Bayesian Nonparameteric Model Reference Adaptive Control using Gaussian Processes

Abstract

Most current Model Reference Adaptive Control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a-priori. For example, widely studied Radial Basis Function Network (RBFN) based MRAC approaches rely on RBFns with pre-allocated centers. Such preallocation requires prior knowledge of the expected operating domain. Hence, if the system operates outside of the expected operating domain due to faults or other unforeseen events, such adaptive elements can become non-effective. This results in only semi-global adaptive controllers. Building on our previous work, this paper presents an alternate view of modeling system uncertainties. We propose to use the Gaussian Process Bayesian Nonparametric (BNP) model which enables us to model uncertainties as distributions over functions. We have shown that these BNP adaptive elements guarantee good closed loop performance with minimal prior domain knowledge of the uncertainty through stochastic stability arguments. In this paper, we also present flight test validation of GP-MRAC. The results indicate that GP-MRAC overcomes the limitations of MRAC employing RBFN with fixed parameters and outperforms RBFN-MRAC in terms of tracking error and modeling the uncertainty.