Event-Triggered and Periodic Event-Triggered Extremum Seeking

This paper introduces two innovative control schemes, event-triggered extremum seeking control (ET-ESC) and periodic event-triggered extremum seeking control (PET-ESC), designed for real-time optimizing multivariable systems. The classical extremum seeking control is augmented with static and dynamic triggering conditions to enable aperiodic and less frequent updates of the system's input signals, offering the so-called resource-aware control design. Our convergence analysis is built upon time-scaling combined with Lyapunov and averaging theories for discontinuous systems. Both ETESC and PET-ESC assign an exponentially stable behavior to the resulting average system, which is equivalent to a practical asymptotic convergence to a small neighborhood of the extremum point. We guarantee Zeno behavior avoidance by establishing a minimum dwell time to avoid infinitely fast switching. In particular, the PET-ESC utilizes impulsive systems within a hybrid systems framework. Performance optimization matches one of the classical continuous-time extremum algorithms while balancing system performance with actuation resource consumption. Our ET-ESC and PET-ESC algorithms are the first of their kind and allow for arbitrarily large inter-sampling times unlocking the restriction imposed by existing sampled-data ESC. Extensive simulations validate the feasibility and effectiveness of our designs, illustrating the advantages of ET-ESC and PET-ESC. (c) 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.