Gaussian Processes for Learning and Control: A Tutorial with Examples

Many challenging real-world control problems require adaptation and learning in the presence of uncertainty. Examples of these challenging domains include aircraft adaptive control under uncertain disturbances [1], [2], multiple-vehicle tracking with space-dependent uncertain dynamics [3], [4], robotic-arm control [5], blimp control [6], [7], mobile robot tracking and localization [8], [9], cart-pole systems and unicycle control [10], gait optimization in legged robots [11] and snake robots [12], and any other system whose dynamics are uncertain and for which limited data are available for model learning. Classical model reference adaptive control (MRAC) [13]-[15] and reinforcement learning (RL) methods [16]-[23] have been developed to address these challenges and rely on parametric adaptive elements or control policies whose number of parameters or features are fixed and determined a priori. One example of such an adaptive model are radial basis function networks (RBFNs), with RBF centers pre-allocated based on expected operating domains [24], [25].