Reachability of Nonlinear Systems with Unknown Dynamics

TL;DR

This paper presents a method to conservatively approximate the reachable set of a nonlinear system with unknown dynamics using local information and bounds on dynamics change, demonstrated on an UAV model.

Contribution

It introduces a novel approach to estimate the reachable set of systems with largely unknown dynamics from limited local data and dynamics bounds.

Findings

Successfully approximates reachable sets with limited local dynamics information

Provides conservative guarantees for system trajectories under unknown dynamics

Demonstrates applicability on a simplified UAV model

Abstract

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 paper 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 a conservative approximation 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 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.