Stable Control Design For Nonlinear Time-delay Systems With Unknown Output Functions

Compared to linear systems,nonlinear systems can more accurately characterize the essential characteristics of the system being studied.Therefore,control design of nonlinear systems has always been the focus and difficulty in the field of control theory.It is widely used in robot systems,power systems,and ecosystems.On the other hand,the law of change based on things usually depends on the fact of the current state and the state of the past period.It can be concluded that most systems have time-delay.They have a great impact on the stability of the control system.It is easy to cause system performance degradation and even cause system instability.Therefore,in the past two decades,the stability of a class of so-called nonlinear control systems with time-varying delays has attracted much attention.The main research contents of this paper are as follows:?.Global output feedback stabilization of time-delay nonlinear systems based on double gain designThis part addresses the problem of global output feedback stabilization for a class of time-varying delay nonlinear systems with polynomial growth rate.The systems under investigation possess two remarkable features: the output is perturbed by an unknown sensitivity function which is not differentiable but continuous,and the nonlinearities are bounded by a polynomial function of the output multiplied by unmeasurable state variables.The new full-order observer is established by introducing a dynamic gain and filtering unknown nonlinearities and time-varying delay.With the help of the transformation skill and the reasonable combination of several systems,this paper proposes a linear output feedback controller with the dynamic gain,and completes the performance analysis based on the construction of two integral Lyapunov functions.Finally,a simulation example is presented to demonstrate the effectiveness of control strategy.?.Output feedback regulation of time-delay nonlinear systems with unknown continuous output function and unknown growth rateThis part is concerned with the global regulation via output feedback for the timedelay nonlinear systems with unknown continuous output function and unknown growth rate.Different from the existing literatures,the output is perturbed by an unknown continuous function,and nonlinearities are upper bounded by unmeasured states multiplying an unknown constant and a polynomial of the output.A unified methodology is proposed to construct a new type of full-order observer with a dynamic gain by filtering unknown nonlinearities and time-varying delay.In light of a delicate scaling transformation,a combined system is derived to perform the one-step assignment of the controller instead of traditional backstepping recursive design.The stability analysis is completed by reductio and another scaling transformation with the upper bound of the dynamic gain.The efficiency of the proposed control scheme is demonstrated by two simulation examples including a practical one.