Editorial New Trends in Nonlinear Control Systems and ...
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Editorial New Trends in Nonlinear Control Systems and Applications Zhitao Liu, 1 Deqing Huang, 2 Yifan Xing, 3 Chuanke Zhang, 4 Zhengguang Wu, 1 and Xiaofu Ji 5 1 State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou 310027, China 2 Department of Aeronautics, Imperial College London, London SW7 2AZ, UK 3 Frick Chemistry Laboratory, Princeton University, Princeton, NJ 08544, USA 4 Department of Electrical Engineering and Electronics, e University of Liverpool, Liverpool L69 3GJ, UK 5 Department of Electrical Engineering, School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China Correspondence should be addressed to Zhitao Liu; [email protected] Received 15 March 2015; Accepted 15 March 2015 Copyright © 2015 Zhitao Liu et al. is 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. Nature is nonlinear in general as the responses of physics and engineering systems are nonlinear. e approximate method is a simple and good tool to deal with nonlinear effects sometimes, but it usually damages the original characteristics of nonlinear systems and leads to inaccuracy, misunderstand- ing, or incorrect conclusions. e designer must be acquainted with the basic techniques available for considering nonlinear systems. He must be able to analyze the effects of unwanted nonlinearities in the system and to synthesize nonlinearities into the system to improve dynamic performance [1]. In the past few years, nonlinear control systems have experienced a growing popularity and these developments are motivated by extensive applications, in particular, to such area as mechanical systems, aircraſt flight control systems, and electrical systems. A number of new ideas, approaches, and results have appeared in the field of nonlinear control systems. For all control systems, stability is the primary require- ment. One of the most widely used stability concepts in control theory is Lyapunov stability. Lyapunov stability theory was used extensively in system analysis and design, and many nonlinear system technologies are developed based on it. e notions of energy and dissipation are related to Lyapunov theory and a theory for dissipative systems is developed in [2]. Energy and dissipation are the fundamental concepts in science and engineering practice, where it is com- mon to view dynamical systems as energy-transformation devices. e control problem can then be recast as finding a dynamical system and an interconnection pattern to make the overall energy function take the desired form. is energy shaping approach is the essence of passivity-based control (PBC), a controller design technique that is very well known in mechanical systems and electrical systems now [3]. e notions of control Lyapunov functions and input-to- state stability for nonlinear control systems were introduced in [4]. e successes of this theory have been due in large part to its ability to analyze complicated structures on the basis of the behavior of elementary subsystems in a suitable input- output sense (stable, passive, etc.), in conjunction with the use of tools such as the small gain theorem to characterize interconnections. e theory has been applied to chemical process and biology. Differential geometry has also been proved to be an effective means of analysis and design for nonlinear control systems, and the notions of controllability and observability of nonlinear systems were investigated [5]. Isidori introduced the notion of zero dynamics and gave the geometry control theory in [6]. ere are many interesting applications of geometrical control theory, for example, aircraſt flying at high angles of attack, walking robots, and quantum systems [1]. e estimation for some internal information or states naturally arises in control systems, as one cannot use sensors to measure the signals in some conditions. en the problem of observer design is also important for nonlinear control Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2015, Article ID 637632, 2 pages http://dx.doi.org/10.1155/2015/637632
Transcript of Editorial New Trends in Nonlinear Control Systems and ...
EditorialNew Trends in Nonlinear Control Systems and Applications
Zhitao Liu,1 Deqing Huang,2 Yifan Xing,3 Chuanke Zhang,4
Zhengguang Wu,1 and Xiaofu Ji5
1State Key Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University,Hangzhou 310027, China2Department of Aeronautics, Imperial College London, London SW7 2AZ, UK3Frick Chemistry Laboratory, Princeton University, Princeton, NJ 08544, USA4Department of Electrical Engineering and Electronics, The University of Liverpool, Liverpool L69 3GJ, UK5Department of Electrical Engineering, School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212013, China
Correspondence should be addressed to Zhitao Liu; [email protected]
Received 15 March 2015; Accepted 15 March 2015
Copyright © 2015 Zhitao Liu 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.
Nature is nonlinear in general as the responses of physics andengineering systems are nonlinear. The approximate methodis a simple and good tool to deal with nonlinear effectssometimes, but it usually damages the original characteristicsof nonlinear systems and leads to inaccuracy,misunderstand-ing, or incorrect conclusions.Thedesignermust be acquaintedwith the basic techniques available for considering nonlinearsystems. He must be able to analyze the effects of unwantednonlinearities in the system and to synthesize nonlinearitiesinto the system to improve dynamic performance [1].
In the past few years, nonlinear control systems haveexperienced a growing popularity and these developmentsare motivated by extensive applications, in particular, to sucharea as mechanical systems, aircraft flight control systems,and electrical systems. A number of new ideas, approaches,and results have appeared in the field of nonlinear controlsystems.
For all control systems, stability is the primary require-ment. One of the most widely used stability concepts incontrol theory is Lyapunov stability. Lyapunov stability theorywas used extensively in system analysis and design, andmanynonlinear system technologies are developed based on it.
The notions of energy and dissipation are related toLyapunov theory and a theory for dissipative systems isdeveloped in [2]. Energy and dissipation are the fundamentalconcepts in science and engineering practice, where it is com-mon to view dynamical systems as energy-transformation
devices. The control problem can then be recast as findinga dynamical system and an interconnection pattern to makethe overall energy function take the desired form.This energyshaping approach is the essence of passivity-based control(PBC), a controller design technique that is very well knownin mechanical systems and electrical systems now [3].
The notions of control Lyapunov functions and input-to-state stability for nonlinear control systems were introducedin [4].The successes of this theory have been due in large partto its ability to analyze complicated structures on the basis ofthe behavior of elementary subsystems in a suitable input-output sense (stable, passive, etc.), in conjunction with theuse of tools such as the small gain theorem to characterizeinterconnections. The theory has been applied to chemicalprocess and biology.
Differential geometry has also been proved to be aneffective means of analysis and design for nonlinear controlsystems, and the notions of controllability and observabilityof nonlinear systems were investigated [5]. Isidori introducedthe notion of zero dynamics and gave the geometry controltheory in [6]. There are many interesting applications ofgeometrical control theory, for example, aircraft flying at highangles of attack, walking robots, and quantum systems [1].
The estimation for some internal information or statesnaturally arises in control systems, as one cannot use sensorsto measure the signals in some conditions.Then the problemof observer design is also important for nonlinear control
Hindawi Publishing CorporationAbstract and Applied AnalysisVolume 2015, Article ID 637632, 2 pageshttp://dx.doi.org/10.1155/2015/637632
2 Abstract and Applied Analysis
systems. Many kinds of observer designs for nonlinearcontrol systems and applications are shown in [7].
Another important research field for nonlinear controlsystems is to design controllers to deal with uncertainty,mainly due to lack of knowledge of the system parameters,modeling errors, and external disturbances. According tothese requirements, adaptive control is developed to estimatethe unknown parameters and has grown to be one of the rich-est fields in terms of algorithms, design techniques, analyticaltools, and modifications [8, 9]. However, an adaptive schemedesign for a disturbance-free plant model may go unstablein the presence of small disturbances; then robust adaptivecontrol is developed, which can deal with the parameteruncertainties, modeling errors, and external disturbances[10].
Modern heuristic black-box type control approaches fornonlinear control systems, also called intelligent control, suchas neural networks, machine learning, and fuzzy logic, havebeen used widely. It does not necessarily require an analyticalmodel, and they are developed on the basis of data. Thesemethodologies could be applied to big data research, whichis very interesting research field in computer science.
Last but not least, a special kind of nonlinear controlsystems, hybrid dynamical system, exhibits characteristics ofboth continuous-time and discrete-time dynamical systems[11]. It actually arises in a great variety of applications, such asmanufacturing systems, air traffic management, automotiveengine control, and chemical process. Hybrid dynamical sys-tems have also a central role in networked embedded controlsystems which interact with the physical world and humanoperators, like cyber-physical systems (CPS). So far, manytheories and technologies for hybrid dynamical systems havebeen developed.
The field of nonlinear control systems has a bright futuresince there are many important and interesting challenges.The applications of nonlinear control systems, such as energy,health care, robots, biology, and big data research, will makethe advanced theories and technologies be developed quickly.We hope that the readers of system theory will find theirinteresting research topics for nonlinear control systems inthis special issue.
Zhitao LiuDeqing Huang
Yifan XingChuanke ZhangZhengguang Wu
Xiaofu Ji
References
[1] K. J. Astrom and P. R. Kumar, “Control: a perspective,” Auto-matica, vol. 50, no. 1, pp. 3–43, 2014.
[2] J. C. Willems, “Dissipative dynamical systems. I. Generaltheory,”Archive for RationalMechanics and Analysis, vol. 45, pp.321–351, 1972.
[3] R. Ortega, A. Lorıa, P. J. Nicklasson, and H. Sira-Ramırez,Passivity-Based Control of Euler-Lagrange Systems: Mechanical,Electrical and Electromechanical Applications, Springer, Berlin,Germany, 1998.
[4] E. D. Sontag and Y. Wang, “On characterizations of the input-to-state stability property,” Systems&Control Letters, vol. 24, no.5, pp. 351–359, 1995.
[5] R. Brockett, “The early days of geometric nonlinear control,”Automatica, vol. 50, no. 9, pp. 2203–2224, 2014.
[6] A. Isidori, Nonlinear Control Systems, Communications andControl Engineering Series, Springer, Berlin, Germany, Thirdedition, 1995.
[7] G. Besancon, Nonlinear Observers and Applications, Springer,Berlin, Germany, 2007.
[8] K. J. Astrom and B. Wittenmark, Adaptive Control, DoverPublications, Mineola, NY, USA, 2008.
[9] G. Tao, Adaptive Control Design and Analysis, John Wiley &Sons, Hoboken, NJ, USA, 2003.
[10] P. A. Ioannou and J. Sun,Robust Adaptive Control, PrenticeHall,1995.
[11] R.Goebel, R.G. Sanfelice, andA. R. Teel,HybridDynamical Sys-tems: Modeling, Stability, and Robustness, Princeton UniversityPress, 2012.
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