# On-The-Fly Control of Unknown Systems: From Side Information to Performance Guarantees through Reachability

arXiv: https://arxiv.org/abs/2011.05524 · HTML: https://mlsanity.com/paper/2011.05524/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Nov 2020.

## Built on by (most cited first, 3 of 3)

- [Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information](https://mlsanity.com/paper/2106.10533/) (2021)
- [Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control](https://mlsanity.com/paper/2301.03565/) (2023)
- [Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes](https://mlsanity.com/paper/2504.01007/) (2025)

## Abstract (arXiv)

We develop data-driven algorithms for reachability analysis and control of systems with a priori unknown nonlinear dynamics. The resulting algorithms not only are suitable for settings with real-time requirements but also provide provable performance guarantees. To this end, they merge noisy data from only a single finite-horizon trajectory and, if available, various forms of side information. Such side information may include knowledge of the regularity of the dynamics, algebraic constraints on the states, monotonicity, or decoupling in the dynamics between the states. Specifically, we develop two algorithms, textttDaTaReach and textttDaTaControl, to over-approximate the reachable set and design control signals for the system on the fly. textttDaTaReach constructs a differential inclusion that contains the unknown dynamics. Then, in a discrete-time setting, it over-approximates the reachable set through interval Taylor-based methods applied to systems with dynamics described as differential inclusions. We provide a bound on the time step size that ensures the correctness and termination of textttDaTaReach. textttDaTaControl enables convex-optimization-based control using the computed over-approximation and the receding-horizon control framework. Besides, textttDaTaControl achieves near-optimal control and is suitable for real-time control of such systems. We establish a bound on its suboptimality and the number of primitive operations it requires to compute control values. Then, we theoretically show that textttDaTaControl achieves tighter suboptimality bounds with an increasing amount of data and richer side information. Finally, experiments on a unicycle, quadrotor, and aircraft systems demonstrate the efficacy of both algorithms over existing approaches.