Model Reference Adaptive Control For Time-delay Systems

This paper mainly studies the problem of output-feedback model reference adaptive control(MRAC)for a class of single-input single-output(SISO)linear systems with the known state time-delays.Although the problem had been studied,a premise hypothesis is founded which is difficult to achieve in the process of its derivation.And when the Lyapunov-Krasovskii(L-K)functional is constructed to analysis the stability of the system,the selection of its parameters is less clear.So the main work of this paper is:1.According to the main idea which is proposed in the references for the linear systems with the known state time-delays,it is to compensate the delayed states of the system with the delayed states of the reference model.And based on the method of dealing with time-delay term and the design idea of adaptive controller.The definition of general solution in the generalized inverse matrix is used to improve its premise hypothesis,that is,the measurable vectors is used to express a part of the state of the nonminimal representation of the reference model.Then different adaptive algorithms are selected,and the L-K functional with adjustable parameters is constructed using the exponential function with the natural number e as the bottom.And then the performance of the system is analyzed again under the circumstance of adaptive controller structure.2.The problem of output-feedback MRAC for the same systems is studied.Through the analysis of the previous,we know that the controller structure which had been designed in the references can not achieve the control goal of the exact asymptotic tracking of the output of the system under the condition of the premise hypothesis improved,and can only make the tracking error as small as possible by choosing appropriate adaptive gains.Therefore,on the basis of its improvement,we construct a special L-K functional with adaptive gain and design an additional control component.So according to the different representation of time-delay term,four kinds of adaptive controllers with the same structure are presented which can achieve the exact asymptotic tracking of the output of the system.