Reachability of Nonlinear Systems With Unknown Dynamics

• 成果类型: Article
• 署名作者: Shafa, Taha; Ornik, Melkior
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3170855
• 发表日期: 2023
• 页码: 2407-2414
• 关键词: Control systems; system dynamics; trajectory; Vehicle dynamics; uncertainty; Aerospace electronics; Aerospace control; Aerospace systems; Autonomous systems; nonlinear control systems; reachable set computation; uncertain systems

摘要

Determining the reachable set for a given nonlinear control system is crucial for system control and planning. However, computing such a set is impossible if the system's dynamics are not fully known. This article is motivated by a scenario where a system suffers an adverse event mid-operation, resulting in a substantial change to the system's dynamics, rendering them largely unknown. Our objective is to conservatively approximate the system's reachable set solely from its local dynamics at a single point and the bounds on the rate of change of its dynamics. We translate this knowledge about the system dynamics into an ordinary differential inclusion. We then derive an underapproximation of the velocities available to the system at every system state. An inclusion using this approximation can be interpreted as a control system; the trajectories of the derived control system are guaranteed to be the trajectories of the unknown system. To illustrate the practical implementation and consequences of our work, we apply our algorithm to a simplified model of an unmanned aerial vehicle.