Feedback Linearization using Gaussian Processes

Data-driven approaches from machine learning provide powerful tools to identify dynamical systems with limited prior knowledge of the model structure. This paper utilizes Gaussian processes, a Bayesian nonparametric approach, to learn a model for feedback linearization. By using a proper kernel structure, the training data for identification is collected while an existing controller runs the system. Using the identified dynamics, an improved controller, based on feedback linearization, is proposed. The analysis shows that the resulting system is globally uniformly ultimately bounded. We further derive a relationship between the training data of the system and the size of the ultimate bound to which the system converges with a certain probability. A simulation of a robotic system illustrates the proposed method.