Prescribed-Time Reach-Avoid-Stay Specifications for Unknown Systems: A Spatiotemporal Tubes Approach

Abstract

The paper considers controller synthesis problems for control-affine nonlinear systems with unknown dynamics, aiming to fulfill reach-avoid-stay specifications in a prescribed time. The research’s primary aim is to devise a closed-form, approximation-free control strategy that ensures the system’s trajectory reaches a target set, avoids an unsafe set, and complies with state constraints. To address this challenge, the paper introduces a spatiotemporal tube framework that encapsulates both reaching and avoiding requirements via reachability tubes and a circumvent function, respectively. Following this, the paper presents the control strategy and validates its effectiveness through a robot navigation case study.