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Control of Oscillations and Chaos, 1997. Proceedings., 1997 1st International Conference

Date 27-29 Aug. 1997

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  • 1997 1st International Conference, Control of Oscillations and Chaos Proceedings (Cat. No.97TH8329)

    Publication Year: 1997
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    Freely Available from IEEE
  • Index [of authors]

    Publication Year: 1997 , Page(s): 0_19 - 0_22
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    Freely Available from IEEE
  • A kth order reaction: application of high codimension bifurcation theory

    Publication Year: 1997 , Page(s): 508 - 511 vol.3
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    High codimension bifurcation theory is applied to a PI controlled continuous stirred tank reactor with an exothermic kth order reaction, in order to explain the arising complex dynamic phenomena. Special attention is paid to the detection of high codimension bifurcations View full abstract»

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  • Chaotic and stochastic processes: Markov modeling approach

    Publication Year: 1997 , Page(s): 488 - 491 vol.3
    Cited by:  Papers (1)
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    This paper focuses on a modeling approach being investigated for chaotic and stochastic dynamic systems. A novel approach of applying Markov chains to these systems is proposed. Equivalent transformation from the Markov model to a parametric model is also discussed View full abstract»

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  • Bifurcation analysis of low-order nonlinear control systems with delay

    Publication Year: 1997 , Page(s): 478 - 483 vol.3
    Cited by:  Papers (1)
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    Some well known results of bifurcation theory are applied in terms of classical frequency domain tools of control engineering. Attention is paid to delayed low-order systems with saturation nonlinearities. The analysis shows the effect of the delay in the parametric stability regions of the system View full abstract»

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  • Dynamic Green's function method applied to vibrations of piezoelectric shells

    Publication Year: 1997 , Page(s): 381 - 388 vol.3
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    In order to efficiently calculate thermoelastic deformations and also Green's functions Maysel's formula is a proper tool in many applications. It can be embedded within multiple field analyses when considering the isothermal background. By generalizing Maysel's formula, it becomes possible to include both the piezoelectric effects and inertia Either some or each of the layers of a composite shell made of piezoelectric materials behave as distributed actuators so that the shell becomes an intelligent or smart structure. To extinguish vibrations say of a shell, an electrical field with a proper control must be applied. The construction of dynamic Green's functions makes the mechanical part of the control problem readily available. A version of that multiple field analysis is presented with the best auxiliary problem constructed in the background. In such a manner, all kinds of symmetries present in the actual coupled problem are preserved, and, for the sake of simplifying the auxiliary problem, constraints on the shell are relaxed. The three-dimensional formulation is at first specialized for the case of thin layered shells of revolution, and applied to an infinite circular cylindrical shell with two ring supports, the piezoelectric influence function being derived. Solutions of the (relaxed) auxiliary problem are more readily available in the frequency space. As a consequence, the time convolution in the dynamic version of Maysel's formula is replaced by a Fourier integral, which is eventually subjected to the fast Fourier transformation View full abstract»

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  • Structural turbulence in boundary value problems

    Publication Year: 1997 , Page(s): 492 - 497 vol.3
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    Consideration is given to certain boundary value problems for a PDE description of the turbulent processes in ideal media, specifically, in idealized electric circuits with distributive parameters. We describe properties of attractors of individual trajectories and of a global attractor for the infinite dimensional dynamical system induced by these problems. In particular, we evaluate their topological characteristics (entropy, fractal dimension, etc.). We discuss scenarios for self-birthing structures and describe the spatial-temporal evolution of structures. We consider a self-stochasticity phenomenon based on the fact that the attractor of a deterministic system contains random functions View full abstract»

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  • Bounded tracking controllers for the chaotic (forced) Duffing equation

    Publication Year: 1997 , Page(s): 415 - 418 vol.3
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    This paper deals with the design of feedback controllers for a chaotic dynamical system like the Duffing equation. Lyapunov theory is used to show that the proposed bounded controllers achieve global convergence for any desired trajectory. Some simulation examples illustrate the presented ideas View full abstract»

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  • Rejection of bounded harmonic external disturbances with unknown frequencies and amplitudes

    Publication Year: 1997 , Page(s): 461 - 464 vol.3
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    For linear time-invariant multivariable systems the problem of rejection bounded harmonic external disturbances with unknown frequencies and amplitudes is formulated. Its solution is based on H suboptimal control by appropriate choice of weighting matrices View full abstract»

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  • A control engineering approach to the control and synchronization of chaos using the MCS algorithm

    Publication Year: 1997 , Page(s): 423 - 426 vol.3
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    This paper is concerned with the problem of controlling and synchronizing chaotic systems through an appropriately synthesized adaptive strategy, namely the minimal control synthesis (MCS) algorithm is used to solve the stated problem. First, a traditional control strategy is used, which does not rely on any explicit property of chaotic systems, except for the boundedness of chaotic evolution. Next, by assuming the plant to be chaotic, some properties of chaotic systems are exploited to achieve the control, as in the Ott-Grebogi-Yorke (OGY) method (1990). Hence, an adaptive control engineering approach is merged with the OGY method to control and synchronize chaotic systems View full abstract»

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  • Transition to chaos and basins of attraction in the impact oscillator

    Publication Year: 1997 , Page(s): 512 - 515 vol.3
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    The impact oscillator is the simplest mechanical system with the strong nonlinearity, which is caused by a sudden change of stiffness during the contact of impacting bodies. When the time duration of the impact is assumed negligibly short, then the Newton elementary theory of impact can be used for the investigation of the system dynamics. The paper introduces a short review of results, explains the substance of different ways from periodic to chaotic impact motions, and shows the basins of attraction in the manifold response of the system View full abstract»

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  • Neural algorithms of optimal and adaptive control of mechanical systems

    Publication Year: 1997 , Page(s): 532 - 535 vol.3
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    Methods and principles of optimal and adaptive control of mechanical systems are discussed, as well as principles of their neural implementation for optimal control in real time. Optimal programmed controllers, feedback controllers, adaptive controllers and programmers of optimal movements of nonlinear mechanical systems with reversible dynamics are synthesised. Methods of optimal and adaptive controller and programmer parameters adjustment are proposed, and parallel (neural) architectures for their implementation are discussed View full abstract»

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  • The artificial neural network for image contour extraction

    Publication Year: 1997 , Page(s): 536 - 538 vol.3
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    The solutions of some modern applied image processing problems require the use intellectual image analysis tools. We deal with one of such problems-processing of cosmic and aerial images. The possibilities of automatic interpretation of the aerial and cosmic images of the Earth surface are restricted by natural and diverse factors: seasonal, daily and other similar to image variations and geometric transformations. In automatic processing of images with complicated distortions, the traditional correlation-based image processing methods fail when dealing with the mentioned image distortions. It is shown that the analysis of curve forms which correspond to object contours on the image, is the most suitable tool for solving this problem. The neural algorithm presented was applied to contour extraction on real LANDSAT images View full abstract»

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  • PI control of periodic oscillations of relay systems

    Publication Year: 1997 , Page(s): 469 - 473 vol.3
    Cited by:  Papers (1)
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    In automatic control applications, the relay nonlinearity is used to describe a sensor or actuator behavior. Such nonlinearity combined with stabilizing feedback loops often leads to limit cycles for the closed loop system. We study the control of such limit cycles by use of a proportional+integral control law with the delayed output of a relay sensor View full abstract»

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  • Attractors of dynamical systems

    Publication Year: 1997 , Page(s): 498 - 503 vol.3
    Cited by:  Papers (1)
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    The definition of an attractor of a dissipative dynamical system is introduced. Classification of existing types of attractors and analysis of their characteristics are presented. The discussed problems are illustrated by the results of numerical simulation using a number of real examples. It gives the possibility to understand easily the main properties, similarities and differences of the considered types of attractors View full abstract»

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  • Controlling the uncertain Duffing oscillator

    Publication Year: 1997 , Page(s): 419 - 422 vol.3
    Cited by:  Papers (1)
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    In this paper, an adaptive feedback controller is developed based on the Lyapunov stability theory for an uncertain chaotic Duffing oscillator where only an approximate range of the three key system parameters are known. The proposed method can be extended to handle some other uncertain chaotic dynamical systems with mild modifications View full abstract»

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  • Dynamic forms of equilibrium of a bar compressed by a dead force

    Publication Year: 1997 , Page(s): 399 - 402 vol.3
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    The report presents the stationary solutions of nonlinear equations of motion of a console beam compressed by a dead force View full abstract»

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  • Attractor-basin and bifurcation analysis in an impact system: chaotic uncontrolled versus controlled steady response

    Publication Year: 1997 , Page(s): 582 - 585 vol.3
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    Numerical simulations are performed aimed at checking the effectiveness of a previously developed theoretical procedure for control of transient chaos in reducing also the steady-state chaotic dynamics of an impact mechanical system. Attractor-basin phase portraits and bifurcation diagrams are built to show good agreement between the theoretical predictions and the actual response of the system View full abstract»

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  • Near optimal control for resonant oscillatory systems

    Publication Year: 1997 , Page(s): 435 - 438 vol.3
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    The paper is concerned with optimal control problems for near-resonant motions of two-frequency quasi-conservative nonlinear weakly controlled systems. It is assumed that the conservative subsystem exhibits a single primary resonance with a known near resonant domain. Escape from this near resonant domain can be identified with the failure of resonance, and the main goal of the implication of control forces is to hold the system in this restricted domain. Away from the resonant domain the optimal control problems can be treated by the averaging method that is known to fail near the resonant surface. In this paper we develop a special version of the hierarchical averaging approach. The hierarchical averaging procedure is extended to the optimal control problems. As the result, the averaged system of the maximum principle is obtained, and the convergence of the approximate solution to the solution of the initial optimal control problem is proved View full abstract»

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  • On the detection of period doubling bifurcations in nonlinear feedback systems

    Publication Year: 1997 , Page(s): 465 - 468 vol.3
    Cited by:  Papers (1)
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    In this work the detection of period doubling bifurcations is obtained using a frequency domain approach. The original approach has been applied efficiently in approximating periodic solutions from Hopf bifurcations while in this paper the emphasis is in the prediction of the first period doubling sequence. An application using higher-order harmonic balance approximations (HBA) is shown for the illustration of the technique View full abstract»

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  • Learning the grammar of a chaotic dynamical system in a format suitable for controlling symbol dynamics and communications

    Publication Year: 1997 , Page(s): 573 - 577 vol.3
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    The unique possibility of encoding information into symbol dynamics corresponding to a chaotic transmitter has been demonstrated by Hayes and Grebogi (1993, 1994) and the authors (1997). To take advantage of sensitive dependence by using only small deliberate parameter perturbations requires that we respect the grammar of the symbol dynamics which represents the physical dynamical system. We present a new algorithm to learn the observed grammar of a symbol dynamics in terms of observed transitions between bins defined by the symbol generating partition View full abstract»

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  • Controlling oscillation by noncritical eigenvalue assignment

    Publication Year: 1997 , Page(s): 565 - 568 vol.3
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    Linear feedback stabilization of nonlinear systems in critical cases (NSICC) is studied in this paper. The noncritical eigenvalues are assumed completely controllable. The stability and linear feedback stabilizability are attacked by means of center manifold method and Lyapunov stability analysis. The construction of linear feedback stabilizing law is given on the basis of noncritical eigenvalue assignment View full abstract»

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  • Time-delay stabilization of the buck converter

    Publication Year: 1997 , Page(s): 590 - 593 vol.3
    Cited by:  Papers (6)
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    Time-delay autosynchronization (TDAS) can be used to stabilize unstable periodic orbits in dynamical systems. The technique involves continuous feedback of signals delayed by the orbit's period so that the feedback signal vanishes on the target periodic orbit and hence the stabilized periodic orbit is a solution of the original dynamical system. Furthermore, this control method only requires the knowledge of the period of the unstable orbit. The amount of feedback gain needed to achieve stabilization varies with the bifurcation parameter(s) of the system, resulting in a domain of control. We compute the domain of control of the unstable periodic orbits of the buck converter for a given TDAS scheme. We obtain a closed analytical expression for the curve g:S1→C whose index determines the stability, and this index is then numerically computed. We run several simulations of the controlled system and discuss the results View full abstract»

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  • Analysis of frequency-of-oscillations-controlled systems

    Publication Year: 1997 , Page(s): 439 - 441 vol.3
    Cited by:  Papers (3)
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    A number of frequency-domain criteria destined for analysis of the locking-in problem in various fields of mechanics and engineering are presented. The stabilisation of a nonlinear system by harmonic signals and the global behaviour of synchronous machine models are discussed View full abstract»

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  • Identification of a fluidized bed system: model structure and validation issues

    Publication Year: 1997 , Page(s): 516 - 521 vol.3
    Cited by:  Papers (2)
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    The identification of nonlinear polynomial models from the data of the measurement of pressure fluctuations in a 10 cm ID plexiglass fluidized bed filled with polystyrene particles is discussed. The model structure and validation issues are addressed in the light of recent developments of identification algorithms. It is shown that rather simple models can reproduce the chaotic behaviour of the aforementioned system View full abstract»

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