Backstepping for Partially Unknown Nonlinear Systems Using Gaussian Processes

In this letter, a backstepping control approach is developed and analyzed for a setting where the system model is partially unknown and is modeled using Gaussian processes. The proposed approach encompasses the classical backstepping and command filtered approaches as special cases. The tracking error is globally uniformly ultimately bounded, and the performance is shown to be improved by adding new training data. The stability analysis is carried out by employing a quadratic Lyapunov function and Tikhonov’s theorem. The proposed method outperforms an established adaptive backstepping approach given sufficient training data.