Adaptive-optimal control under time-varying stochastic uncertainty using past learning

An adaptive-optimal control architecture is presented for adaptive control of constrained aerospace systems with matched uncertainties that are subject to dynamic stochastic change. The architecture brings together three key elements, ie, model predictive control–based reference command shaping, Gaussian process (GP)–based Bayesian nonparametric model reference adaptive control (MRAC), and online GP clustering over nonstationary GPs. Model predictive control optimizes reference model and its shaped output is passed into GP–based MRAC, which is used to learn the model in presence of significant time-varying stochastic uncertainty while maintaining stability. Based on a likelihood ratio test, the changepoints are detected and learned. Lastly, the models are created and clustered by non-Bayesian clustering algorithm. The key salient feature of our architecture is that not only can it detect changes but also it uses online GP clustering to enable the controller to utilize past learning of similar models to significantly reduce learning transients. Furthermore, persistence of excitation conditions are significantly relaxed due to the use of GP-MRAC. Stability of the architecture is argued theoretically and performance is validated empirically on different scenarios for wing rock dynamics.