Event-triggered based on-line optimization for a class of nonlinear systems

We consider the problem of robust on-line optimization of a class of continuous-time nonlinear systems by using a discrete-time controller/optimizer, interconnected with the plant in a sampled-data structure. In contrast to classic approaches where the controller is updated after a fixed sufficiently long waiting time has passed, we design an event-based mechanism that triggers the control action only when 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 rate of the closed-loop dynamics is achieved. Since the closed-loop system combines discrete-time and continuous-time dynamics, and in order to guarantee robustness and semi-continuous dependence of solutions on parameters and initial conditions, we use the framework of hybrid set-valued dynamical systems to analyze the stability properties of the system. Numerical simulations illustrate the results.