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arXiv · 2206.11103

On-the-fly control of unknown nonlinear systems with sublinear regret

Abraham P. Vinod·Arie Israel·Ufuk Topcu
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Abstract

We study the problem of data-driven, constrained control of unknown nonlinear dynamics from a single ongoing and finite-horizon trajectory. We consider a one-step optimal control problem with a smooth, black-box objective, typically a composition of a known cost function and the unknown dynamics. We investigate an on-the-fly control paradigm, i.e., at each time step, the evolution of the dynamics and the first-order information of the cost are provided only for the executed control action. We propose an optimization-based control algorithm that iteratively minimizes a data-driven surrogate function for the unknown objective. We prove that the proposed approach incurs sublinear cumulative regret (step-wise suboptimality with respect to an optimal one-step controller) and is worst-case optimal among a broad class of data-driven control algorithms. We also present tractable reformulations of the approach that can leverage off-the-shelf solvers for efficient implementations.

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Abraham P. Vinod, Arie Israel, Ufuk Topcu. 2022-06-22. On-the-fly control of unknown nonlinear systems with sublinear regret. https://arxiv.org/abs/2206.11103

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