A Design of Model Reference Adaptive Control for the Retarded Time Delay System

Abstract

This paper presents a model reference adaptive control for the retarded time delay system, which is a continuous-time linear system with a time delay in the state. The time delay can be compensated by the linear filter which belongs to the finite Laplace trnsformation. The adaptive controller estimates unknown integral kernels of the filter and unknown parameters of the time delay system. At the same, time the controller makes the output of the time delay system follow that of the prespecified reference model. A convergence proof of the output error between the time delay system and the model is given under a boundness assumption on the all state included in the control system. The result is verified by a simple numerical simulation performed on a 2nd order retarded time delay system.