Global controllability tests for geometric hybrid control systems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2020Embargo end date: 01 Jan 2019 Spain English Publisher:Elsevier BVJournal:Nonlinear Analysis: Hybrid Systems, volume 38, page 100,935 (issn: 1751-570X,

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Authors: Barberó Liñan, María; Cortés, Jorge; Martín de Diego, David; Martínez, Sonia; Muñoz Lecanda, Miguel Carlos;

doi: 10.1016/j.nahs.2020.100935 , 10.48550/arxiv.1905.02490

arXiv: 1905.02490

handle: 10261/226348 , 2117/331649

Global controllability tests for geometric hybrid control systems

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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.

27 pages, 5 figures

Country

Spain

Related Organizations

Universidad Politécnica de Madrid
Spain
Technical University of Catalonia
University of California, San Diego
United States
Universitat Politècnica de Catalunya
Spain
University of California System
United States

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Keywords

Controllability, Mathematics - Differential Geometry, applications, :51 Geometry::51H Topological geometry [Classificació AMS], Transversality, orbits, Geometry, Orbits, controllability, Topology, Topologia, Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica, Hybrid control systems, 93C30, 93B05, 93B27, FOS: Mathematics, Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems), :Matemàtiques i estadística::Geometria::Geometria computacional [Àrees temàtiques de la UPC], :Matemàtiques i estadística::Topologia::Topologia algebraica [Àrees temàtiques de la UPC], Mathematics - Optimization and Control, :54 General topology::54H Connections with other structures, applications [Classificació AMS], Vector fields Orbits, Operator-theoretic methods, Geometric methods, Geometria, hybrid control systems, Classificació AMS::51 Geometry::51H Topological geometry, Differential Geometry (math.DG), Optimization and Control (math.OC), Classificació AMS::54 General topology::54H Connections with other structures, applications, Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria computacional, Classificació AMS::54 General topology::54H Connections with other structures, vector fields, Vector fields, transversality

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