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Contraction L1-Adaptive Control using Gaussian Processes. In Learning for Dynamics and Control

Gahlawat, A. (January 2021, Proceedings of Machine Learning Research)

null (Ed.)

We present a control framework that enables safe simultaneous learning and control for systems subject to uncertainties. The two main constituents are contraction theory-based L1-adaptive (CL1) control and Bayesian learning in the form of Gaussian process (GP) regression. The CL1 controller ensures that control objectives are met while providing safety certificates. Furthermore, the controller incorporates any available data into GP models of uncertainties, which improves performance and enables the motion planner to achieve optimality safely. This way, the safe operation of the system is always guaranteed, even during the learning transients. Keywords: Safe Learning, Planning, Adaptive Control, Gaussian Process Regression

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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.

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