Simple Adaptive Control - A Stable Direct Model Reference Adaptive Control Methodology - A Brief Survey
In spite of successful proofs of stability and even successful demonstrations of performance, the eventual use of Model Reference Adaptive Control (MRAC) methodologies in practical real world systems has met a rather strong resistance from practitioners and has remained very limited. Apparently, the practitioners have a hard
time understanding the conditions that can guarantee stable
operations of adaptive control systems under realistic operational environments. Besides, it is difficult to measure the robustness of adaptive control system stability and allow it to be compared with the common and widely used measure of phase margin and gain margin that is utilized by present, mainly LTI, controllers. Furthermore, recent counterexamples seem to show that adaptive systems may
diverge even when all required conditions are fulfilled. This paper attempts to revisit the fundamental qualities of the common direct model reference adaptive control methodology based on gradient and to show that some of its basic drawbacks have been addressed and eliminated within the so-called Simple Adaptive Control and other simplified and passivity-based Adaptive Control methodologies.
The sufficient conditions that guarantee stability are clearly stated and lead to similarly clear proofs of stability. The paper also shows that the previous counterexamples to MRAC become just simple, successful, and stable applications of SAC.