On-the-Fly Control of Unknown Systems: From Side Information to Performance Guarantees Through Reachability

• 成果类型: Article
• 署名作者: Djeumou, Franck; Vinod, Abraham P.; Goubault, Eric; Putot, Sylvie; Topcu, Ufuk
• 署名单位: University of Texas System; University of Texas Austin; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3217260
• 发表日期: 2023
• 页码: 4857-4872
• 关键词: Nonlinear dynamical systems; optimal control; optimization; reachability analysis; uncertain systems

摘要

In this article, 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, DaTaReach and DaTaControl, to overapproximate the reachable set and design control signals for the system on the fly. DaTaReach constructs a differential inclusion that contains the unknown dynamics. Then, in a discrete-time setting, it overapproximates 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 DaTaReach. DaTaControl enables convex-optimization-based control using the computed overapproximation and the receding-horizon control framework. Besides, DaTaControl 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 DaTaControl 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.