Showing papers in "IEEE Transactions on Circuits and Systems I-regular Papers in 1997"
TL;DR: The topic of synchronization of the response of systems has received considerable attention and this concept is revisited in the light of the classical notion of observers from (non)linear control theory.
Abstract: In the literature on dynamical systems analysis and the control of systems with complex behavior, the topic of synchronization of the response of systems has received considerable attention. This concept is revisited in the light of the classical notion of observers from (non)linear control theory,.
716 citations
TL;DR: In this article, several theorems on the stability of impulsive control systems are presented, which are then used to find the conditions under which the chaotic systems can be asymptotically controlled to the origin.
Abstract: Impulsive control of a chaotic system is ideal for designing digital control schemes where the control laws are generated by digital devices which are discrete in time. In this paper, several theorems on the stability of impulsive control systems are presented. These theorems are then used to find the conditions under which the chaotic systems can be asymptotically controlled to the origin by using impulsive control. Given the parameters of the chaotic system and the impulsive control law, an estimation of the upper bound of the impulse interval is given. We also present a theory of impulsive synchronization of two chaotic systems. A promising application of impulsive synchronization of chaotic systems to a secure communication scheme is presented. In this secure communication scheme, the transmitted signals are divided into small time frames. In each time frame, the synchronization impulses and the scrambled message signal are embedded. Conventional cryptographic methods are used to scramble the message signal. Simulation results based on a typical chaotic system; namely, Chua's oscillator, are provided.
715 citations
TL;DR: It is shown that, by inserting a nonlinear term of the system state in the MIMO linear sliding mode, a new terminal sliding mode is developed for MIMo linear systems.
Abstract: A new terminal sliding mode control of MIMO linear systems is proposed in this paper. It is shown that, by inserting a nonlinear term of the system state in the MIMO linear sliding mode, a new terminal sliding mode is developed for MIMO linear systems. A terminal sliding mode controller can then be designed to drive the system state variables to reach and retain in the terminal sliding mode. By suitably designing the parameter matrices of the terminal sliding mode, the system state variables reach the system origin in finite time and the closed loop system is infinite stable in the terminal sliding mode.
447 citations
TL;DR: In this paper, the authors evaluated the impact of chaotic spreading codes on communication systems with asynchronous code division multiple access (CDMA) using a truncated and quantized chaotic time series.
Abstract: This paper and its companion are devoted to the evaluation of the impact of chaos-based techniques on communications systems with asynchronous code division multiple access. Sequences obtained by repeating a truncated and quantized chaotic time series are compared with classical m-sequences and Gold sequences by means of a performance index taken from communication theory which is here defined and thoroughly discussed. This analysis reveals that, unlike conventional sequences, chaotic spreading codes can be generated for any number of users and allocated bandwidth. Numerical simulations are reported, showing that systems based on chaotic spreading sequences perform generally better than the conventional ones. Some analytical tools easing the comprehension of these advantages are summarized.
363 citations
TL;DR: A new chaos-based secure communication scheme is proposed in an attempt to thwart the attacks proposed recently, but the transmitted signal is not used to encrypt the message and a more complicated method of encryption is used.
Abstract: In this letter, a new chaos-based secure communication scheme is proposed in an attempt to thwart the attacks proposed recently. Instead of encoding the message signal in a chaotic system directly, we use two chaotic signals in our scheme. One of the chaotic signals is used to synchronize the chaotic encrypter and the chaotic decrypter. The other is used to encrypt the plain signal by using a multishift cipher scheme. Thus the transmitted signal is not used to encrypt the message and a more complicated method of encryption is used.
342 citations
TL;DR: A unified approach for the analysis and comparison of conventional and chaotic communications systems is provided to clarify the role of synchronization and to classify possible demodulation methods for chaotic communications.
Abstract: In a digital communications system, data is transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample functions sent through the channel are weighted sums of one or more sinusoids; in a chaotic communications system, the sample functions are segments of chaotic waveforms. At the receiver, the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by noncoherent detection, where one or more characteristics of the sample functions are estimated. In a coherent receiver, synchronization is the most commonly used technique for recovering the sample functions from the received waveform. These sample functions are then used as reference signals for a correlator. Synchronization-based receivers have advantages over noncoherent ones in terms of noise performance and bandwidth efficiency. These advantages are lost if synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communication without synchronization may be preferable. The main aim of this paper is to provide a unified approach for the analysis and comparison of conventional and chaotic communications systems. In Part I, the operation of sinusoidal communications techniques is surveyed in order to clarify the role of synchronization and to classify possible demodulation methods for chaotic communications.
335 citations
TL;DR: In this article, control theory is used to formalize hyperchaos synchronization as a nonlinear observer design issue and a new systematic tool to synchronize a class of hyperchaotic systems via a scalar transmitted signal is developed.
Abstract: In this work control theory is used to formalize hyperchaos synchronization as a nonlinear observer design issue. Following this approach, a new systematic tool to synchronize a class of hyperchaotic systems via a scalar transmitted signal is developed. The proposed technique has been applied to synchronize two well-known hyperchaotic systems.
250 citations
TL;DR: The design and experimental verification of a 50 kHz prototype system is presented, and quantitative performance comparisons are made between synchronized clocking, independent clocked, and interleaved clocking of the converter cells.
Abstract: This paper introduces a distributed approach to interleaving paralleled power converter cells. Unlike conventional methods, the distributed approach requires no centralized control, automatically accommodates varying numbers of converter cells, and is highly tolerant of subsystem failures. A general methodology for achieving distributed interleaving is proposed, along with a specific implementation approach. The design and experimental verification of a 50 kHz prototype system is presented, and quantitative performance comparisons are made between synchronized clocking, independent clocking, and interleaved clocking of the converter cells. The experimental results corroborate the analytical predictions and demonstrate the tremendous benefits of the distributed interleaving approach.
236 citations
TL;DR: In this article, a new CMOS rail-to-rail second generation current conveyor circuits are proposed, which operate from supply voltages down to +1.1 V with standby current of 56 /spl mu/A.
Abstract: New CMOS rail to rail second generation current conveyor circuits are proposed. First a class A current conveyor circuit which operates from a single supply of 1.5 V with a rail to rail voltage swing capability is given. The circuit is then modified to work as a class AB while maintaining the rail to rail swing capability. The class AB circuit works from supply voltages down to +1.1 V with standby current of 56 /spl mu/A. These new current conveyor realizations are insensitive to the threshold voltage variation caused by the body effect, which minimizes the layout area and makes both circuits a valuable addition to the analog VLSI libraries. PSpice simulation confirms the attractive properties of the proposed circuits.
236 citations
TL;DR: In this article, an integrated noise source (INS) was fabricated in a standard 1.2 /spl mu/m digital CMOS technology, which was coupled into a comparator to generate a random digital bit stream.
Abstract: An integrated noise source (INS) has been fabricated in a standard 1.2 /spl mu/m digital CMOS technology. Wideband white noise is generated from the amplified thermal noise of large resistors, which in turn is coupled into a comparator to generate a random digital bit stream. The INS generates 100 mV rms of analog output noise over a bandwidth of 3.2 MHz and operates from a single 5 V power supply with a quiescent current of 7.4 mA. The circuit has an area of 2.92 mm/sup 2/. Potential applications of the INS include data encryption, mathematical simulation, and circuit test and measurement.
205 citations
TL;DR: In this paper, the generalized state-space averaging (GSSA) method is applied to power electronic converters and shown to work well only within specific converter topologies and parametric limits, where the model approximation order is not defined by the topology number of components.
Abstract: Power electronic converters are periodic time-variant systems, because of their switching operation. The generalized state-space averaging method is a way to model them as time independent systems, defined by a unified set of differential equations, capable of representing circuit waveforms. Therefore, it can be a convenient approach for designing controllers to he applied to switched converters. This brief shows that the generalized state-space averaging method works well only within specific converter topologies and parametric limits, where the model approximation order is not defined by the topology number of components. This point is illustrated with detailed examples from several basic dc/dc converter topologies.
TL;DR: In this paper, the authors studied the bifurcation paths exhibited by a simple second-order DC/DC boost converter under current-programmed control with and without voltage feedback.
Abstract: This paper studies the bifurcation paths exhibited by a simple second-order DC/DC boost converter under current-programmed control with and without voltage feedback. Previous work in this area has reported two distinct types of bifurcation paths, namely via regions of quasi-periodic orbits and period-doubling. This paper demonstrates that the two different types of bifurcation paths can, in fact, be viewed as part of another bifurcation in which the quasi-periodic sequence transmutes into the period-doubling sequence, and that such a bifurcation is observed regardless of the presence of the outer voltage feedback loop as long as a suitable set of bifurcation parameters is chosen. The describing iterative map is derived in closed form and is used to develop the main results via a series of computer experiments. The characteristic multipliers are calculated and the first onset of flip-bifurcation is predicted. Computer simulation based on an exact piecewise switched model confirms the predicted bifurcations. The exhibition of quasi-periodic orbits is confirmed by computation of the Lyapunov exponent. Finally, a series of return maps are generated to provide an alternative viewpoint to the reported bifurcations in terms of a transmutation from a tent-like map to a logistic-like map.
TL;DR: A method of robust nonlinear H/sub /spl infin// master-slave synchronization for chaotic Lur'e systems with applications to secure communication and the controllers are designed by solving a nonlinear optimization problem which takes into account both channel noise and parameter mismatch.
Abstract: We propose a method of robust nonlinear H/sub /spl infin// master-slave synchronization for chaotic Lur'e systems with applications to secure communication. The scheme makes use of vector field modulation and either full static state or linear dynamic output error feedback control. The master-slave systems are assumed to be nonidentical and channel noise is taken into account. Binary valued continuous time message signals are recovered by minimizing the L/sub 2/-gain from the exogenous input to the tracking error for the standard plant representation of the scheme. The exogenous input takes into account the message signal, channel noise and parameter mismatch. Matrix inequality conditions for dissipativity with finite L/sub 2/-gain of the standard plant form are derived based on a quadratic storage function. The controllers are designed by solving a nonlinear optimization problem which takes into account both channel noise and parameter mismatch. The method is illustrated on Chua's circuit.
TL;DR: In this paper, the Lyapunov exponents transversal to the synchronization manifold are used to explain the locally riddled basins of attraction in skew tent maps, leading to quite different global dynamic behavior especially when the ideal system is perturbed by parameter mismatch or noise.
Abstract: In this tutorial paper, various phenomena linked to the synchronization of chaotic systems are discussed using the simple example of two coupled skew tent maps. The phenomenon of locally riddled basins of attraction is explained using the Lyapunov exponents transversal to the synchronization manifold. The skew tent maps are coupled in two different ways, leading to quite different global dynamic behavior especially when the ideal system is perturbed by parameter mismatch or noise. The linear coupling leads to intermittent desynchronization bursts of large amplitude, whereas for the nonlinear coupling the synchronization error is asymptotically uniformly bounded.
TL;DR: This paper indicates how to extend the original subspace-based approach to the general case of blind identification of multiple input multiple output linear finite impulse response systems having a number of inputs less than the number of outputs.
Abstract: This contribution addresses the blind identification of multiple input multiple output linear finite impulse response systems having a number of inputs less than the number of outputs. Recent publications have proposed an efficient second-order identification method in the single input multiple output case. Based on a subspace analysis, it allows a perfect recovery of the system parameters and excitation in a noise-free environment. Some extensions to the case of multiple inputs are also available under quite specific conditions. In this paper we indicate how to extend the original subspace-based approach to the general case.
TL;DR: In this article, a formal study of the theoretical performance of switched-capacitor (SC) dc-dc voltage multiplier circuits is given, and a question concerning the necessary number of circuit elements to realize a given conversion ratio is addressed.
Abstract: A formal study of the theoretical performance of switched-capacitor (SC) dc-dc voltage multiplier circuits is given. A question concerning the necessary number of circuit elements to realize a given conversion ratio is addressed. In response to the question the bound on attainable voltage ratio for a given number of capacitors k and the bound on the number of switches required in any circuit configuration have been established. The maximum step-up or step-down ratio is given by the kth Fibonacci number, while the bound on the number of switches required in any SC circuit is 3k-2. The complete set of attainable DC conversion ratios is found. A canonical circuit realization of the maximum voltage ratio is discussed and illustrative examples are included. Necessary and sufficient conditions for the realizability of a dc conversion ratio are determined and formal proofs are given.
TL;DR: An upper bound on parameter variations which guarantees the asymptotic stability of a perturbed 2-D discrete system is considered and it is shown that the upper bound stated here is less conservative than the existing ones.
Abstract: Based on the Fornasini-Marchesini second local state-space (LSS) model, criteria that sufficiently guarantee the asymptotic stability of 2-D discrete systems are given. A sufficient condition for a 2-D nonlinear discrete system to be free of overflow oscillations is then shown in the case when a 2-D discrete system is employed by saturation arithmetic. Finally, an upper bound on parameter variations which guarantees the asymptotic stability of a perturbed 2-D discrete system is considered. It is shown that the upper bound stated here is less conservative than the existing ones.
TL;DR: In this paper, a new approach for communication using chaotic signals is presented, in which the transmitter contains a chaotic oscillator with a parameter that is modulated by an information signal.
Abstract: In this paper, a new approach for communication using chaotic signals is presented. In this approach, the transmitter contains a chaotic oscillator with a parameter that is modulated by an information signal. The receiver consists of a synchronous chaotic subsystem augmented with a nonlinear filter for recovering the information signal. The general architecture is demonstrated for Lorenz and Rossler systems using numerical simulations. An electronic circuit implementation using Chua's circuit is also reported, which demonstrates the practicality of the approach.
TL;DR: In this article, a Wiener system consisting of a linear dynamic subsystem followed by a memoryless nonlinear one is identified, where the a priori information about both the impulse response of the dynamic part of the system and the nonlinear characteristics is nonparametric.
Abstract: A Wiener system, i.e., a system consisting of a linear dynamic subsystem followed by a memoryless nonlinear one is identified. The system is driven by a stationary white Gaussian stochastic process and is disturbed by Gaussian noise. The characteristic of the nonlinear part can be of any form. The dynamic subsystem is asymptotically stable. The a priori information about both the impulse response of the dynamic part of the system and the nonlinear characteristics is nonparametric. Both subsystems are identified from observations taken at the input and output of the whole system. The kernel regression estimate is applied to estimate the invertible part of the nonlinearity. An estimate to recover the impulse response of the dynamic part is also given. Pointwise consistency of the first and consistency of the other estimate is shown. The results hold for any nonlinear characteristic, and any asymptotically dynamic subsystem. Convergence rates are also given.
TL;DR: It turns out, that the encoder necessarily exhibits chaotic behavior if it satisfies the design axioms.
Abstract: A systematic top down design of discrete-time continuous-value coder systems for information encryption is presented. From the axioms, that the coder should be a maximally disturbed and invertible (according to the information signal) channel a general structure containing a static nonlinearity and a dynamical subsystem is derived and the system characteristics are specified. It turns out, that the encoder necessarily exhibits chaotic behavior if it satisfies the design axioms. Some examples of systems are given which belong to the designed structural class. Realizations as well as the reliability under the condition of weak disturbances are considered in Part II and a cryptographical analysis is performed in Part III of this paper.
TL;DR: In this paper, a complete family of two-switch pulsewidth-modulated (PWM) with active clamping DC/DC converters, featuring soft commutation of the semiconductors at zero-voltage (ZVS), is presented.
Abstract: This paper presents a technique to generate a complete family of two-switch pulsewidth-modulated (PWM) with active clamping DC/DC converters, featuring soft commutation of the semiconductors at zero-voltage (ZVS). The main purpose of this technique is to integrate these converters under a same theoretical principle to derive the topologies in a comprehensive form and generate new circuits. All the converters have the advantage of soft commutation (ZVS) with minimum switch voltage stress due to the clamping action. Besides operating at constant frequency and with reduced commutation losses, these converters have output characteristics similar to the PWM hard-switching counterpart, which means that there is no circulating reactive energy that would cause large conduction losses. Principle of operation, theoretical analysis, simulation and experimental results of one particular converter taken as an example, are provided in this paper.
TL;DR: Two general procedures for adaptive synchronization law design based on speed-gradient method are proposed, based on passification of error system (making it passive by feedback) and computer simulation results confirming theoretical analysis are given.
Abstract: A problem of synchronizing two nonlinear multidimensional systems with unknown parameters is considered. Two general procedures for adaptive synchronization law design based on speed-gradient method are proposed. Conditions ensuring the synchronization are given. The second procedure is based on passification of error system (making it passive by feedback). The results are illustrated by examples: synchronizing a pair of Chua's circuits and a pair of circuits with tunnel diodes. Computer simulation results confirming theoretical analysis are given.
TL;DR: In this paper, the free state evolution of two-dimensional (2-D) positive systems is analyzed and related to the spectral properties of the matrix sum A+B, and conditions guaranteeing that all local states on the same separation set C/sub t/ assume the same direction as t goes to infinity are provided.
Abstract: Two-dimensional (2-D) positive systems are 2-D state-space models whose variables take only nonnegative values and, hence, are described by a family of nonnegative matrices. The free state evolution of these systems is completely determined by the set of initial conditions and by the pair of nonnegative matrices, (A.B), that represent the shift operators along the coordinate axes. In this paper, internal stability of 2-D positive systems is analyzed and related to the spectral properties of the matrix sum A+B. Also, some aspects of the asymptotic behavior are considered, and conditions guaranteeing that all local states on the same separation set C/sub t/ assume the same direction as t goes to infinity, are provided. Finally, some results on the free evolution of positive systems corresponding to homogeneous distributions of the initial local states around a finite mean value, are presented.
TL;DR: In this article, the authors proposed an optimized compensation strategy with current buffer, which allows a high gain-bandwidth product to be achieved avoiding the drawbacks which arises with voltage buffer and nulling resistor approaches.
Abstract: The compensation with current buffer overcomes the typical drawbacks of the compensations based on nulling resistor or voltage buffer, but it is not as straightforward as the other two approaches. Indeed, a constraint on the current-buffer input resistance has to be met in order to achieve frequency compensation, since complex conjugate poles arise in the loop transfer function. Design equations for an optimized compensation strategy with current buffer are determined. They allow a high gain-bandwidth product to be achieved avoiding the drawbacks which arises with voltage buffer and nulling resistor approaches.
TL;DR: The authors propose an enhanced model based upon Feldmann et al.'s model, which is difficult to reconstruct and is sensitive to parameter mismatches, and the encrypted signal is shown to be uniformly distributed.
Abstract: The authors enumerate several defects in present day chaotic inverse system approaches, such as, the chaotic mapping may be reconstructed from a few plaintexts and their corresponding ciphertexts, and the self-synchronizing subsystem is so insensitive to its parameter mismatches that its parameters are generally not suitable for ciphers. Based upon Feldmann et al.'s model, we propose an enhanced model to overcome above problems. The new model is difficult to reconstruct and is sensitive to parameter mismatches, and the encrypted signal is shown to be uniformly distributed.
TL;DR: In this article, the effect of phase synchronization of chaotic oscillators is described and the effects of phase and frequency locking by external periodic force, as well as due to weak interaction of non-identical chaotic oscillator.
Abstract: We describe the effect of phase synchronization of chaotic oscillators. It is shown that phase can be defined for continuous time dynamical oscillators with chaotic dynamics, and effects of phase and frequency locking can be observed, We introduce several tools which characterize this weak synchronization and demonstrate phase and frequency locking by external periodic force, as well as due to weak interaction of nonidentical chaotic oscillators. In the synchronous state the phases of two systems are locked, while the amplitudes remain chaotic and noncorrelated. The intermittency phenomenon at the synchronization transition is considered. The application to the analysis of bivariate experimental data is discussed.
TL;DR: In this paper, a new feedforward control circuit suitable for applications in the dc-dc pulsewidth modulated (PWM) boost converter operated in the continuous conduction mode (CCM) is proposed.
Abstract: A new feedforward control circuit suitable for applications in the dc-dc pulsewidth modulated (PWM) boost converter operated in the continuous conduction mode (CCM) is proposed. Its principle of operation is described, analyzed for steady state, and experimentally verified. The peak value of the sawtooth voltage at the noninverting input of a PWM modulator is held constant and the voltage at the inverting input of the PWM modulator varies in proportion to the converter dc input voltage. As a result, the complement of the on-duty cycle (1-D) is proportional to the dc converter input voltage, yielding the converter output voltage theoretically independent of the converter input voltage. The circuit is very simple and significantly improves line regulation of the output voltage. The measured open-loop line regulation at fixed loads was less than 5% for the converter dc input voltage change by 400%. The load regulation was also good even without a negative feedback loop.
TL;DR: A nonlinear bifurcation controller that makes use of a feedback reference signal and a linear autoregressive formulation for the gain is described that is effective at stabilizing two diverse cardiac maps to a variety of periodic orbits.
Abstract: This brief describes methods based on time-delay feedback (TDF) for bifurcation control of nonlinear models of chaotic cardiac activity. We describe a nonlinear bifurcation controller that makes use of a feedback reference signal and a linear autoregressive formulation for the gain. This controller is effective at stabilizing two diverse cardiac maps to a variety of periodic orbits. We contrast our approach with the OGY method which has been used to control some chaotic biological processes and recently, some nonchaotic, stochastic ones.
TL;DR: In this article, the problem of identifiability of chaotic systems is defined and discussed in the context of possibilities for finding the unknown chaotic receiver parameters, including skew tent maps, Henon maps, Markov maps and Chua's circuit.
Abstract: This paper deals with the problem of synchronization of chaotic systems when the driven (slave, receiver) system has the same structure as the master (driving, emitter) system but its parameters are unknown. It is shown that the concept of synchronization provides an efficient way to find the unknown slave system parameters. Parameter mismatch between master and slave systems and high sensitivity of response to changes of these parameters were so far considered as crucial for security issues. This paper shows evidence that this claimed advantage becomes in fact a major drawback in chaos communication schemes since parameters ran easily be found using adaptive synchronization and optimization tools. The general problem of identifiability of chaotic systems is defined and discussed in the context of possibilities for finding the unknown chaotic receiver parameters. Several typical systems used in experiments in chaos communication are tested for identifiability showing direct applications of the introduced concepts. In particular examples of the skew tent map, Henon map, Markov maps and Chua's circuit are considered in detail illustrating the problems of global and local identifiability.
TL;DR: In this paper, the authors developed Lyapunov functions for power systems which have dynamic reactive power loads, which enable the investigation of the interaction between generator (angle) and load dynamics in multimachine power systems.
Abstract: This paper develops Lyapunov functions for power systems which have dynamic reactive power loads. These functions are extensions of earlier Lyapunov functions derived for structure preserving power system models having static loads. In order to obtain strict Lyapunov functions, the transient response of the dynamic load must have a logarithmic dependence on voltage. A Lyapunov function is initially generated using a "first integral" analysis. A Popov criterion analysis is then undertaken for comparison. The developed Lyapunov functions enable the investigation of the interaction between generator (angle) and load dynamics in multimachine power systems.