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 , , multiple-vehicle tracking with space-dependent uncertain dynamics , , robotic-arm control , blimp control , , mobile robot tracking and localization , , cart-pole systems and unicycle control , gait optimization in legged robots  and snake robots , and any other system whose dynamics are uncertain and for which limited data are available for model learning. Classical model reference adaptive control (MRAC) - and reinforcement learning (RL) methods - 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 , .