http://www.ifac-papersonline.net/ en Copyright 02:44 PM Wednesday 19, 2013 IFAC-PapersOnline http://www.ifacpapersonline.com 02:44 PM Wednesday 19, 2013 02:44 PM Wednesday 19, 2013 ET webmaster@ifac-papersonline.net webmaster@ifac-papersonline.net http://www.ifac-papersonline.net/Detailed/29920.html 04:00 PM Wednesday 31, 1969 http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29921.html 04:00 PM Wednesday 31, 1969 In this talk, we explain the history and the use of chaos theory by economists people and by he financial community. Economists have not in general a lot of data, thus their approach is mainly theoretical: they consider analytical models and analyse their behaviour with respect o the evolution of the parameters. When chaotic behaviour can appear, they are interested to control it. In finance, working with intra daily data permit to have a lot of data and the approach is completely different. It is mainly experimental: people use non parametric tools. They try to detect chaotic behaviour inside data sets by the knowledge of an attractor. Thus, they need tests to detect the chaotic behaviour of their data. They need also to reconstruct orbits inside the attractor when it exists and to estimate the Lyapunov exponents which characterize the behaviour of the data. When the attractor is determined (using embedding for instance) and the orbits well estimated, it is possible to make forecasts inside the attractor which is the main objective of the finance community using this approach. Short term forecasts can be easily obtained, but also long term forecasts. Indeed, chaotic systems as stochastic processes can present long memory behaviour with respect to the evolution of their autocorrelation function. Thus, it is possible to make long term forecasts inside an attractor. The question of mean term prediction is still opened. Another important problem concerns the deconvolution of the financial data which are strong noisy: an approach which seems promising is based on wavelets theory. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29922.html 04:00 PM Wednesday 31, 1969 This paper proposes a synchronization scheme for a class of continuous-time chaotic systems. We show that two systems belonging to the class of generalized Lorenz systems can be synchronized using an adaptive feedback controller. This controller is added to the response system to force a subset of its state variables to oscillate synchronously with their counterpart of the drive system. We show that the controller gain vector is tuned without any knowledge of the system model. To illustrate the efficiency of the proposed scheme, we present numerical simulations to synchronize two-by-two a Lorenz-like system, Chen system and Lü system. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29923.html 04:00 PM Wednesday 31, 1969 This paper proposes an adaptive fuzzy control system based on sliding mode like observer for a class of unknown chaotic systems. The design of the underlying update law as well as the robust control term is based on an appropriate filtering of the sliding surface. This particularly allows to overcome the output observation error filtering or the necessity of the famous SPR condition. The performances of the proposed control system are illustrated throughout a simulation results involving a Duffing forced oscillation system. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29924.html 04:00 PM Wednesday 31, 1969 In this paper, a new method of chaotic-system synchronization based on adaptive backstepping with modular design is presented. This approach offers a systematic design procedure for adaptive synchronization of a large class of continuous-time chaotic systems known in research literature. This method is more advantageous than synchronization method via backstepping with tuning functions, proposed by C. Wang and S.S. GE (2001). It uses a simpler controller and the choice of the update law is more flexible. Simulation results are presented to show the effectiveness of the approach. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29925.html 04:00 PM Wednesday 31, 1969 A method for multiplexing information-bearing chaotic waveforms is demonstrated experimentally. This scheme increases the channel capacity of a chaotic communication system and provides some masking of the information content. In the transmitter, symbolic information is simultaneously encoded in two chaotic drive circuits using small perturbations. The waveforms are summed and transmitted as a single scalar signal. At the receiver, a pair of response oscillators synchronizes to the drive and de-multiplexes the signal. The transmitted information in each channel is extracted using a peak return threshold. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29926.html 04:00 PM Wednesday 31, 1969 This paper deals with a control-oriented encoding/decoding scheme for digital information, involving unidirectionally coupled chaotic systems for secure communication purposes. From the transmitter viewpoint, the proposed approach essentially consists in a closed-loop encoding scheme where the (digital) data are injected within the dynamics of the (chaotic) encoder, via a control law aiming at forcing the encoder to track a chaotic reference model. From the receiver viewpoint, the decoding is achieved by means of both a controlled synchronization between the transmitter and the receiver, and a controlled tracking of a reference model (a replica of the transmitter one). The paper then focuses on recovering of the message in case of a transmitted scalar signal (namely, an encoder state trajectory) which does not directly (i.e., explicitly) contains the information. Finally, the usage (context, constraints, ...) of such a communication scheme is discussed, and an illustrative example based on Chua's circuits is presented. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29927.html 04:00 PM Wednesday 31, 1969 The most common and useful tool for the characterization of chaos is given by the Lyapunov exponents. In this paper, the computation of the entire Lyapunov exponents of the coupled logistic map lattice is considered. For this, the Jacobian matrix of coupled map lattice with constant coupling strength is first determined. The conditions of multiplicative ergodic theorem for nonlinear coupled map lattice are proven and then the Jacobian matrix of this map in order to computing Lyapunov exponents is calculated. The feasibility of this approach is illustrated in one system. The method for controlling spatiotemporal chaos based on Lyapunov exponents is also explained. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29928.html 04:00 PM Wednesday 31, 1969 This paper presents the basic idea and the mathematical formulation of the delayed feedback control (DFC) methodology. Stability analysis including the well-known odd number limitation of the DFC is reviewed. Some new advances in characterization of the limitation of the DFC are presented. Finally, some open problems in this research field are discussed. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29929.html 04:00 PM Wednesday 31, 1969 In this paper, time delays effects on master-slaves synchronization are tackled in the case of a network of a diffusely coupled identical systems. Using Lyapunov methods and LMI (Linear matrix inequality) framework, a new condition is given to ensure global exponential stability. The criteria concerns N identical oscillators that can be modeled as Lur'e systems. The approach is successfully applied to network of chaotic chua's circuits that can be used in chaotic cryptography. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29930.html 04:00 PM Wednesday 31, 1969 This paper presents a condition of global exponential stability for nonlinear identical systems. This condition is found by using Lyapunov theory and the LMI framework. A linear controller is designed to ensure the synchronization of two identical van der Pol oscillators coupled by a pure delay element. The result can be extrapolated to a chain of coupled oscillators in order to assure the control of the radiation pattern for an antenna array. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29931.html 04:00 PM Wednesday 31, 1969 The saturated dynamics of a Single Pass Free Electron Laser is here considered within a simplified mean field approach. A method is proposed to increase the size of the macro-particle. This approach is based on the reconstruction of invariant tori of the dynamics of test particles. To this aim a dedicated control term is derived, the latter acting as a small apt perturbation of the system dynamics. Implications of these findings are discussed in relation to the optimization of the laser source. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29932.html 04:00 PM Wednesday 31, 1969 This research examines the small amplitude, irregular behaviour of the water level of a single tank under closed loop feedback control. The tank provided a physical system that could be studied and modelled. By using ordinary differential equation models, derived from tests on the physical system, simulation studies were also carried out to try to reproduce the measured dynamics. From the simulation studies and from measured results, the form of the time series of the changes in the tank level, the associated spectra, the sensitivity shown to initial conditions, and Lyapunov exponent's calculations indicated chaotic dynamics were present. The route to chaos was identified as one of global bifurcation, with the controller gain used as the control parameter. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29933.html 04:00 PM Wednesday 31, 1969 Various robust control techniques such as Integral Block Control, Sliding Mode Control and H-infinity Control are combined to design a controller, forcing an electro-hydraulic actuator driven by a servovalve to track a chaotic reference trajectory. This approach enables to compensate the inherent nonlinearities of the actuator and reject external disturbances. The capabilities of the approach are illustrated in a simulation study. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29934.html 04:00 PM Wednesday 31, 1969 In this paper, in order to de-noise a chaotic signal, We compare the time-frequency deconvolution method with the wavelets method. We apply our results on different dynamical systems and show the capability of wavelets' method to reconstruct the attractor of a chaotic time series. Then, we de-noise different data sets in order to re-built their attractor using the wavelets method. The application concern temperatures and wind fluctuations, electricity spot prices and financial data sets. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29935.html 04:00 PM Wednesday 31, 1969 This contribution deals with an investigation on optimization of the feedback control of chaos based on method of an artificial intelligence, namely the evolutionary algorithms. The main aim of this work is to show that evolutionary algorithms are capable of optimization of deterministic chaos control. The optimizations were realized in several ways, each one for another set of control parameters or another cost function. Two evolutionary algorithms were used: differential evolution and SOMA (Self-Organizing Migrating Algorithm). For both algorithms each simulation was repeated several times to show and check robustness of used methods. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29936.html 04:00 PM Wednesday 31, 1969 Analytical conditions and practical methods of their realization are proposed for solving a problem of tracking a command signal for a nonlinear disturbed system. Nonlinear plants which linear part has unknown parameters and nonlinear part and disturbance are bounded and unknown are considered. The paper illustrates a possibility of applications of proposed algorithms to control libration angle of satellite. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29937.html 04:00 PM Wednesday 31, 1969 A hybrid design method of pulse energy conversion system (PECS) nonlinear controllers is proposed in this paper. The hybrid method makes possible to avoid bifurcation phenomena in controller dynamics at the design stage. Application of the proposed method allows to eliminate an uncertainty of switching frequency to system open loop crossover frequency ratio choice, to estimate designed controller quality indices (overshoot, settling time and steady-state error) taking into consideration its essentially nonlinear nature and to guarantee bifurcation phenomena absence with high probability. An example of this hybrid method application is demonstrated for the DC-DC buck converter controller design. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29938.html 04:00 PM Wednesday 31, 1969 Research of dynamics of hysteresis regulators with clocked commutation is presented. Physical reasoning of stability loses is given. Method of hysteresis adaptation is offered to improve accuracy of regulation of the hysteresis regulators with clocked commutation in dc/ac voltage convertors. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29939.html 04:00 PM Wednesday 31, 1969 The strange behavior of Direct Torque Controlled (DTC) Induction Machine (IM) due to nonlinearity is studied. The nonlinearity is the result of hysteresis comparators. Recurrence Plots (RP) beside the bifurcation diagram are applied to reveal the possible states of the system such as periodic, subharmonic and chaotic states. RP makes it possible to identify various system states without the knowledge of all state variables in a multi-dimensional system, it is enough to acquire only time series of an observable state. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29940.html 04:00 PM Wednesday 31, 1969 Array processors are widespread in real-time systems. In the ten years phase-locked loops have widely been used in array processors as control devices correcting a clock skew. In this paper new type of floating phase-locked loops for array processorsis designed. For the floating phase locked loops new stability conditions are obtained. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29941.html 04:00 PM Wednesday 31, 1969 The paper represents some experimental results on synchronization of two metronomes attached to a common support beam. The experiments demonstrate possible in-phase, anti-phase synchronization as well as intermediate seemingly chaotic regimes. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29942.html 04:00 PM Wednesday 31, 1969 In this paper partial synchronization of diffusively coupled Chua systems is presented. Partial synchronization is defined as the situation where some circuits synchronize with each other, while others do not. An experimental setup, consisting of maximal four Chua circuits operating in the double scroll regime, is used to show the existence of linear invariant manifolds corresponding to the partial synchronized state. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29943.html 04:00 PM Wednesday 31, 1969 Iterations of 1D simple maps such as logistic, tent, cubic ones are very well studied. However perturbed versions of these maps (close in uniform norm but with strongly varying derivatives) can exhibit completely different behavior. We encounter such situation when dealing with chaos stabilization via small control. In this paper we present analytical investigation of this effect for one particular case -- piecewise linear perturbation of the tent map. Surprisingly, iterations of this map converge to the unique fixed point very fast for all initial points. The result is in sharp contrast with iterations of the original tent map but explains fast stabilization of unstable periodic orbits by predictive control, proposed in Polyak & Maslov (2005); Polyak (2005). http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif http://www.ifac-papersonline.net/Detailed/29944.html 04:00 PM Wednesday 31, 1969 Sigma delta modulation is a popular form of A/D and D/A conversion. This nonlinear device exhibits a high degree of complex nonlinear behaviour, including chaotic dynamics. One of the main unsolved problems in the theory of sigma delta modulation concerns the ability to analytically derive conditions for the boundedness of solutions of a high order sigma delta modulator (SDM). In this work, we describe how a sigma delta modulator may be rephrased within the context of systems theory. We present several theoretical results concerning bounded solutions of general high order SDMs, including necessary and sufficient conditions for the lack of a finite escape time, necessary conditions for bounded solutions based on the nature of the output sequences, and topological properties of the solutions, which are a precursor to the study of chaotic solutions of SDMs. http://www.ifac-papersonline.net/static/luna/images/ifac/icon-download.gif