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1
Content available Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs - application to chaos synchronization
Moysis Lazaros, Tripathi Meenakshi, Gupta Mahendra Kumar, Marwan Muhammad, Volos Christos
Archives of Control Sciences
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2022
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Vol. 32, No. 1
105--121
EN
This work addresses the problem of adaptive observer design for nonlinear systems satisfying incremental quadratic constraints. The output of the system includes nonlinear terms, which puts an additional strain on the design and feasibility of the observer, which is guaranteed under the satisfaction of an LMI, and a set of algebraic constraints. A particular case where the output nonlinearity matches the unknown parameter coefficient is also discussed. The result is illustrated through a numerical example for the chaos synchronization of the Rössler system.
2
Content available Chaos synchronization of uncertain coronary artery systems through sliding mode
Qian D. W., Xi Y. F., Tong S. W.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2019
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Vol. 67, nr 3
455--462
EN
The chaotic phenomena of coronary artery systems are hazardous to health and may induce illness development. From the perspective of engineering, the potential harm can be eliminated by synchronizing chaotic coronary artery systems with a normal one. This paper investigates the chaos synchronization problem in light of the methodology of sliding mode control (SMC). Firstly, the nonlinear dynamics of coronary artery systems are presented. Since the coronary artery systems suffer from uncertainties, the technique of derivative-integral terminal SMC is employed to achieve the chaos synchronization task. The stability of such a control system is proven in the sense of Lyapunov. To verify the feasibility and effectiveness of the proposed method, some simulation results are illustrated in comparison with a benchmark.
3
Content available Synchronization of fractional order Rabinovich-Fabrikant systems using sliding mode control techniques
Kumar Sanjay, Singh Chaman, Prasad Sada Nand, Shekhar Chandra, Aggarwal Rajiv
Archives of Control Sciences
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2019
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Vol. 29, No. 2
307--322
EN
In this research article, we present the concepts of fractional-order dynamical systems and synchronization methodologies of fractional order chaotic dynamical systems using slide mode control techniques. We have analysed the different phase portraits and time-series graphs of fractional order Rabinovich-Fabrikant systems. We have obtained that the lowest dimension of Rabinovich-Fabrikant system is 2.85 through utilization of the fractional calculus and computational simulation. Bifurcation diagrams and Lyapunov exponents of fractional order Rabinovich-Fabrikant system to justify the chaos in the systems. Synchronization of two identical fractional-order chaotic Rabinovich-Fabrikant systems are achieved using sliding mode control methodology.
4
Content available Synchronization of an uncertain Duffing oscillator with higher order chaotic systems
Kabziński J.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 4
625--634
EN
The problem of practical synchronization of an uncertain Duffing oscillator with a higher order chaotic system is considered. Adaptive control techniques are used to obtain chaos synchronization in the presence of unknown parameters and bounded, unstructured, external disturbances. The features of the proposed controllers are compared by solving Duffing–Arneodo and Duffing–Chua synchronization problems.
5
Content available Hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems
Serrano F., Rossell J. M.
Acta Mechanica et Automatica
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2017
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Vol. 11, no. 2
96--103
EN
In this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyperchaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropria.
6
Content available Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities
Vaidyanathan S., Volos C., Pham V.-T., Madhavan K., Idowu B. A.
Archives of Control Sciences
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2014
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Vol. 24, no. 3
375--403
EN
In this research work, a six-term 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel jerk system are obtained as L1 = 0.07765,L2 = 0, and L3 = −0.87912. The Kaplan-Yorke dimension of the novel jerk system is obtained as DKY = 2.08833. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.
7
Content available Different synchronization schemes for chaotic Rikitake systems
Ali Khan M.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 2
383--393
EN
This paper presents the chaos synchronization by designing a different type of controllers. Firstly, we propose the synchronization of bi-directional coupled chaotic Rikitake systems via hybrid feedback control. Secondly, we study the synchronization of unidirectionally coupled Rikitake systems using hybrid feedback control. Lastly, we investigate the synchronization of unidirectionally coupled Rikitake chaotic systems using tracking control. Comparing all the results, finally, we conclude that tracking control is more effective than feedback control. Simulation results are presented to show the efficiency of synchronization schemes.
8
Content available Application of artificial neural networks in parametrical investigations of the energy flow and synchronization
Dąbrowski A., Jach A., Kapitaniak T.
Journal of Theoretical and Applied Mechanics
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2010
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Vol. 48 nr 4
871-896
EN
Dynamics of nonlinear systems is a very complicated problem with many aspects to be recognized. Numerous methods are used to investigate such systems. Their careful analysis is connected with long-time simulations. Thus, there is great need for methods that would simplify these processes. In the paper, an application of Artificial Neural Networks (ANNs) supporting the recognition of the energy flow and the synchronization with use of Impact Maps is introduced. This connection applies an idea of the Energy Vector Space in the system with impacts. An energy flow direction change with the synchronization as a transitional state is shown. A new type of the index allowing one to control the system dynamic state is introduced. Results of the numerical simulations are used in the neural network teaching process. Results of a comparison of the straight impact map simulation and the neural network prediction are shown. Prediction of system parameters for the energy flow synchronization state with use of the neural network is presented.
PL
Dynamika układów nieliniowych jest bardzo komplikowanymzagadnieniem z wieloma aspektami wciąż pozostającymi bez rozwiązania. Do badań takich układów stosuje się wiele różnych metod. Wnikliwa analiza związana jest najczęściej z bardzo czasochłonnymi symulacjami numerycznymi. Istnieje w związku z tym duże zapotrzebowanie na opracowanie metod upraszczających ten proces. W artykule pokazano zastosowanie sztucznych sieci neuronowych (ANN) wspomagających badania przepływu i synchronizacji energii. W badaniach zastosowano Mapy Uderzeń, będące efektem przedstawienia dynamiki układu z uderzeniami w przestrzeni energetyczno-wektorowej. Pokazano zmiany przepływu energii z przejściowym stanem synchronizacji. Wprowadzono nowy rodzaj parametru pozwalającego na określanie stanu dynamicznego układu z uderzeniami. Wyniki przeprowadzonych symulacji numerycznych zostały wykorzystane w procesie uczenia sztucznej sieci neuronowej. Przedstawiono następnie porównanie wyników symulacji i rozwiązania uzyskanego z sieci neuronowej oraz przewidywania parametrów układu, dla których występuje synchronizacja przepływu energii.
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