Output Feedback Control For A Class Of Uncertain Nonlinear Time-delay Systems

Nonlinearities,uncertain parameters and time-delay are main factors,which affect systems' performance in practical control systems.Hence,it is of great significance to investigate the problem of output-feedback for uncertain nonlinear time-delay systems from both theoretical and engineering application.Based on the Lyapunov stability theory and homogenous theory,by adopting adding a power integrator technique,dynamic gain method and homogenous domain approach,this paper considers the problems of global output-feedback,adaptive output-feedback control for several class of uncertain nonlinear time-delay systems.The main contents are concluded as follows:(1)The problem of global output-feedback for a class of nonlinear time-delay systems with unknown output function.The nonlinearities satisfy the lower-triangular homogenous growth condition.A full-order observer is constructed without requiring precise information of the output function,and an output-feedback controller is designed using adding a power integrator technique.Based on homogenous domain approach,a scaling gain is introduced into the controller and observer.By constructing appropriate Lyapunov-Krasovskill functional and scaling gain,the output-feedback controller can render the closed-loop system globally asymptotically stable.Finally,the results are extended to a class of uncertain feedforward nonlinear systems,whose nonlinearities satisfy the upper-triangular homogenous growth condition.The simulation results demonstrate the effectiveness of the proposed control scheme.(2)The problem of global output-feedback for a class of uncertain nonlinear time-delay systems is investigated in this paper.The nonlinearities of the systems are bounded by both low-order and high-order terms.First,for the nominal system,a state-feedback controller is designed using adding a power integrator technique.Two individual homogeneous observers are implemented together to handle the high-order and low-order nonlinearities.Then,an output-feedback controller is developed using the states of observers.For the transformed system,an appropriate Lyapunov-Krasovskill functional and scaling gain is chosen to render the closed-loop system globally asymptotically stable.Finally,the results are extended to the systems whose nonlinearities are assumed to satisfy feedforward homogenous growth condition.The proposed control scheme is applied to a class of control systems with time-delay feedback.The effectiveness of the proposed design procedure is illustrated by numerical simulation.(3)With respect to a class of nonlinear time-delay systems,whose nonlinearities are assumed to satisfy homogenous growth condition with unknown growth rate.Based on dynamic scaling gain method,an observer with two dynamic gains is constructed.First,an output-feedback controller is designed using adding a power integrator technique.Then,the adaptive laws are developed for the gains via homogenous domain approach and homogenous theory.Finally,by picking appropriate Lyapunov-Krasovskill functional together with Barbalat's lemma,it is proved that all the signals of the closed-loop system are bounded and the system's states globally converge to the equilibrium point.The simulation results illustrate the effectiveness of the proposed control scheme.