An Uncertainty-Based Control Lyapunov Approach for Control-Affine Systems Modeled by Gaussian Process

Data-driven approaches in control allow for identification of highly complex dynamical systems with minimal prior knowledge. However, properly incorporating model uncertainty in the design of a stabilizing control law remains challenging. Therefore, this letter proposes a control Lyapunov function framework which semiglobally asymptotically stabilizes a partially unknown fully actuated control affine system with high probability. We propose an uncertainty-based control Lyapunov function which utilizes the model fidelity estimate of a Gaussian process model to drive the system in areas near training data with low uncertainty. We show that this behavior maximizes the probability that the system is stabilized in the presence of power constraints using equivalence to dynamic programming. A simulation on a nonlinear system is provided.