Study On The Control Problem Of Uncertain Nonlinear Systems With State Dela

In recent years,with the rapid development of science and technology and the acceleration of industrialization,the precision of instruments required by production and life is increasingly high.Simple linear models can no longer meet the modeling requirements of complex industrial systems,and nonlinear models have become the mainstream of current research.Since the unknown nonlinear function,unknown time-varying delay and unknown disturbance exist in real systems,which may lead to system performance degradation and even destroy the system stability,it is of great significance to solve various control problems of uncertain nonlinear time-delay systems.In this paper,the control problem of a class of nonlinear time-delay systems is studied.Combining Backstepping approach,adaptive control,Lyapunov-Krasovskii functional,neural network approximation theory,dynamic and static gain function and other theories and design tools,a series of control schemes are designed for uncertain nonlinear systems with unknown state delays,unknown nonlinear functions and other uncertainties based on the existing research results.The specific research contents are summarized as follows:1)The global stabilization of a class of nonlinear strict-feedback systems is studied by using adaptive parameter estimation method and Backstepping technique.With the help of a sufficiently smooth projection operator,the virtual control law-related static gain functions are established to counteract the influence of the unmeasurable system states with unknown time delays.New Lyapunov-Krasovskii functionals with static gain function are designed in each step of the Backstepping process,and a memoryless state feedback control scheme is proposed,such that all signals of nonlinear time-delay systems are globally uniformly ultimately bounded(GUUB).2)The problem of output feedback control design for a class of strict-feedback nonlinear systems with unknown state time delays is studied.Two output feedback control schemes based on full-order and reduced-order observers are considered respectively.The system is divided into two parts according to the order of the state matrix and the coordinate transformation.The introduction of static gain avoids solving LMI inequality.Lyapunov-Krasovskii functional with static gain is designed to develop new memoryless control strategies.The above work ensures that all signals in the closed-loop system are bounded and the system is asymptotically stable.3)The output feedback control problem for a class of nonlinear time-delay systems is studied.A state observer is designed to estimate the unmeasured system states,and a new Lyapunov-Krasovskii functional with control gain is proposed to compensate for time-varying delays which appears in all the state variables.The constant static gain is used to establish the relationship between the virtual control law and each Lyapunov-Krasovskii functional in the Backstepping process,thus suppressing the additional terms generated by the derivation of Lyapunov-Krasovskii functions.It is proved that the system is asymptotically stable driven by a controller with appropriate design parameters.4)An adaptive neural control scheme based on static gain function is proposed for a class of nonlinear time-delay systems with unmatched uncertainties.The combination of Backstepping technique based on static gain function,Lyapunov-Krasovskii functional and radial basis function neural network(RBF NN)approximation method eliminates the influence of unknown time-varying delays and unknown nonlinearities.The additional term generated by the derivative of Lyapunov-Krasovskii functional is divided into two parts,one part is processed by the virtual control laws,and the other part is suppressed by the static gain function.Then,a memoryless adaptive neural controller is constructed,and all signals of the closed-loop system are semi-globally uniformly ultimately bounded(SGUUB).5)The output feedback neural network control problem for a class of nonlinear timedelay systems is studied.A reduced order observer with sufficiently smooth dynamic gain is designed.Based on this observer,in the first part of this chapter,a semi-global adaptive neural network control scheme is proposed by using neural networks to approximate unknown continuous functions and Backstepping approach.In the second part,a sufficiently smooth switching function is designed,such that the system can be controlled by the neural network in the approximate region and controlled by the robust controller outside the approximate region,thus a global adaptive neural network control scheme is designed.The stability of the system and the boundedness of the closed-loop signal are analyzed by using Lyapunovkrasovskii functional.6)The simulation results of all the designed control schemes prove the effectiveness of the control scheme.