Solution Concepts and Analysis of Spatially Invariant Hybrid Systems: Exploring Zeno and beyond**This work is supported by the Innovational Research Incentives Scheme under the VICI grant 'Wireless control systems: A new frontier in automation' (No. 11382) awarded by STW (Dutch Science Foundation) and NWO (The Netherlands Organization for Scientific Research)
| Autor: | S. H. J. Heijmans, D.P. Borgers, Wpmh Maurice Heemels |
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| Rok vydání: | 2016 |
| Předmět: |
0301 basic medicine
Lyapunov function 0209 industrial biotechnology Network packet 02 engineering and technology Invariant (physics) 03 medical and health sciences symbols.namesake 030104 developmental biology 020901 industrial engineering & automation Control and Systems Engineering Control theory Bounded function Control system Hybrid system symbols Solution concept Zeno's paradoxes Mathematics |
| Zdroj: | IFAC-PapersOnLine. 49:164-169 |
| ISSN: | 2405-8963 |
| DOI: | 10.1016/j.ifacol.2016.10.157 |
| Popis: | In this paper we consider hybrid systems, consisting of an infinite number of interconnected spatially invariant (identical) hybrid subsystems described using the hybrid inclusions framework. It can be shown that such interconnections can be very useful in, e.g., the modeling of interconnected networked subsystems that use packet-based communication for the exchange of information, including autonomously driving platoons of vehicles. Interestingly however, due to the infinite-dimensionality of the overall interconnected hybrid system, establishing proper definitions of solutions becomes a difficult task as standard solution concepts do not apply to the systems under study since Zeno behavior (an infinite number of jumps in a bounded time interval) is inevitable. Therefore, we introduce an alternative and natural solution concept for this class of systems, allowing solutions to be defined beyond Zeno points. In addition, based on this novel solution concept, we derive Lyapunov-based conditions for a specific, but relevant class of infinite-dimensional hybrid systems, as used for modeling, for instance, networked control systems, that guarantee UGAS (or UGES) or L p -stability of the overall interconnected system. |
| Databáze: | OpenAIRE |
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