Robust flexible adaptation gain based CRM for guaranteed transient performance

Abstract

High adaptation gain in model reference adaptive control (MRAC) with closed-loop reference models (CRMs) is a necessary requirement to ensure guaranteed transient performance with better tracking and fast convergence. The high adaptation gain, however, may excite unmodelled dynamics, leading to instability, making the differential equations of the adaptive law stiff and causing numerical instability. Therefore, it becomes apparent that a compromise is required on either convergence speed and transient performance or system stability. This paper attempts to address these issues with a novel CRM-MRAC architecture with flexible adaptation gain, which varies as a function of the derived parameter estimation error. The proposed adaptive scheme mathematically ensures a designable upper bound of the $L_{\infty }$ norm; it also ensures the absence of high-frequency oscillations in the control input, thereby making the system more robust and stable. The effectiveness of the proposed work has been validated with simulation studies on a standard numerical example and the performance has been compared with recent similar works.