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

TL;DR

This paper presents two algorithms for real-time control of unknown nonlinear systems using limited data and side information, enabling safe and near-optimal control with theoretical guarantees.

Contribution

The authors develop DaTaReach and DaTaControl algorithms that over-approximate system reachability and design control inputs using minimal data and side information.

Findings

DaTaReach effectively over-approximates the reachable set.

DaTaControl achieves near-optimal control with suboptimality bounds.

Algorithms outperform existing methods on unicycle and quadrotor control tasks.

Abstract

We investigate the problem of data-driven, on-the-fly 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, $\texttt{DaTaReach}$ and $\texttt{DaTaControl}$, to over-approximate the reachable set and design control signals for the system on the fly. $\texttt{DaTaReach}$ 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. $\texttt{DaTaControl}$ 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 $\texttt{DaTaControl}$ to achieve tighter suboptimality bounds. Finally, we demonstrate the efficacy of $\texttt{DaTaControl}$ over existing approaches on the problems of controlling a unicycle and quadrotor systems.