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

Abstract

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 underlying dynamics, monotonicity, or decoupling in the dynamics between the states. Specifically, we propose 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 dynamics. 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.

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

“…This paper significantly extends our previous work [19] by incorporating more side information, a proof of correctness and termination of DaTaReach via a bound on the time step size to use in the discrete-time setting, an explicit bound on the number of primitive operations required by DaTaControl to terminate, and additional numerical experiments. Contributions.…”

Data-Driven Reachability Analysis From Noisy Data

“…Over-approximating reachable sets from data are considered in [12] based on interval Taylor-based methods applied to systems with dynamics described as differential inclusions; however, the proposed approach only works under the assumption of prior nonlinear terms bound. Another interesting method is introduced in [13], where the model is assumed to be partially known, and data is used to learn an additional Lipschitz continuous state-dependent uncertainty, where the unknown part is assumed to be bounded by a known set.…”

Data-Driven Reachability Analysis from Noisy Data

“…A probabilistic reachability analysis is proposed for general nonlinear systems using level sets of Christoffel functions in [16] where they provide a guarantee that the output of the algorithm is an accurate reachable set approximation in a probabilistic sense. Overapproximating reachable sets from data are considered in [17] based on interval Taylor-based methods applied to systems with dynamics described as differential inclusions; however, the proposed approach only works under the assumption of noise-free data. Another interesting method is introduced in [18], where the model is assumed to be partially known and data is used to learn an additional Lipschitz continuous statedependent uncertainty, where the unknown part is assumed to be bounded by a known set.…”