A neuro-adaptive architecture for extremum seeking control using hybrid learning dynamics

This paper presents a novel approach to achieve online multivariable hybrid optimization of response maps associated to set-valued dynamical systems, without requiring the use of averaging theory. In particular, we propose a prescriptive framework for the analysis and design of a class of adaptive control architectures based on neural networks (NN) and learning dynamics described by hybrid dynamical systems (HDS). The NNs are used as model-free gradient approximators that are online tuned in order to obtain an arbitrarily precise estimation on a compact set of the gradient of the response map of the system under control. For the closed-loop system a semi-global practical asymptotic stability result is obtained, and the results are illustrated via numerical examples.