A Robust Event-Triggered Approach for Fast Sampled-Data Extremization and Learning

This paper presents a general framework for the analysis and design of a class of model-free, robust, and efficient sampled-data-based algorithms for extremization and learning in continuous-time nonlinear systems that generate response maps with an optimal operational set. In particular, we consider plants described by differential inclusions, interconnected in a sampled-data setting with a robust learning algorithm characterized by a constrained difference inclusion. In contrast to standard sampled-data-based approaches, where the learning dynamics are updated after a fixed sufficiently long sampling time has passed, we design a robust dynamic event-based mechanism that triggers the control action as soon as the rate of change of the output of the plant is sufficiently small. By using this event-based update rule, a significant improvement in the convergence time of the closed-loop system can be achieved. Using the framework of set-valued hybrid dynamical systems, we establish for the closed-loop system the existence of a uniformly asymptotically stable compact set, which, by an appropriate tuning of the control parameters, can be made arbitrarily close to the optimal operational set. Our results generalize existing results for periodic sampled-data extremum seeking, and can be used to solve model-free multivariable smooth/nonsmooth constrained optimization problems, as well as learning problems in game theoretical scenarios.