Model Reference Adaptive Control System Design for Linear Time-Varying Systems with unstructured and bounded varying functions

Abstract

In recent years, many methods of model reference adaptive control system (MRACS) for a linear time-varying (LTV) plant are proposed. These methods are assumed that the structure of plant parameters is known in advance. However it is difficult to get priori information of plant parameters. In this paper, a MRACS design for a LTV system based on high order estimator (HOE) is proposed. By applying dynamic certainty equivalence (DyCE) to LTV plants, a new MRACS law of LTV system is derived without knowing the structure of the plant parameters. The MRACS law is generated by using high order derivatives of a estimated parameter, so that robust HOE with a normalization signal and a modification for the system introduced. Our proposed method can attain better performance than conventional methods, such that the estimation with variable forgetting factor (VF) and the gradient projection method (GPM). The robust HOE establishes the boundedness of all the estimated parameters under the condition that the estimated parameter and the first derivative of the parameter are bounded. It is shown that all signals in the adaptive loop is bounded and the output error converges to a closed set. The proposed method is compared to the familiar schemes, the gradient projection method and the estimation based on forgetting factor through numerical simulations, and the effectiveness of our proposed method is shown consequently.