Reach-Avoid Differential Games Based on Invariant Generation

TL;DR

This paper extends reach-avoid differential game analysis to infinite time horizons using Hamilton-Jacobi reachability, enabling perpetual safety guarantees in complex systems like jet engines.

Contribution

It introduces a novel approach for infinite horizon reach-avoid games leveraging viscosity solutions, expanding beyond finite horizon methods.

Findings

Successfully applied to a jet-engine model

Demonstrated perpetual safety enforcement

Validated numerical methods for high-dimensional systems

Abstract

Reach-avoid differential games play an important role in collision avoidance, motion planning and control of aircrafts, and related applications. The central problem is the computation of the set of initial states from which the ego player can enforce the satisfiability of safety specifications over a specified time horizon. Previous methods addressing this problem mostly focus on finite time horizons. We study this problem in the context of the infinite time horizon, where the ego player aims to perpetually force the system to satisfy certain safety specification while the mutual other player attempts to enforce a violation of this safety specification. The problem is studied within the Hamilton-Jacobi reachability framework with unique Lipschitz continuous viscosity solutions. The continuity and uniqueness property of the viscosity solution facilitates the use of contemporary numerical methods to solve this problem with an appropriate number of state variables. An example adopted from a Moore-Greitzer jet-engine model is employed to illustrate our approach.