editorial modeling and control of complex dynamic...

EditorialModeling and Control of Complex Dynamic Systems 2014

Zhiwei Gao,1 De-Xing Kong,2 and Michael Z. Q. Chen3

1Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK2Department of Mathematics, Zhejiang University, Hangzhou 310027, China3Department of Mechanical Engineering, The University of Hong Kong, Hong Kong Island, Hong Kong

Correspondence should be addressed to Zhiwei Gao; [email protected]

Received 31 December 2014; Accepted 31 December 2014

Copyright © 2015 Zhiwei Gao et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Nowadays, practical dynamic systems have become moreand more complex, which may be characterized by a modelsubjected to environmental uncertainties, communicationtime delays, stochastic perturbations, hybrid dynamics, dis-tributed dynamics, chaotic dynamics, collective behaviours,and so forth [1, 2]. As a result, modeling and control of acomplex system either from the viewpoint of mathematicaltheoreticalmethods or the view of real-time application pointhave been an interesting but challenging research topic. Thisis the third-year special issue from which one may see somerecent research progresses in this research field. The specialissue received 63 submissions, and 6 papers are selected aftera peer-review procedure, indicating an acceptance rate of lessthan 10%.

2. Modeling and Analysis of ComplexDynamic Systems

Modeling is a fundamental work which is always a startingpoint for control, optimisation, and implementation. Inthis special issue, there are three papers focused on theinvestigation of the modeling issues.

In the work entitled “Mathematical Modeling of Tran-sient Responses in a Large Scale Multiconductor System”contributed by C. Sheng and X. Zhang, a novel reduced-order macromodeling algorithm is proposed for calculatingthe lightning transient responses in the lightning protectionsystems of the structures. In this study, the block Arnoldialgorithm is utilized for reducing the matrix dimension.The computed lightning transient responses in a lightning

protection system are demonstrated to conform reasonably tothose from experimental measurements, which confirm thevalidity of the proposed model.

Nonlinearity is one of the distinguished properties of acomplex dynamic system, which has brought challenges insystems modeling. In the paper “Nonlinear Torsional Vibra-tion Dynamics Behaviors of Rolling Mill’s Multi-DOF MainDrive System under Parametric Excitation,” authored by D.Han et al., the nonlinear torsional vibration dynamical modelof the multi-DOF rolling mill’s main drive system underjoint angle parametric excitation is built. In the study, themultiscale method is used to evaluate the nonlinear dynamicbehaviour of the torsional system by analysing the amplitude-frequency characteristic equation and amplitude-frequencyresponse equation. The employed modeling method is vali-dated by the numerical example of the 1780 rolling-mill maindrive system.

A radio frequency (RF) power amplifier is a typicalnonlinear system. Even when the transistor is operating ina quasilinear region, driven by a small variant input signal,the output signal is still nonlinear due to the physics of thetransistor. In the paper entitled “Evolution of Black-BoxMod-els based on Volterra Series,” contributed by D. D. Silveiraet al., a modern classification of the behavioural models ofthe RF power amplifiers is discussed. An evolution of thebehavioural models is reviewed from the basic basebandpower series to the recent parallel multirate pruned Volterraseries models. Some comments on the future trends in poweramplifiers behavioural modeling are also provided.

Another fundamental work is the existence analysis ofthe solutions to dynamic equations that describes a practical

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2015, Article ID 571415, 2 pageshttp://dx.doi.org/10.1155/2015/571415

2 Journal of Applied Mathematics

process. In the paper entitled “On the Existence of GlobalWeak Solutions for a Weakly Dissipative Hyperelastic RodWave Equation,” contributed by H. Yan et al., the exis-tence of the global weak solutions to the weakly dissipativehyperelastic rod wave equation is investigated. By using thelimit of the viscous approximations to the equation and theestimates derived from the equation itself, the existence of theglobal weak solution is addressedwith rigorousmathematicalproofs.

3. Application Research of ComplexDynamic Systems

As the development and application of clean energy such aswind power, solar panel, marine and wave energy, electricvehicles, CHP, and CCHP engines, the future power networkis becoming distributed and the power flow is turning intobidirectional flow. As a result, there is an increasing attentionon the research of the energy storage in the future powernetwork.

In the paper “A New Pricing Scheme for ControllingEnergy Storage Devices in Future Smart Grid,” contributedby J. Zhu et al., a universal pricing scheme for controllingenergy storage devices in future smart grid is proposed,whichis designed to efficiently reduce the value of any convexobjective function defined by the grid operators. Simulationresults have demonstrated the stability and profitability ofthe present pricing scheme. The proposed pricing schemecan be applied to control the behaviour of the energystorage devices installed for the integration of the currentintermittent renewable energy and would havemuch broaderapplications in the future.

As the development of the wireless sensors and wirelesssensor network, the modern automation industry has bene-fited fromusingwireless sensor based control andmonitoringtechniques. It is noticed that robustness, scalability, powerconsumption, memory resources, and computation abilityare the main constraints of wireless sensor networks, whichhave limited the wireless sensor based control and moni-toring performance. In order to overcome the constraintsof wireless sensor networks, gossip algorithm has attractedresearch attention due to its distributed computation ability.

In the work “Nonlinear Gossip Algorithms for WirelessSensor Networks,” authored by C. Shi et al., nonlinear gossipalgorithms for wireless sensor networks are investigated. Theproposed gossip algorithm can converge to the average of theinitial values with probability one. In addition, the proposedalgorithm is a general version, as the traditional linear gossipalgorithm can be viewed as a special case of the presentnonlinear gossip algorithm. The paper also points out thathow to determine and accelerate the convergence rate of thenonlinear gossip algorithms is an issue needed to be furtherinvestigated.

4. Conclusion

Complex dynamic system is a rather broad research filed,whose researches are motivated by a variety of practical engi-neering systems or social, economic, and ecological concerns.

Modeling, control, and optimisation aremajor research issuesfor complex dynamic systems. We anticipate that this specialissue would provide a bit of light to the readers on what andhow the research topic has been developed recently.

Acknowledgments

Sincere thanks are addressed to all the authors whoresponded to the call of the special issue. The guest editorteam is deeply indebted to the volunteer contributions fromthe reviewers.

Zhiwei GaoDe-Xing Kong

Michael Z. Q. Chen

References

[1] Z. Gao, D. Kong, and C. Gao, “Modeling and control of complexdynamic systems: applied mathematical aspects,” Journal ofAppliedMathematics, vol. 2012, Article ID 869792, 5 pages, 2012.

[2] Z. Gao, D. Kong, C. Gao, and M. Chen, “Modeling andcontrol of complex dynamic systems 2013,” Journal of AppliedMathematics, vol. 2013, Article ID 151372, 3 pages, 2013.

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