Data-Driven Optimal Control of Affine Systems: A Linear Programming Perspective

Andrea Martinelli, Matilde Gargiani, Marina Draskovic, John Lygeros

Abstract: In this letter, we discuss the problem of optimal control for affine systems in the context of data-driven linear programming. First, we introduce a unified framework for the fixed point characterization of the value function, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> -function and relaxed Bellman operators. Then, in a model-free setting, we show how to synthesize and estimate Bellman inequalities from a small but sufficiently rich dataset. To guarantee exploration richness, we complete the extension of Willems’ fundamental lemma to affine systems.