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Erschienen in:
A Novel Design Approach of a Nonlinear Resistor Based on a Memristor Emulator Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Dynamic Analysis, Adaptive Control and Synchronization of a Novel Highly Chaotic System with Four Quadratic Nonlinearities

verfasst von : Sundarapandian Vaidyanathan

Erschienen in: Advances in Chaos Theory and Intelligent Control

Verlag: Springer International Publishing

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Abstract

In this work, we describe an eight-term novel highly chaotic system with four quadratic nonlinearities. The phase portraits of the novel highly chaotic system are illustrated and the dynamic properties of the highly chaotic system are discussed. The novel highly chaotic system has three unstable equilibrium points. We show that the equilibrium point at the origin is a saddle point, while the other two equilibrium points are saddle foci. The novel highly chaotic system has rotation symmetry about the \(x_3\) axis. The Lyapunov exponents of the novel highly chaotic system are obtained as \(L_1 = 11.0572\), \(L_2 = 0\) and \(L_3 = -28.0494\), while the Kaplan-Yorke dimension of the novel chaotic system is obtained as \(D_{KY} = 2.3942\). Since the Maximal Lyapunov Exponent (MLE) of the novel chaotic system has a large value, viz. \(L_1 = 11.0572\), the novel chaotic system is highly chaotic. Since the sum of the Lyapunov exponents is negative, the novel highly chaotic system is dissipative. Next, we derive new results for the global chaos control of the novel highly chaotic system with unknown parameters via adaptive control method. We also derive new results for the global chaos synchronization of the identical novel highly chaotic systems with unknown parameters via adaptive control method. The main adaptive control results are established using Lyapunov stability theory. MATLAB simulations are shown to depict the phase portraits of the novel highly chaotic system and also the adaptive control results derived in this work.

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Vorheriges Kapitel A Novel 3-D Circulant Highly Chaotic System with Labyrinth Chaos
Nächstes Kapitel Analysis, Adaptive Control and Synchronization of a Novel 3-D Chaotic System with a Quartic Nonlinearity and Two Quadratic Nonlinearities
Literatur
1.
Lorenz EN (1963) Deterministic periodic flow. J Atmos Sci 20(2):130–141CrossRef
2.
Rössler OE (1976) An equation for continuous chaos. Phys Lett A 57(5):397–398
3.
Arneodo A, Coullet P, Tresser C (1981) Possible new strange attractors with spiral structure. Commun Math Phys 79(4):573–576MathSciNetCrossRefMATH
4.
5.
6.
7.
Cai G, Tan Z (2007) Chaos synchronization of a new chaotic system via nonlinear control. J Uncertain Syst 1(3):235–240
8.
Tigan G, Opris D (2008) Analysis of a 3D chaotic system. Chaos, Solitons Fractals 36:1315–1319
9.
10.
Zhu C, Liu Y, Guo Y (2010) Theoretic and numerical study of a new chaotic system. Intell Inform Manag 2:104–109
11.
12.
Sundarapandian V (2013) Analysis and anti-synchronization of a novel chaotic system via active and adaptive controllers. J Eng Sci Technol Rev 6(4):45–52
13.
Sundarapandian V, Pehlivan I (2012) Analysis, control, synchronization, and circuit design of a novel chaotic system. Math Comput Model 55(7–8):1904–1915MathSciNetCrossRefMATH
14.
Vaidyanathan S (2013) A new six-term 3-D chaotic system with an exponential nonlinearity. Far East J Math Sci 79(1):135–143
15.
Vaidyanathan S (2013) Analysis and adaptive synchronization of two novel chaotic systems with hyperbolic sinusoidal and cosinusoidal nonlinearity and unknown parameters. J Eng Sci Technol Rev 6(4):53–65
16.
Vaidyanathan S (2014) A new eight-term 3-D polynomial chaotic system with three quadratic nonlinearities. Far East J Math Sci 84(2):219–226
17.
Vaidyanathan S (2014) Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities. Eur Phys J: Special Topics 223(8):1519–1529
18.
Vaidyanathan S (2014) Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities. Int J Model Ident Control 22(1):41–53
19.
Vaidyanathan S (2014) Generalised projective synchronisation of novel 3-D chaotic systems with an exponential non-linearity via active and adaptive control. Int J Model Ident Control 22(3):207–217
20.
Vaidyanathan S (2015) A 3-D novel highly chaotic system with four quadratic nonlinearities, its adaptive control and anti-synchronization with unknown parameters. J Eng Sci Technol Rev 8(2):106–115
21.
Vaidyanathan S (2015) Analysis, properties and control of an eight-term 3-D chaotic system with an exponential nonlinearity. Int J Model Ident Control 23(2):164–172
22.
Vaidyanathan S, Azar AT (2015) Analysis, control and synchronization of a nine-term 3-D novel chaotic system. In: Azar AT, Vaidyanathan S (eds) Chaos modelling and control systems design, Studies in computational intelligence, vol 581. Springer, Germany, pp 19–38
23.
Vaidyanathan S, Madhavan K (2013) Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system. Int J Control Theory Appl 6(2):121–137
24.
Vaidyanathan S, Pakiriswamy S (2015) A 3-D novel conservative chaotic system and its generalized projective synchronization via adaptive control. J Eng Sci Technol Rev 8(2):52–60
25.
Vaidyanathan S, Volos C (2015) Analysis and adaptive control of a novel 3-D conservative no-equilibrium chaotic system. Arch Control Sci 25(3):333–353MathSciNet
26.
Vaidyanathan S, Volos C, Pham VT, Madhavan K, Idowu BA (2014) Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities. Arch Control Sci 24(3):375–403
27.
Vaidyanathan S, Rajagopal K, Volos CK, Kyprianidis IM, Stouboulos IN (2015) Analysis, adaptive control and synchronization of a seven-term novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in LabVIEW. J Eng Sci Technol Rev 8(2):130–141
28.
Vaidyanathan S, Volos CK, Kyprianidis IM, Stouboulos IN, Pham VT (2015) Analysis, adaptive control and anti-synchronization of a six-term novel jerk chaotic system with two exponential nonlinearities and its circuit simulation. J Eng Sci Technol Rev 8(2):24–36
29.
Vaidyanathan S, Volos CK, Pham VT (2015) Analysis, adaptive control and adaptive synchronization of a nine-term novel 3-D chaotic system with four quadratic nonlinearities and its circuit simulation. J Eng Sci Technol Rev 8(2):181–191
30.
Vaidyanathan S, Volos CK, Pham VT (2015) Global chaos control of a novel nine-term chaotic system via sliding mode control. In: Azar AT, Zhu Q (eds) Advances and applications in sliding mode control systems, Studies in computational intelligence, vol 576. Springer, Germany, pp 571–590
31.
Pehlivan I, Moroz IM, Vaidyanathan S (2014) Analysis, synchronization and circuit design of a novel butterfly attractor. J Sound Vib 333(20):5077–5096CrossRef
32.
Sampath S, Vaidyanathan S, Volos CK, Pham VT (2015) An eight-term novel four-scroll chaotic system with cubic nonlinearity and its circuit simulation. J Eng Sci Technol Rev 8(2):1–6
33.
Pham VT, Vaidyanathan S, Volos CK, Jafari S (2015) Hidden attractors in a chaotic system with an exponential nonlinear term. Eur Phys J—Special Topics 224(8):1507–1517CrossRef
34.
Azar AT (2010) Fuzzy systems. IN-TECH, Vienna
35.
Azar AT, Vaidyanathan S (2015) Chaos modeling and control systems design, Studies in computational intelligence, vol 581. Springer, Germany
36.
Azar AT, Vaidyanathan S (2015) Computational intelligence applications in modeling and control, Studies in computational intelligence, vol 575. Springer, Germany
37.
Azar AT, Vaidyanathan S (2015c) Handbook of Research on advanced intelligent control engineering and automation. Advances in computational intelligence and robotics (ACIR), IGI-Global, USA
38.
Azar AT, Zhu Q (2015) Advances and applications in sliding mode control systems, Studies in computational intelligence, vol 576. Springer, Germany
39.
Zhu Q, Azar AT (2015) Complex System modelling and control through intelligent soft computations, Studies in fuzzines and soft computing, vol 319. Springer, Germany
40.
Kengne J, Chedjou JC, Kenne G, Kyamakya K (2012) Dynamical properties and chaos synchronization of improved Colpitts oscillators. Commun Nonlinear Sci Numer Simul 17(7):2914–2923MathSciNetCrossRef
41.
Sharma A, Patidar V, Purohit G, Sud KK (2012) Effects on the bifurcation and chaos in forced Duffing oscillator due to nonlinear damping. Commun Nonlinear Sci Numer Simul 17(6):2254–2269MathSciNetCrossRef
42.
Li N, Pan W, Yan L, Luo B, Zou X (2014) Enhanced chaos synchronization and communication in cascade-coupled semiconductor ring lasers. Commun Nonlinear Sci Numer Simul 19(6):1874–1883CrossRef
43.
Yuan G, Zhang X, Wang Z (2014) Generation and synchronization of feedback-induced chaos in semiconductor ring lasers by injection-locking. Optik—Int J Light Electr Optics 125(8):1950–1953CrossRef
44.
45.
Petrov V, Gaspar V, Masere J, Showalter K (1993) Controlling chaos in Belousov-Zhabotinsky reaction. Nature 361:240–243CrossRef
46.
Vaidyanathan S (2015) Adaptive synchronization of chemical chaotic reactors. Int J ChemTech Res 8(2):612–621
47.
Vaidyanathan S (2015) Anti-synchronization of Brusselator chemical reaction systems via adaptive control. Int J ChemTech Res 8(6):759–768
48.
Vaidyanathan S (2015) Dynamics and control of Brusselator chemical reaction. Int J ChemTech Res 8(6):740–749
49.
Vaidyanathan S (2015) Dynamics and control of Tokamak system with symmetric and magnetically confined plasma. Int J ChemTech Res 8(6):795–803
50.
Vaidyanathan S (2015) Synchronization of Tokamak systems with symmetric and magnetically confined plasma via adaptive control. Int J ChemTech Res 8(6):818–827
51.
Das S, Goswami D, Chatterjee S, Mukherjee S (2014) Stability and chaos analysis of a novel swarm dynamics with applications to multi-agent systems. Eng Appl Artif Intell 30:189–198CrossRef
52.
Kyriazis M (1991) Applications of chaos theory to the molecular biology of aging. Exp Gerontol 26(6):569–572CrossRef
53.
Vaidyanathan S (2015) 3-cells cellular neural network (CNN) attractor and its adaptive biological control. Int J PharmTech Res 8(4):632–640
54.
Vaidyanathan S (2015) Adaptive backstepping control of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(2):256–261
55.
Vaidyanathan S (2015) Adaptive biological control of generalized Lotka-Volterra three-species biological system. Int J PharmTech Res 8(4):622–631
56.
Vaidyanathan S (2015) Adaptive chaotic synchronization of enzymes-substrates system with ferroelectric behaviour in brain waves. Int J PharmTech Res 8(5):964–973
57.
Vaidyanathan S (2015) Adaptive synchronization of generalized Lotka-Volterra three-species biological systems. Int J PharmTech Res 8(5):928–937
58.
Vaidyanathan S (2015) Chaos in neurons and adaptive control of Birkhoff-Shaw strange chaotic attractor. Int J PharmTech Res 8(5):956–963
59.
Vaidyanathan S (2015) Lotka-Volterra population biology models with negative feedback and their ecological monitoring. Int J PharmTech Res 8(5):974–981
60.
Vaidyanathan S (2015) Synchronization of 3-cells cellular neural network (CNN) attractors via adaptive control method. Int J PharmTech Res 8(5):946–955
61.
Gibson WT, Wilson WG (2013) Individual-based chaos: Extensions of the discrete logistic model. J Theor Biol 339:84–92MathSciNetCrossRef
62.
Suérez I (1999) Mastering chaos in ecology. Ecol Model 117(2–3):305–314CrossRef
63.
Lang J (2015) Color image encryption based on color blend and chaos permutation in the reality-preserving multiple-parameter fractional Fourier transform domain. Optics Commun 338:181–192CrossRef
64.
Zhang X, Zhao Z, Wang J (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Sig Process Image Commun 29(8):902–913CrossRef
65.
Rhouma R, Belghith S (2011) Cryptoanalysis of a chaos based cryptosystem on DSP. Commun Nonlinear Sci Numer Simul 16(2):876–884MathSciNetCrossRefMATH
66.
Usama M, Khan MK, Alghatbar K, Lee C (2010) Chaos-based secure satellite imagery cryptosystem. Comput Math Appl 60(2):326–337MathSciNetCrossRefMATH
67.
Azar AT, Serrano FE (2014) Robust IMC-PID tuning for cascade control systems with gain and phase margin specifications. Neural Comput Appl 25(5):983–995CrossRef
68.
Azar AT, Serrano FE (2015) Adaptive sliding mode control of the Furuta pendulum. In: Azar AT, Zhu Q (eds) Advances and applications in sliding mode control systems, Studies in computational intelligence, vol 576. Springer, Germany, pp 1–42
69.
Azar AT, Serrano FE (2015) Deadbeat control for multivariable systems with time varying delays. In: Azar AT, Vaidyanathan S (eds) Chaos modeling and control systems design, Studies in computational intelligence, vol 581. Springer, Germany, pp 97–132
70.
Azar AT, Serrano FE (2015) Design and modeling of anti wind up PID controllers. In: Zhu Q, Azar AT (eds) Complex system modelling and control through intelligent soft computations, Studies in fuzziness and soft computing, vol 319. Springer, Germany, pp 1–44
71.
Azar AT, Serrano FE (2015) Stabilizatoin and control of mechanical systems with backlash. In: Azar AT, Vaidyanathan S (eds) Handbook of research on advanced intelligent control engineering and automation. Advances in computational intelligence and robotics (ACIR), IGI-Global, USA, pp 1–60
72.
Feki M (2003) An adaptive chaos synchronization scheme applied to secure communication. Chaos, Solitons Fractals 18(1):141–148MathSciNetCrossRefMATH
73.
Murali K, Lakshmanan M (1998) Secure communication using a compound signal from generalized chaotic systems. Phys Lett A 241(6):303–310CrossRefMATH
74.
Zaher AA, Abu-Rezq A (2011) On the design of chaos-based secure communication systems. Commun Nonlinear Syst Numer Simul 16(9):3721–3727MathSciNetCrossRefMATH
75.
Mondal S, Mahanta C (2014) Adaptive second order terminal sliding mode controller for robotic manipulators. J Franklin Inst 351(4):2356–2377MathSciNetCrossRef
76.
Nehmzow U, Walker K (2005) Quantitative description of robot-environment interaction using chaos theory. Robot Auton Syst 53(3–4):177–193CrossRef
77.
Volos CK, Kyprianidis IM, Stouboulos IN (2013) Experimental investigation on coverage performance of a chaotic autonomous mobile robot. Robot Auton Syst 61(12):1314–1322CrossRef
78.
Qu Z (2011) Chaos in the genesis and maintenance of cardiac arrhythmias. Prog Biophys Mol Biol 105(3):247–257CrossRef
79.
80.
81.
Li Z, Chen G (2006) Integration of fuzzy logic and chaos theory, Studies in fuzziness and soft computing, vol 187. Springer, Germany
82.
Huang X, Zhao Z, Wang Z, Li Y (2012) Chaos and hyperchaos in fractional-order cellular neural networks. Neurocomputing 94:13–21CrossRef
83.
Kaslik E, Sivasundaram S (2012) Nonlinear dynamics and chaos in fractional-order neural networks. Neural Networks 32:245–256CrossRefMATH
84.
Lian S, Chen X (2011) Traceable content protection based on chaos and neural networks. Appl Soft Comput 11(7):4293–4301CrossRef
85.
Guégan D (2009) Chaos in economics and finance. Ann Rev Control 33(1):89–93CrossRef
86.
87.
Sundarapandian V (2010) Output regulation of the Lorenz attractor. Far East J Math Sci 42(2):289–299MathSciNetMATH
88.
Vaidyanathan S (2011) Output regulation of Arneodo-Coullet chaotic system. Commun Comput Inform Sci 133:98–107
89.
Vaidyanathan S (2011) Output regulation of the unified chaotic system. Commun Comput Inform Sci 198:1–9
90.
Sundarapandian V (2013) Adaptive control and synchronization design for the Lu-Xiao chaotic system. Lecture notes in electrical engineering, vol 131, pp 319–327
91.
Vaidyanathan S (2012) Adaptive controller and syncrhonizer design for the Qi-Chen chaotic system. Lecture notes of the institute for computer sciences, Social-informatics and telecommunications engineering, vol 84, pp 73–82
92.
Vaidyanathan S (2013) A ten-term novel 4-D hyperchaotic system with three quadratic nonlinearities and its control. Int J Control Theory Appl 6(2):97–109
93.
Vaidyanathan S (2013) Analysis, control and synchronization of hyperchaotic Zhou system via adaptive control. Adv Intell Syst Comput 177:1–10
94.
Vaidyanathan S (2014) Qualitative analysis and control of an eleven-term novel 4-D hyperchaotic system with two quadratic nonlinearities. Int J Control Theory Appl 7:35–47
95.
Vaidyanathan S, Azar AT (2015) Analysis and control of a 4-D novel hyperchaotic system. Studies in computational intelligence vol 581, pp 3–17
96.
Vaidyanathan S, Volos C, Pham VT (2014) Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation. Arch Control Sci 24(4):409–446
97.
Vaidyanathan S, Volos C, Pham VT, Madhavan K (2015) Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation. Nonlinear Dyn 25(1):135–158
98.
Vaidyanathan S, Volos CK, Pham VT (2015) Analysis, control, synchronization and SPICE implementation of a novel 4-D hyperchaotic Rikitake dynamo system without equilibrium. J Eng Sci Technol Rev 8(2):232–244
99.
Vaidyanathan S (2012) Global chaos control of hyperchaotic Liu system via sliding control method. Int J Control Theory Appl 5(2):117–123
100.
Vaidyanathan S (2012) Sliding mode control based global chaos control of Liu-Liu-Liu-Su chaotic system. Int J Control Theory Appl 5(1):15–20
101.
Njah AN, Sunday OD (2009) Generalization on the chaos control of 4-D chaotic systems using recursive backstepping nonlinear controller. Chaos, Solitons Fractals 41(5):2371–2376CrossRefMATH
102.
Vaidyanathan S, Idowu BA, Azar AT (2015) Backstepping controller design for the global chaos synchronization of Sprott’s jerk systems. Studies in computational intelligence, vol 581, pp 39–58
103.
Vincent UE, Njah AN, Laoye JA (2007) Controlling chaos and deterministic directed transport in inertia ratchets using backstepping control. Phys D 231(2):130–136MathSciNetCrossRefMATH
104.
Karthikeyan R, Sundarapandian V (2014) Hybrid chaos synchronization of four-scroll systems via active control. J Electr Eng 65(2):97–103
105.
Sarasu P, Sundarapandian V (2011) Active controller design for generalized projective synchronization of four-scroll chaotic systems. Int J Syst Signal Control Eng Appl 4(2):26–33
106.
Sarasu P, Sundarapandian V (2011) The generalized projective synchronization of hyperchaotic Lorenz and hyperchaotic Qi systems via active control. Int J Soft Comput 6(5):216–223
107.
Vaidyanathan S, Rajagopal K (2011) Hybrid synchronization of hyperchaotic Wang-Chen and hyperchaotic Lorenz systems by active non-linear control. Int J Syst Signal Control Eng Appl 4(3):55–61
108.
Vaidyanathan S, Rasappan S (2011) Global chaos synchronization of hyperchaotic Bao and Xu systems by active nonlinear control. Commun Comput Inform Sci 198:10–17CrossRef
109.
Vaidyanathan S, Azar AT, Rajagopal K, Alexander P (2015) Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control. Int J Model Ident Control 23(3):267–277
110.
Vaidyanathan S, Pham VT, Volos CK, (2015) A 5-D hyperchaotic Rikitake dynamo system with hidden attractors. Eur Phys J: Special Topics 224(8):1575–1592
111.
Sarasu P, Sundarapandian V (2012) Generalized projective synchronization of two-scroll systems via adaptive control. Int J Soft Comput 7(4):146–156CrossRef
112.
Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of hyperchaotic Lorenz and hyperchaotic Chen systems by adaptive control. Int J Syst Signal Control Eng Appl 4(2):18–25
113.
Sundarapandian V, Karthikeyan R (2011) Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control. Eur J Sci Res 64(1):94–106
114.
Sundarapandian V, Karthikeyan R (2012) Adaptive anti-synchronization of uncertain Tigan and Li systems. J Eng Appl Sci 7(1):45–52CrossRefMATH
115.
Vaidyanathan S (2012) Anti-synchronization of Sprott-L and Sprott-M chaotic systems via adaptive control. Int J Control Theory Appl 5(1):41–59
116.
Vaidyanathan S (2015) Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities. Int J Model Ident Control 23(4):380–392
117.
Vaidyanathan S, Pakiriswamy S (2013) Generalized projective synchronization of six-term Sundarapandian chaotic systems by adaptive control. Int J Control Theory Appl 6(2):153–163
118.
Vaidyanathan S, Rajagopal K (2012) Global chaos synchronization of hyperchaotic Pang and hyperchaotic Wang systems via adaptive control. Int J Soft Comput 7(1):28–37CrossRefMATH
119.
Sundarapandian V, Sivaperumal S (2011) Sliding controller design of hybrid synchronization of four-wing chaotic systems. Int J Soft Comput 6(5):224–231CrossRef
120.
Vaidyanathan S (2014) Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control. Int J Model Ident Control 22(2):170–177
121.
Vaidyanathan S, Sampath S (2012) Anti-synchronization of four-wing chaotic systems via sliding mode control. Int J Autom Comput 9(3):274–279CrossRef
122.
Vaidyanathan S, Sampath S, Azar AT (2015) Global chaos synchronisation of identical chaotic systems via novel sliding mode control method and its application to Zhu system. Int J Model Ident Control 23(1):92–100
123.
Rasappan S, Vaidyanathan S (2013) Hybrid synchronization of \(n\)-scroll Chua circuits using adaptive backstepping control design with recursive feedback. Malays J Math Sci 73(1):73–95MathSciNet
124.
Rasappan S, Vaidyanathan S (2014) Global chaos synchronization of WINDMI and Coullet chaotic systems using adaptive backstepping control design. Kyungpook Math J 54(1):293–320
125.
Suresh R, Sundarapandian V (2013) Global chaos synchronization of a family of \(n\)-scroll hyperchaotic Chua circuits using backstepping control with recursive feedback. Far East J Math Sci 7(2):219–246MathSciNetMATH
126.
Vaidyanathan S, Rasappan S (2014) Global chaos synchronization of \(n\)-scroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arab J Sci Eng 39(4):3351–3364CrossRef
127.
Khalil HK (2001) Nonlinear systems, 3rd edn. Prentice Hall, New Jersey
Metadaten
Titel
Dynamic Analysis, Adaptive Control and Synchronization of a Novel Highly Chaotic System with Four Quadratic Nonlinearities
verfasst von
Sundarapandian Vaidyanathan
Copyright-Jahr
2016
Buch
Advances in Chaos Theory and Intelligent Control

Print ISBN: 978-3-319-30338-3

Electronic ISBN: 978-3-319-30340-6

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-30340-6_17