Recursive Gaussian Process-based Adaptive Control: Theoretical Framework and Application to an Airborne Wind Energy System

Abstract

This paper presents a unique adaptive control methodology that fuses real-time Gaussian process (GP) modeling with statistically-driven design space reduction in order to converge upon an optimal set of control parameters. The proposed approach represents a dramatic departure from traditional adaptive control techniques that assume significant underlying structural knowledge of the system model, in addition to representing a significant departure from traditional GP-based regression, which has traditionally been applied to iterative design optimization problems rather than real-time control. Within the proposed adaptive control strategy, GP modeling is tailored to control systems with relatively short time steps through the use of a recursive GP (RGP)-based update to process new information as it is made available, which circumvents the need to retain a complete database of prior data. Exploration of the design space is achieved by selecting design points associated with large prediction variance. At each time step, suboptimal points within the design space are rejected based upon the uncertainty characterization from the GP model and statistical hypothesis testing. The RGP-based adaptive control law has been validated using a numerical model of an airborne wind energy system.