Robust (Point-wise) Optimal Adaptive Control

Abstract: Employing modern control Lyapunov methods with modern adaptive control methods leads to an adaptive control system with strong trajectory tracking performance with sub-optimality properties. Concurrent learning adaptive elements provide the robustness needed to handle large parameter variation. Extension of the method improves robustness of safety margins to uncertainty when using control barrier functions.

This work represents our first attempt at merging modern nonlinear control techniques with modern adaptive control techniques. Doing so leads to some interesting differences when compared to classical model reference adaptive control. In fact, the approach looks more like earlier methods of adaptive control (from the 90's) that did not include a model reference. However, with contemporary insights into how to structure adaptive control methods, we are now able to say more about the performance of these techniques.¹

The last decade and some change has also seen an increase in research towards safety or safety constraint satisfaction during closed-loop operation. Barriers and control barrier functions arose from the controls community's efforts. Since adaptive control adapts online uncertain parameters to meet a target Lyapunov stability specification, it is sensible to expect for adaptive control to integrate well with control barrier functions.² In fact, doing so significantly improves performance of a system with a barrier constraint and uncertainty in the dynamics.