L₁-GP: L₁ Adaptive Control with Bayesian Learning

We present L₁-GP, an architecture based on L₁ adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the L₁ adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the L₁ control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations.