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

Abstract

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, the use 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.

Simple Adaptive Control for Spacecraft Proximity Operations

“…This can only be achieved if K p is sufficiently large, which is not the case with Eq. (42). To do so, the inverse of the following high gain PD controller is used as the parallel feedforward…”

“…Stability of the adaptive system with respect to boundedness is therefore guaranteed from the Lyapunov stability theory, and all state errors (and output errors), as well as adaptive control gains are bounded. Furthermore, LaSalle's invariance principle for nonautonomous systems 11,40,41,42 can be used to demonstrate that {e x , K I (t)} ultimately reaches the domain defined by e x ≡ 0. Since e x ≡ 0 implies e x (t) = 0 and e y (t) = 0, asymptotic stability of the state and output tracking errors is guaranteed.…”

Extensions in adaptive model tracking with mitigated passivity conditions

“…Furthermore, these claims also seemed to be backed by counterexamples that actually made the standard Model Reference Adaptive Control (MRAC) diverges even if the so-called ''sufficient'' conditions were satisfied. 18 Although the same counterexamples were successfully used with SAC, 19,20 it was later realized that they did not satisfy even the mitigated conditions of Ref. 15 .…”

“…However, instead of showing divergence or being in any Extensions in adaptive model tracking with mitigated passivity conditions way problematic, these ''counterexamples'' seemed to demonstrate the simplicity and performance of SAC 19,20 and they served as the trigger that ultimately led to the theoretical analysis of stability of tracking with mitigated passivity conditions. For readers convenience, we reproduce some results of Ref.…”

Transient performance improvement of model reference adaptive control: LMI‐based resetting

“…[1][2][3][4] Nevertheless, the improvement of its transient performance has long been a challenging problem. [1][2][3][4] Nevertheless, the improvement of its transient performance has long been a challenging problem.…”