Robust Linear Quadratic Regulator: Exact Tractable Reformulation

Abstract

We consider the problem of controlling an unknown stochastic linear dynamical system subject to an infinitehorizon discounted quadratic cost. Existing approaches for handling the corresponding robust optimal control problem resort to either conservative uncertainty sets or various approximations schemes, and to our best knowledge, the current literature lacks an exact, yet tractable, solution. We propose a class of novel uncertainty sets for the system matrices of the linear system. We show that the resulting robust linear quadratic regulator problem enjoys a closed-form solution described through a generalized algebraic Riccati equation arising from dynamic game theory.

Efficient Learning of a Linear Dynamical System with Stability Guarantees

“…The numerical reverse I-projection relies on a result from infinite-horizon dynamic programming, e.g., see (Başar and Bernhard 1995, Chapter 3) or (Bertsekas 2007), and the following exact constraint relaxation result borrowed from (Jongeneel 2019, Lemma A-0.1); see also (Jongeneel, Summers, and Mohajerin Esfahani 2019). We repeat this to keep the paper self-contained.…”