Event-Triggered Feedback Optimization for Uncertain Nonlinear Systems: A Small-Gain Approach

This paper addresses the event-triggered feedback optimization problem for a class of nonlinear systems in strict-feedback form with dynamic uncertainties. The system has access to real-time gradients of the objective function along its output trajectory, which is a milder requirement than having access to the objective function’s analytical form. By employing backstepping and gain assignment techniques, two event-triggered mechanisms and a feedback optimization protocol are developed that construct the closed-loop system as a feedback interconnection of multiple Input-to-State Stable (ISS) subsystems. The small-gain theorem is applied to guarantee closed-loop stability, ensuring that the proposed protocol drives the system output to the optimal solution while excluding Zeno behavior. We further relax the uncertain system dynamics to allow nonvanishing terms at the equilibrium point and bounds given by nonlinear functions involving unknown parameters. Unlike existing small-gain methods for event-triggered control, the proposed approach avoids constructing set-valued maps and incorporates the optimization objective into the small-gain analysis. The effectiveness of the approach is demonstrated through its application to a source-seeking problem.