highorder terms and low-order terms,a dual-observer is constructed to estimate the states of the system,and then,the output feedback controller of the system is constructed.By using the Barbalat lemma and Lyapunov stability theory,it is proved that the closed-loop system is globally asymptotically stable.The simulation results can illustrate the effectiveness of the proposed adaptive output feedback controller.