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.

Abstract: GP-MRAC extends BKR-CL to incorporate Bayesian estimation through Gaussian process regression. Like BKR-CL, it is fully data-driven and starts with the zero function (i.e., an empty kernel machine) and builds up the learnt representation with data collected during online operation. Combining machine learning analysis methods with controls-based Lyapunov stability analysis leads to proven stability of the method.

Abstract: BKR-CL describes an adaptive control technique employing machine learning tools and analysis to prove stabilization of a neuro-adaptive control system that learns the network structure online and in real-time. As part of the analysis, we observe that persistent excitation of the neural network is not equivalent to persistent excitation of the states. The observation is used to define an online network restructuring technique that ensure good approximation capabilities given an upper bound on the network size.
Proof of stabilization for the neuroadaptive control technique relies on Lyapunov stability theory.