Uncertainty-Based Perturb and Observe for Fast Optimization of Unknown, Time-Varying Processes

Model-free adaptive optimization methods are capable of optimizing unknown, time-varying processes even when other optimization methods are not. However, their practical application is often limited by perturbations that are used to gather information on the unknown cost and its gradient. The aim of this paper is to develop a perturb-and-observe (P&O) method that reduces the need for such perturbations while still achieving fast and accurate tracking of time-varying optima. To this end, a (time-varying) model of the cost is constructed in an online fashion, taking into account the uncertainty on the measured performance cost as well as the decreasing reliability of older measurements. Perturbations are only used when this is expected to lead to improved performance over a certain time horizon. Convergence conditions are provided under which the strategy converges to a neighborhood of the optimum. Finally, simulation results demonstrate that uncertainty-based P\&O can reduce the number of perturbations significantly while still tracking a time-varying optimum accurately.