A Design Method and Stability of Continuous-Time MRACS with Exponential Rate of Convergence

Abstract

This paper presents a design scheme of a model reference adaptive control system with a desired rate of exponential convergence for continuous-time single-input single-output linear systems. It is shown that the algorithm will ensure that the signals in the system remain bounded for any time and that the output tracking error goes to zero exponentially.
The design scheme proposed in this paper is based on the extended method without using strictly positive real function and the method uses filters and an error model with desired dynamics to specify the convergence rate arbitrarily. The overall adaptive control loop is proved to be stable with non zero plant initial values and under the condition that the unstability degree of the plant is greater than the convergence rate of adjusting laws. It requires the assumption of richness of signals, which is essentially necessary to have exponential convergence.
Some simulation runs are presented to show the stabilty of the overall adaptive system.