On-The-Fly Control of Unknown Smooth Systems from Limited Data

Franck Djeumou (1) , Abraham Vinod (1) , Eric Goubault (2) , Sylvie Putot (2) , Ufuk Topcu (1)

1 University of Texas at Austin [Austin]
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We investigate the problem of data-driven, on-thefly control of systems with unknown nonlinear dynamics where data from only a single finite-horizon trajectory and possibly side information on the dynamics are available. Such side information may include knowledge of the regularity of the dynamics, monotonicity of the states, or decoupling in the dynamics between the states. Specifically, we develop two algorithms, DaTaReach and DaTaControl, to over-approximate the reachable set and design control signals for the system on the fly. DaTaReach constructs a differential inclusion that contains the unknown vector field. Then, it computes an over-approximation of the reachable set based on interval Taylor-based methods applied to systems with dynamics described as differential inclusions. DaTaControl enables convex-optimization-based, near-optimal control using the computed over-approximation and the receding-horizon control framework. We provide a bound on its suboptimality and show that more data and side information enable DaTaControl to achieve tighter suboptimality bounds. Finally, we demonstrate the efficacy of DaTaControl over existing approaches on the problems of controlling a unicycle and quadrotor systems.

Domaines: Systèmes et contrôle [cs.SY]

Franck Djeumou, Abraham Vinod, Eric Goubault, Sylvie Putot, Ufuk Topcu. On-The-Fly Control of Unknown Smooth Systems from Limited Data. 2021 American Control Conference (ACC), May 2021, New Orleans, France. pp.3656-3663, ⟨10.23919/ACC50511.2021.9483367⟩. ⟨hal-03800674⟩