Synchronization of chaotic systems using fuzzy impulsive control

This study is concerned with the synchronization problem for a class of chaotic systems with multiple time-delays and transmitted noise. A dynamic compensator is proposed to achieve the synchronization between master and slave chaotic systems with multiple timedelays. First, the neural-network (NN) model is employed to approximate the chaotic systems with multiple time delays. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on the LDI state-space representation, an exponential stability criterion of error dynamics derived in terms of Lyapunov's direct method is proposed to ensure that the trajectories of the slave system can approach those of master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized to realize the exponential synchronization of the chaotic master-slave systems. Finally, this study provides a numerical example with simulations is given to illustrate the concepts discussed throughout this work.

Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

Tracking control for the output using an observer-based H ∞ fuzzy synchronization of time-varying delayed discrete- and continuous-time chaotic systems is proposed in this paper. First, from a practical point of view, the chaotic systems here consider the influence of time-varying delays, disturbances, and immeasurable states. Then, to facilitate a uniform control design approach for both discrete- and continuous-time chaotic systems, the dynamic models along with time-varying delays and disturbances are reformulated using the T-S (Takagi–Sugeno) fuzzy representation. For control design considering immeasurable states, a fuzzy observer achieves master-slave synchronization. Third, combining both a fuzzy observer for state estimation and a controller (solved from generalized kinematic constraints) output tracking can be achieved. To make the design more practical, we also consider differences of antecedent variables between the plant, observer, and controller. Finally, using Lyapunov’s stability approach, the results are sufficient conditions represented as LMIs (linear matrix inequalities). The contributions of the method proposed are threefold: (i) systemic and unified problem formulation of master-slave synchronization and tracking control for both discrete and continuous chaotic systems; (ii) practical consideration of time-varying delay, immeasurable state, different antecedent variables (of plant, observer, and controller), and disturbance in the control problem; and (iii) sufficient conditions from Lyapunov’s stability analysis represented as LMIs which are numerically solvable observer and controller gains from LMIs. We carry out numerical simulations on a chaotic three-dimensional discrete-time system and continuous-time Chua’s circuit. Satisfactory numerical results further show the validity of the theoretical derivations.

Neural-network based approach on delay-dependent robust stability criteria for dithered chaotic systems with multiple time-delay

In 2013 the Editor of Journal of Vibration and Control and SAGE became aware of a peer review ring involving assumed and fabricated identities that appeared to centre around Peter Chen at National Pingtung University of Education, Taiwan (NPUE). SAGE and the Editor then began a complex investigation into the case during the rest of 2013 and 2014. Following an unsatisfactory response from Peter Chen, NPUE was notified. NPUE were serious in addressing the Journal and SAGE’s concerns. NPUE confirmed that the institution was investigating Peter Chen. SAGE subsequently uncovered a citation ring involving the above mentioned author and others. We regret that individual authors have compromised the academic record by perverting the peer review process and apologise to readers. On uncovering problems with peer review and citation SAGE immediately put steps in place to avoid similar vulnerability of the Journal to exploitation in the future. More information may be found at www.sagepub.co.uk/JVC_Statement_2014 . The Journal and SAGE understand from NPUE that Peter Chen has resigned his post at NPUE. The following articles are retracted because after thorough investigation evidence points towards them having at least one author or being reviewed by at least one reviewer who has been implicated in the peer review ring and/or citation ring. All authors have had an opportunity to respond to the allegations and proposed actions. OnlineFirst articles (these articles will not be published in an issue) Chen CY, Chen T-H, Chen Y-H, Yu S-E and Chung P-Y (2013) Information technology system modeling an integrated C-TAM-TPB model to the validation of ocean tidal analyses Journal of Vibration and Control Epub ahead of print 7 May 2013. doi: 10.1177/1077546312472924 Chang R-F, Chen CY, Su F-P and Lin H-C (2013) A two-step approach for broadband digital signal processing technique Journal of Vibration and Control Epub ahead of print 26 April 2013. doi: 10.1177/1077546312472925 Chen TH, Chang CJ, Yu SE, Chung PY and Liu C-K (2013) Nonlinear information analysis and system management technique: the influence of design experience and control complexity Journal of Vibration and Control Epub ahead of print 12 April 2013. doi: 10.1177/1077546312473321 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of a 3T flow model using vibrating NXT: II. Model validation Journal of Vibration and Control Epub ahead of print 10 April 2013. doi: 10.1177/1077546312470481 Chen CY, Shih BY, Chen YH, Yu SE and Liu YC (2013) The exploration of 3T flow model using vibrating NXT: I. model formulation Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312467360 Lin M-L and Chen C-W (2013) Stability analysis of fuzzy-based NN modeling for ecosystems using fuzzy Lyapunov methods Journal of Vibration and Control Epub ahead of print 6 February 2013. doi: 10.1177/1077546312466687 Chen CY, Chen TH, Chen YH and Chiu J (2012) A multi-stage method for deterministic-statistical analysis: a mathematical case and measurement studies Journal of Vibration and Control Epub ahead of print 20 December 2012. doi: 10.1177/1077546312466579 Shih BY, Lin MC and Chen CY (2012) Autonomous navigation system for radiofrequency identification mobile robot e-book reader Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312466578 Chang RF, Chen CY, Su FP, Lin HC and Lu C-K (2012) Multiphase SUMO robot based on an agile modeling-driven process for a small mobile robot Journal of Vibration and Control Epub ahead of print 13 December 2012. doi: 10.1177/1077546312464993 Shih B-Y, Lin Y-K, Cheng M-H, Chen C-Y and Chiu C-P (2012) The development of an application program interactive game-based information system Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464682 Chen C-Y, Chang C-J and Lin C-H (2012) On dynamic access control in web 2.0 and cloud interactive information hub: technologies Journal of Vibration and Control Epub ahead of print 12 December 2012. doi: 10.1177/1077546312464992 Shin BY, Chen CY and Hsu KH (2012) Robot cross platform system using innovative interactive theory and selection algorithms for Android application Journal of Vibration and Control Epub ahead of print 13 November 2012. doi: 10.1177/1077546312463757 Articles published in an issue Chen C-W (2014) Applications of neural-network-based fuzzy logic control to a nonlinear time-delay chaotic system Journal of Vibration and Control 20 (4): 589-605. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312461370 Chen C-W (2014) A review of intelligent algorithm approaches and neural-fuzzy stability criteria for time-delay tension leg platform systems Journal of Vibration and Control 20 (4): 561-575. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463759 Chen C-Y, Chang C-J and Lin C-H (2014) On dynamic access control in web 2.0 and cloud interactive information hub: trends and theories Journal of Vibration and Control 20 (4): 548-560. Epub ahead of print 5 November 2012. doi: 10.1177/1077546312463762 Lin M-L and Chen C-W (2014) Stability conditions for ecosystem modeling using the fuzzy Lyapunov method Journal of Vibration and Control 20 (2): 290-302. Epub ahead of print 23 October 2012. doi: 10.1177/1077546312451301 Chen C-H, Kuo C-M, Hsieh S-H and Chen C-Y (2014) Highly efficient very-large-scale integration (VLSI) implementation of probabilistic neural network image interpolator Journal of Vibration and Control 20 (2): 218-224. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312458822 Chen C-Y (2014) Wave vibration and simulation in dissipative media described by irregular boundary surfaces: a mathematical formulation Journal of Vibration and Control 20 (2): 191-203. Epub ahead of print 22 October 2012. doi: 10.1177/1077546312464258 Chen C-H, Yao T-K, Dai J-H and Chen C-Y (2014) A pipelined multiprocessor system- on-a-chip (SoC) design methodology for streaming signal processing Journal of Vibration and Control 20 (2): 163-178. Epub ahead of print 16 October 2012. doi: 10.1177/1077546312458821 Lin M-L and Chen C-W (2014) Fuzzy neural modeling for n-degree ecosystems using the linear matrix inequality approach Journal of Vibration and Control 20 (1): 82-93. Epub ahead of print 8 October 2012. doi: 10.1177/1077546312458533 Chen C-H, Wu W-X and Chen C-Y (2013) Ant-inspired collective problem-solving systems Journal of Vibration and Control 19 (16): 2481-2490. Epub ahead of print 18 September 2012. doi: 10.1177/1077546312456231 Chen C-H, Yao T-K, Kuo C-M and Chen C-Y (2013) Evolutionary design of constructive multilayer feedforward neural network Journal of Vibration and Control 19 (16): 2413-2420. Epub ahead of print 12 September 2012. doi: 10.1177/1077546312456726 Chen C-W (2013) Applications of the fuzzy-neural Lyapunov criterion to multiple time-delay systems Journal of Vibration and Control 19 (13): 2054-2067. Epub ahead of print 16 August 2012. doi: 10.1177/1077546312451034 Chung P-Y, Chen Y-H, Walter L and Chen C-Y (2013) Influence and dynamics of a mobile robot control on mechanical components Journal of Vibration and Control 19 (13): 1923-1935. Epub ahead of print 20 July 2012. doi: 10.1177/1077546312452184 Chen C-W (2013) Neural network-based fuzzy logic parallel distributed compensation controller for structural system Journal of Vibration and Control 19 (11): 1709-1727. Epub ahead of print 22 June 2012. doi: 10.1177/1077546312442233 Chen C-W, Yeh K, Yang H-C, Liu KFR and Liu C-C (2013) A critical review of structural system control by the large-scaled neural network linear-deferential-inclusion-based criterion Journal of Vibration and Control 19 (11): 1658-1673. Epub ahead of print 18 June 2012. doi: 10.1177/1077546312443377 Chen C-H, Kuo C-M, Chen C-Y and Dai J-H (2013) The design and synthesis using hierarchical robotic discrete-event modeling Journal of Vibration and Control 19 (11): 1603-1613. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449645 Chang CJ, Chen CY and Chou I-T (2013) The design of information and communication technologies: telecom MOD strength machines Journal of Vibration and Control 19 (10): 1499-1513. Epub ahead of print 27 June 2012. doi: 10.1177/1077546312449644 Shih B-Y, Chen C-Y, Li K-H, Wu T-Y, Chen G-Y (2013) A novel NXT control method for implementing force sensing and recycling in a training robot Journal of Vibration and Control 19 (10): 1443-1459. Epub ahead of print 1 June 2012. doi: 10.1177/1077546312446361 Chen C-W, Chen P-C and Chiang W-L (2013) Modified intelligent genetic algorithm-based adaptive neural network control for uncertain structural systems Journal of Vibration and Control 19 (9): 1333-1347. Epub ahead of print 31 May 2012. doi: 10.1177/1077546312442232 Chen C-Y, Shih B-Y, Shih C-H and Wang L-H (2013) Enhancing robust and stability control of a humanoid biped robot: system identification approach. Journal of Vibration and Control 19 (8): 1199-1207. Epub ahead of print 26 April 2012. doi: 10.1177/1077546312442947 Chang C-J, Chen C-Y and Huang C-W (2013) Applications for medical recovery using wireless control of a bluetooth ball with a hybrid G-sensor and human-computer interface technology Journal of Vi

Retraction notice

Many bridges in Taiwan have been in use from the period that Taiwan was governed by the Japanese, over 50 years ago, which is the average ultimate usable lifetime of such structures. Three-quarters of the bridges on major highways have been in use for more than 20 years and numerous bridges on country roads have also been in use for more than 20 years. In other words, most of the bridges in Taiwan are aging and may require repair or replacement. Ambient vibration tests are utilized to measure the response of old bridges, which are difficult to equip with accelerometers. The Fourier transform method is traditionally used to gain important information about ambient vibration records. However, the development of information technology over the last 20 years has meant that there are more kinds of signal management technologies, including the wavelet and Hilbert—Huang transform (HHT) methods. In this study we investigate the characteristics of aging bridges by comparison with their structural properties. We analyze their ambient vibration, and discuss the possible influence of the frequency function. Long-term environmental impacts create many structural problems, but with traditional methods examination of bridge health is difficult. Therefore, in our HHT management system, we examine destroyed bridges. The characteristics and behavior of bridges subjected to random loading can be understood by analysis with the random decrement technique and the frequency response function method.

Retraction notice

In this paper a topic regarding the synchronization of chaotic systems is dealt with: the case of separation and synchronization of many chaotic signals generated by different chaotic circuits and combined together is examined. In particular, an observer based strategy has been adopted, and an approach for the simultaneous stabilization of many Luenberger observers has been investigated to face the problem of separation and synchronization. The design strategy is based on linear matrix inequalities (LMIs). Indeed, the LMI problem is referred to have a solution if a dual optimization problem admits a solution. In our case the feasibility condition, if it does exist, allows us to establish that the separation and synchronization problem for the chosen circuit admits a solution. Some numerical simulations are reported. Further results refer to an experimental circuit showing the suitability of the approach. Furthermore, the use of the proposed scheme to transmit two or more information masked into two or more multiplexed chaotic signals and the design of suitable parameters through the introduced technique based on LMIs are discussed.

This paper proposes a new finite-time controller that realizes multi-switching synchronization of chaotic systems with bounded disturbances using the drive and response system synchronization arrangement. The finite-time controller derives the synchronization error to zero within a specified time. The proposed controller consists of three basic terms; each of them accomplishes a distinct objective: (1) stability of the control loop, (2) smooth and fast convergence behavior of the synchronization error, and (3) disturbance rejection. This study also devises a methodology for designing the finite-time controller and describes a general approach that furnishes a systematic procedure for the analysis of the closed loop. The smooth behavior terminology introduced in (2) refers to the over-damped convergence of the synchronization error signals to zero and the synthesis of chattering-free control effort. The analysis, which assures the global stability of the closed loop, uses the second stability theorem of the Lyapunov, while the finite-time stability technique determines the finite-time convergence. This paper includes simulations of two numerical examples for the validation of the theoretical findings and discusses the comparative analysis. The proposed methodology is suitable to design controllers for a wide range of hyper(chaotic) systems. The contributions of the paper are: (1) describe an innovative generalize analytical methodology for the multi-switching combination synchronization of chaotic systems and (2) propose a novel controller design that insures the finite-time synchronization.

In this paper, fuzzy impulsive control is used for stabilization of chaotic systems based on the Takagi-Sugeno (T-S) model. The stability issue of the general nonlinear impulsive control system is first investigated via comparison criterion. Then, a novel impulsive control scheme is presented for chaotic systems based on the T-S fuzzy model. Some sufficient conditions are given to stabilize the T-S fuzzy model. Our results are proven to be less conservative theoretically and numerically. Moreover, we have also estimated the stable region of the impulsive interval. Finally, the proposed fuzzy impulsive control scheme is successfully applied to stabilize Rössler's system and Chua's circuit. The numerical simulations demonstrate the effectiveness and advantage of our main results.

In this research work, we announce a six-term novel 3-D dissipative chaotic system with two quadratic nonlinearities. First, this work describes the dynamic equations and qualitative properties of the novel chaotic system. We show that the novel chaotic system has three unstable equilibrium points. We also show that the novel chaotic system has a rotation symmetry about the \(x_3\) axis. The Lyapunov exponents of the novel chaotic system are obtained as \(L_1 = 1.2334, L_2 = 0\) and \(L_3 = -4.7329\). Since the sum of the Lyapunov exponents is negative, the novel chaotic system is dissipative. Also, the Kaplan-Yorke dimension of the novel chaotic system is derived as \(D_{KY} = 2.2606\). Next, this work describes the active synchronization of identical novel chaotic systems with known parameters. Furthermore, this work describes the adaptive synchronization of identical novel chaotic systems with unknown parameters. Both the active and adaptive synchronization results are established using Lyapunov stability theory. MATLAB simulations are depicted to illustrate all the main results derived in this work for the six-term novel 3-D novel chaotic system.

In this paper, we present the Takagi–Sugeno (T–S) fuzzy observed based design and synchronization of chaotic and hyper chaotic dynamical systems. Using T–S fuzzy observed based design, the fuzzy logic controllers for chaotic synchronization are constructed via linear matrix inequality (LMI). Lyapunov exponents of 3D and 4D Chen systems have been calculated. This represents the chaoticity and hyper chaoticity of Chen systems. Analytical and computational studies of chaotic and hyper chaotic Chen systems have been performed by using LMI toolbox. The qualitative and simulated results show the validity and the performance of the proposed observer in an excellent agreement.

In this paper, we propose a control method for the synchronization of chaotic systems that does not require the systems to be connected, unlike existing methods such as that proposed by Pecora and Carroll in 1990. The method is based on the reinforcement learning algorithm. We apply our method to two discrete-time chaotic systems with mismatched parameters and achieve M step delay synchronization. Moreover, we extend the proposed method to the synchronization of continuous-time chaotic systems.

The coexistence of anti-synchronization and synchronization in chaotic systems is investigated. A novel algorithm is proposed to determine the variables of the master system that should anti-synchronize with corresponding variables of the slave system. Control strategies that guarantee the coexistence of synchronization and anti-synchronization in the unified chaotic system are presented; while numerical simulations are employed to validate and illustrate the effectiveness of the proposed method.