recent advances on the theory and applications of … advances on the...on a compositional barrier...

EditorialRecent Advances on the Theory andApplications of Hybrid Systems

Rui Wang,1 Guo-Ping Liu,2 Yun-Bo Zhao,3 and Weiguo Xia4

1School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China2Faculty of Advanced Technology, University of South Wales, Pontypridd CF37 1DL, UK3Department of Automation, Zhejiang University of Technology, Hangzhou 310023, China4ACCESS Linnaeus Centre, School of Electrical Engineering, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden

Correspondence should be addressed to Rui Wang; [email protected]

Received 24May 2016; Accepted 24May 2016

Copyright © 2016 Rui Wang et al.This is an open access article distributed under theCreativeCommonsAttribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Hybrid systems are dynamical systems with interactions ofboth continuous and discrete dynamics [1]. Such systemscan be appropriate models for a multitude of practicalsystems in engineering and applied sciences [2, 3]. Fromthe control perspective, a typical example of hybrid systemswould consist of a continuous-time linear time-invariantplant described by linear differential equations and a discrete-time linear time-invariant controller described by lineardifference equations, where the former involves continuous-valued variables that depend on the continuous time, and thelatter involves continuous-valued variables that depend onthe discrete time, thus the hybrid feature of the whole system[4].

Since the interactions of continuous-time and discrete-time dynamics in a hybrid system lead to rich dynamicalbehaviours which may never be encountered in purelycontinuous-time systems, hybrid systems thus stand as ahighly challenging field of research, encompassing a varietyof challenging problems in many aspects such as modeling,simulation, analysis, verification, and controller synthesis[3, 5]. In view of the facts that hybrid systems modeling ispopular in practice, their design and analysis are thereforeof great importance not only in theory but also in practice.We hence felt urged to provide a discussion platform for theresearchers to report their state-of-the-art works in this area,which eventually motivated the organization of this specialissue on the recent advances of the theory and applications ofhybrid systems.

In this special issue we have gathered a number ofresearch works on hybrid systems and the closely relatedtopics.We are very happy to see that these limited numbers ofresearch works have shown a great variety, in a sense givinga fairly complete picture of the state-of-the-art research onhybrid systems.

The works included in this special issue can be roughlydivided into two categories, one focusing on the controlstrategy design and the other on the system performanceanalysis of hybrid systems.

On the one hand, various control strategies for hybridsystems have been discussed in this special issue. Thesecontrol strategies include, for example, an improved averagedwell method for the stabilization of a class of switchedsystem (Q. Su and P. Wang), !∞ output tracking algorithmfor switched cascade nonlinear systems (X. Dong et al.), aglobal eco-driving optimal control strategy for bus transitto minimize the exhaust emission (X. Zheng and L. Zhang),a consensus algorithm under directed switching communi-cation topologies for linear multiagent systems (Y. Zhanget al.), and a control strategy of shifting time involvingmultigroup clutches for a hydromechanical continuouslyvariable transmission (Z. Zhu et al.).

On the other hand, system performance evaluations arealso widely discussed in this special issue. These worksinclude, for example, a new performance index for hybridenergy storage system in a parallel hybrid electrical vehicle(C. Zhang et al.), the convergence analysis for a class of

Hindawi Publishing Corporation

Mathematical Problems in Engineering

Volume 2016, Article ID 6452926, 2 pages

http://dx.doi.org/10.1155/2016/6452926

2 Mathematical Problems in Engineering

periodic boundary value problem of hybrid system withcausal operators (P. Wang et al.), the limit cycle propertiesfor both uncoupled and coupled hybrid systems (A. Favela-Contreras et al.), a numerical safety evaluationmethod basedon a compositional barrier certificate (G. Wang et al.), andthe "2-gain analysis of hybrid systems (T. Osuna et al.), justto name a few.

To conclude, we believe that this special issue containssufficiently interesting materials on hybrid systems as well ascertain related topics, both in theory and in applications. Wehope that people will find this special issue a useful referencefor their future works on hybrid systems.

Rui WangGuo-Ping LiuYun-Bo ZhaoWeiguo Xia

References

[1] J. Lygeros, K.H. Johansson, S.N. Simic, J. Zhang, and S. S. Sastry,“Dynamical properties of hybrid automata,” IEEE Transactionon Automatic Control, vol. 48, no. 1, pp. 2–17, 2003.

[2] M. Bernardo, U. Montanaro, and S. Santini, “Hybrid modelreference adaptive control of piecewise affine systems,” IEEETransactions on Automatic Control, vol. 58, no. 2, pp. 304–316,2013.

[3] P. J. Antsaklis and A. Nerode, “Hybrid control systems: anintroductory discussion to the special issue,” IEEE Transactionon Automatic Control, vol. 43, no. 4, pp. 457–460, 1998.

[4] P. J. Antsaklis, “A brief introduction to the theory and applica-tions of hybrid systems,” in Proceedings of the IEEE Special Issueon Hybrid Systems: Theory and Applications, vol. 88, no. 7, pp.879–887, 2000.

[5] R. Goebel, R. G. Sanfelice, and A. R. Teel, “Hybrid dynamicalsystems,” IEEE Control Systems, vol. 29, no. 2, pp. 28–93, 2009.

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1. Recent advances on the theory and applications of hybrid systemsAccession number: 20162702565611Authors: Wang, Rui (1); Liu, Guo-Ping (2); Zhao, Yun-Bo (3); Xia, Weiguo (4)Author affiliation: (1) School of Aeronautics and Astronautics, Dalian University of Technology, Dalian; 116024,China; (2) Faculty of Advanced Technology, University of South Wales, Pontypridd; CF37 1DL, United Kingdom; (3)Department of Automation, Zhejiang University of Technology, Hangzhou; 310023, China; (4) ACCESS LinnaeusCentre, School of Electrical Engineering, Royal Institute of Technology (KTH), Stockholm; 10044, SwedenCorresponding author: Wang, Rui([email protected])Source title: Mathematical Problems in EngineeringAbbreviated source title: Math. Probl. Eng.Volume: 2016Issue date: 2016Publication year: 2016Article number: 6452926Language: EnglishISSN: 1024123XE-ISSN: 15635147Document type: Journal article (JA)Publisher: Hindawi Publishing Corporation, 410 Park Avenue, 15th Floor, 287 pmb, New York, NY 10022, UnitedStatesNumber of references: 5DOI: 10.1155/2016/6452926Compendex references: YESDatabase: CompendexCompilation and indexing terms, Copyright 2016 Elsevier Inc.Data Provider: Engineering Village

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Record 1 of 1Title: Recent Advances on the Theory and Applications of Hybrid SystemsAuthor(s): Wang, R (Wang, Rui); Liu, GP (Liu, Guo-Ping); Zhao, YB (Zhao, Yun-Bo); Xia, WG (Xia, Weiguo)Source: MATHEMATICAL PROBLEMS IN ENGINEERING Article Number: 6452926 DOI: 10.1155/2016/6452926 Published: 2016 Times Cited in Web of Science Core Collection: 0Total Times Cited: 0Usage Count (Last 180 days): 1Usage Count (Since 2013): 1Cited Reference Count: 5Accession Number: WOS:000378738700001Language: EnglishDocument Type: Editorial MaterialKeyWords Plus: SPECIAL-ISSUEAddresses: [Wang, Rui] Dalian Univ Technol, Sch Aeronaut & Astronaut, Dalian 116024, Peoples R China. [Liu, Guo-Ping] Univ South Wales, Fac Adv Technol, Pontypridd CF37 1DL, M Glam, Wales. [Zhao, Yun-Bo] Zhejiang Univ Technol, Dept Automat, Hangzhou 310023, Zhejiang, Peoples R China. [Xia, Weiguo] Royal Inst Technol KTH, Sch Elect Engn, ACCESS Linnaeus Ctr, S-10044 Stockholm, Sweden.Reprint Address: Wang, R (reprint author), Dalian Univ Technol, Sch Aeronaut & Astronaut, Dalian 116024, Peoples R China.E-mail Addresses: [email protected] Identifiers:

Author ResearcherID Number ORCID Number

Liu, Guo-Ping O-3511-2014 0000-0002-0699-2296 Publisher: HINDAWI PUBLISHING CORPPublisher Address: 315 MADISON AVE 3RD FLR, STE 3070, NEW YORK, NY 10017 USAWeb of Science Categories: Engineering, Multidisciplinary; Mathematics, Interdisciplinary ApplicationsResearch Areas: Engineering; MathematicsIDS Number: DP8HKISSN: 1024-123XeISSN: 1563-514729-char Source Abbrev.: MATH PROBL ENGISO Source Abbrev.: Math. Probl. Eng.Source Item Page Count: 2

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