Funnel-based Control for Reach-Avoid-Stay Specifications

TL;DR

This paper introduces a funnel-based control method for nonlinear systems to achieve reach-avoid-stay specifications, ensuring safety and goal achievement through a closed-form controller and circumvent functions.

Contribution

It presents a novel funnel-based control framework with a closed-form controller for nonlinear systems to satisfy complex safety and reachability specifications.

Findings

Effective in steering trajectories away from unsafe regions

Ensures system reaches target while avoiding unsafe areas

Validated through simulation experiments

Abstract

The paper addresses the problem of controller synthesis for control-affine nonlinear systems to meet reach-avoid-stay specifications. Specifically, the goal of the research is to obtain a closed-form control law ensuring that the trajectories of the nonlinear system, reach a target set while avoiding all unsafe regions and adhering to the state-space constraints. To tackle this problem, we leverage the concept of the funnel-based control approach. Given an arbitrary unsafe region, we introduce a circumvent function that guarantees the system trajectory to steer clear of that region. Subsequently, an adaptive funnel framework is proposed based on the target, followed by the construction of a closed-form controller using the established funnel function, enforcing the reach-avoid-stay specifications. To demonstrate the efficacy of the proposed funnel-based control approach, a series of simulation experiments have been carried out.