Simple adaptive control - a stable direct model reference adaptive control methodology - brief survey

What is it about?

In spite of successful proofs of stability and even successful demonstrations of performance, the eventual use of model reference adaptive control 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 methodology. The sufficient conditions that guarantee stability are clearly stated and lead to similarly clear proofs of stability. The main claim of the paper is that if sufficient information exists for a robust classical design control, same information can be used to implement robust simple adaptive controllers. As many real world applications show, the added value of using add-on adaptive control techniques is pushing the desired performance beyond any previous limits. The paper also shows that the previous counterexamples to model reference adaptive control become just simple, successful, and stable applications of simple adaptive control.

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