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, Q-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.
Topics & Concepts
Affine transformationLemma (botany)Linear programmingContext (archaeology)Bellman equationComputer scienceExtension (predicate logic)Perspective (graphical)Mathematical optimizationOptimal controlMathematicsDynamic programmingFunction (biology)Artificial intelligencePure mathematicsBiologyPoaceaePaleontologyEvolutionary biologyProgramming languageEcologyControl Systems and IdentificationAdvanced Control Systems OptimizationFault Detection and Control Systems