Stable Gaussian Process based Tracking Control of Lagrangian Systems
This work addresses the problem of stable tracking control for Lagrangian systems with unknown dynamics, offering a theoretically grounded approach to gain adaptation based on model uncertainty.
The paper develops a data-driven control law for Lagrangian systems that uses Gaussian Process regression to compensate for unknown dynamics and adapts feedback gains based on model uncertainty, ensuring globally bounded tracking error. Simulations on a robot manipulator demonstrate efficacy.
High performance tracking control can only be achieved if a good model of the dynamics is available. However, such a model is often difficult to obtain from first order physics only. In this paper, we develop a data-driven control law that ensures closed loop stability of Lagrangian systems. For this purpose, we use Gaussian Process regression for the feed-forward compensation of the unknown dynamics of the system. The gains of the feedback part are adapted based on the uncertainty of the learned model. Thus, the feedback gains are kept low as long as the learned model describes the true system sufficiently precisely. We show how to select a suitable gain adaption law that incorporates the uncertainty of the model to guarantee a globally bounded tracking error. A simulation with a robot manipulator demonstrates the efficacy of the proposed control law.