Global controllability tests for geometric hybrid control systems

Abstract

This paper introduces a novel geometric framework to define and study hybrid systems. We exploit the geometry and topology of the set of jump points, where the instantaneous change of dynamics takes place, in order to gain controllability for the system. This approach allows us to describe new global controllability tests for hybrid control systems. We illustrate these results with several 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. ; The authors have been partially supported by Ministerio de Economía y Competitividad (MINECO, Spain) under grant MTM 2015-64166-C2-2P. MBL and DMdD acknowledge financial support from the Spanish Ministerio de Economía y Competitividad, through the research grants PID2019-106715GB-C21, MTM2016-76702-P, I-Link Project (Ref: linkA20079) from CSIC and "Severo Ochoa Programme for Centers of Excellence" in R&D (SEV-2015-0554). MBL has been financially supported by "Programa propio de I+D+I de la Universidad Politécnica de Madrid: Ayudas dirigidas a jóvenes investigadores doctores para fortalecer sus planes de investigación". JC has been financially supported by NSF Award NSF ECCS-1917177. SM has been financially supported by AFOSR Award FA9550-18-1-0158. MCML acknowledges the financial support from the Spanish Ministerio de Economía y Competitividad project MTM2014-54855-P, the Spanish Ministerio de Ciencia Innovación y Universidades project PGC2018-098265-B-C33 and from the Secretary of University and Research of the Ministry of Business and Knowledge of the Catalan Government project 2017-SGR-932.