Global controllability tests for geometric hybrid control systems

TL;DR

This paper introduces a geometric framework for hybrid systems that enables new global controllability tests by analyzing the topology of jump points, showing hybrid systems can be controllable even when continuous systems are not.

Contribution

It provides a novel geometric formulation for hybrid systems and develops new controllability tests based on the topology of jump points.

Findings

Hybrid systems can be controllable even if continuous systems are not.

Controllability depends on the geometry and topology of jump points.

Examples demonstrate the effectiveness of the new controllability tests.

Abstract

Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework we describe some new global controllability tests for hybrid control systems exploiting the geometry and the topology of the set of jump points, where the instantaneous change of dynamics take place. Controllability is understood as the existence of a feasible trajectory for the system joining any two given points. As a result we describe examples where none of the continuous control systems are controllable, but the associated hybrid system is controllable because of the characteristics of the jump set.