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This paper presents a method to design a min-norm Control Lyapunov Function(CLF)-based stabilizing controller for a control-affine system with uncertaindynamics using Gaussian Process (GP) regression. In order to estimate bothstate and input-dependent model uncertainty, we propose a novel compound kernelthat captures the control-affine nature of the problem. Furthermore, by the useof GP Upper Confidence Bound analysis, we provide probabilistic bounds of theregression error, leading to the formulation of a CLF-based stability chanceconstraint which can be incorporated in a min-norm optimization problem. Weshow that this resulting optimization problem is convex, and we call itGaussian Process-based Control Lyapunov Function Second-Order Cone Program(GP-CLF-SOCP). The data-collection process and the training of the GPregression model are carried out in an episodic learning fashion. We validatethe proposed algorithm and controller in numerical simulations of an invertedpendulum and a kinematic bicycle model, resulting in stable trajectories whichare very similar to the ones obtained if we actually knew the true plantdynamics.

Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics