Safely Learning to Control the Constrained Linear Quadratic Regulator

Dean, Sarah, Tu, Stephen, Matni, Nikolai, Recht, Benjamin

arXiv.org Machine Learning 

While data-driven design has considerable potential in contemporary control systems where precise modeling of the dynamics is intractable (e.g., systems with complex contact forces), one of the biggest hurdles to overcome for practical deployment is maintaining safe execution during the learning process. Motivated by this issue, we study the data-driven design of a controller for the constrained Linear Quadratic Regulator (LQR) problem. In constrained LQR, we design a controller for a (potentially unknown) linear dynamical system that minimizes a given quadratic cost, subject to the additional requirement that both the state and input stay within a specified safe region. This is a problem that has received much attention within the model predictive control (MPC) community. For the LQR problem with no constraints, a natural method of exploration for learning the dynamics is to excite the system by injecting white noise. When safety is not an issue, this method is effective and recently Dean et al. [1] provide an end-to-end sample complexity S. Dean, S. Tu, N. Matni, and B. Recht are with the Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, 94709 USA (email: dean sarah@berkeley.edu,

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