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International audience; In this paper, a modelling method of a 25 kV-50 Hz railway line, in a frequency range from 0 to 5 kHz, is presented. A model is proposed to quantify current and voltage harmonics generated by traction converters in different points of the network. An equivalent circuit, taking into account the skin effect for time-domain simulations, is also proposed. A new model, based on state space representation and transfer functions is developed to simplify the study of the interactions between several trains circulating on a line sector. As an example, the amplitudes of the harmonics generated by on-board active rectifiers are computed at several points of the network for a given topology of the overhead line and several positions of two trains on a sector with a junction.

International audience; A tandem cold rolling mill permits to reduce the thickness of a steel strip while ensuring the required mechanical properties. The tandem cold rolling could be modeled as a strongly non-linear differential-algebraic system including state-dependent delays. In order to reach the new products specifications, be inline with new challenges and also to optimize the process, advanced multi-variable control strategies are investigated. This paper will establish, as a main contribution, a model reaching a compromise between a good approximation of the process and its simplicity to control. A linearized model of the cold rolling process including state-dependent delays will be provided and validated numerically. A simulation with a simplistic multi-variable controller will illustrate the use of this model.

In the field of power and drive systems, electrical AC machines are mostly modeled using a set of explicit ordinary differential equations in a state space representation. It is shown, that by using other equation types for simulation, algebraic constraints arising from aggregating several machines to a more complex system can directly be considered. The effects of different model variants on numerical ODE/DAE solvers are investigated in the focus of this work in order perform efficient simulations of larger systems possessing electrical AC machines.

Traffic data can be classified into spatial data and location-based data depending on the frame of measurement involved. Location-based traffic data pertain to information at a certain point, and spatial traffic data pertain to a longer section of the roadway. This larger coverage makes spatial traffic data better indicators of the traffic condition and the level of service of the roadway section. Therefore, spatial traffic data are preferred in any congestion mitigation program. Because the greater spatial coverage makes measurement of spatial traffic data more difficult than that of location-based data, the spatial data are usually estimated from other easily measurable location-based parameters. This paper proposes a methodology to estimate two of the most important spatial traffic parameters—density and space mean speed (SMS)—from the location-based parameters—flow and time mean speed (TMS)—under Indian traffic conditions. The estimation scheme was based on the Kalman filter and incorporated a dynamic macroscopic traffic flow model formulated in the state–space representation. This framework also included an empirical model calibrated with field data and a parameter α, which was used to relate SMS to TMS. The parameter estimation was formulated as an optimization problem, and the estimation scheme was corroborated with a comparison of density estimates with field data. Because the collection of SMS from the field was difficult, travel time collected from probe vehicle data was used as a surrogate measure to corroborate the SMS estimates. The results were promising and agreed well with the traffic behavior observed in the field.

A useful representation of fractional order systems is the state space representation. For the linear fractional systems of commensurate order, the state space representation is defined as for regular integer state space representation with the state vector differentiated to a real order. This paper presents a solution of the linear fractional order systems of commensurate order in the state space. The solution is obtained using a technique based on functions of square matrices and the Cayley–Hamilton theorem. The technique developed for linear systems of integer order is extended to derive analytical solutions of linear fractional systems of commensurate order. The basic ideas and the derived formulations of the technique are presented. Both, homogeneous and inhomogeneous cases with usual input functions are solved. The solution is calculated in the form of a linear combination of suitable fundamental functions. The presented results are illustrated by analyzing some examples to demonstrate the effectiveness of the presented analytical approach.

In this paper, we consider the approximation of general multivariable non commensurate fractional systems by integer order state space models. This work contains two main contributions. First, a new state space representation using the fractional integral operator is introduced. Second, the approximate model carries explicitly the initial conditions of the system. Two examples are given to illustrate the accuracy of the approximation.

For the solution Y of a multivariate random recurrence model Y n = A n Y n − 1 + ζ n in R q we investigate the extremal behaviour of the process y n = z ∗ ′ Y n , n ∈ N , for z ∗ ∈ R q with | z ∗ | = 1 . This extends results for positive matrices A n . Moreover, we obtain explicit representations of the compound Poisson limit of point processes of exceedances over high thresholds in terms of its Poisson intensity and its jump distribution, which represents the cluster behaviour of such models on high levels. As a principal example we investigate a random coefficient autoregressive process.

Adaptive Optics (AO), which enables to correct in real time wavefront deformation induced by atmospheric turbulence, faces a fundamental limitation: anisoplanatism. To counter it, the concept of Wide-Field AO (WFAO) has been proposed. Turbulence is measured in several directions of the field of view, using natural and laser guide stars, and its impact on images is mitigated by a control based on tomographic reconstruction. The Linear Quadratic Gaussian (LQG) approach is well-suited to AO control design in both WFAO and classical AO. LQG enables to estimate and predict the phase with a Kalman filter based on spatial and temporal priors. State-space models and associated controls are laid out. The first on-sky implementation of LQG control on all modes, in classical and multi-object AO, is presented on the CANARY pathfinder. These results have been obtained with identification of tip-tilt models and vibration filtering, which constitutes the first on-sky implementation of this strategy. Spatial priors on the phase in the volume are identified using the LEARN algorithm. Data from the stereoSCIDAR profilometer were also used. Comparisons are provided with integral AO control in standard AO, showing significant gain in performance with LQG. Comparisons with the static reconstructor APPLY (regularized least-squares) in multi-object AO show a gain in performance with LQG in some cases (especially in high-noise conditions). Results confirm feasibility and relevance of LQG control for AO or WFAO instruments.; L'optique adaptative (OA), qui permet de corriger en temps-réel les déformations du front d'onde induites par la turbulence atmosphérique, connaît une limitation fondamentale : l'anisoplanétisme. Pour y remédier, le concept d'OA grand champ (OAGC) a été proposé. La turbulence est mesurée dans plusieurs directions du champ de vue à l'aide d'étoiles guide naturelles et laser, et son impact corrigé sur les images par une commande basée sur une reconstruction tomographique. L'approche linéaire quadratique gaussienne (LQG) est bien adaptée à la conception de lois de commande en OAGC comme en OA classique. Elle permet d'estimer et de prédire la phase à l'aide d'un filtre de Kalman basé sur des a priori spatiaux et temporels. Les modèles d'état et commandes associées sont détaillés. On présente la première mise en œuvre sur le ciel d'une commande LQG sur tous les modes, en OA classique et multi-objet, à l'aide du démonstrateur CANARY. Ces résultats sont obtenus avec identification du modèle de tip-tilt et filtrage des vibrations, ce qui constitue la première mise en œuvre ciel de cette stratégie. Les a priori spatiaux de la phase en volume sont identifiés par la méthode LEARN. Des données issues du profilomètre stereoSCIDAR ont aussi été utilisées. Des comparaisons sont proposées avec une commande intégrateur en OA classique, avec un gain significatif en performances pour le LQG. Les comparaisons avec le reconstructeur statique APPLY (moindres carrés régularisés) en OA multi-objet mettent en évidence un gain du LQG dans certains cas (fort bruit en particulier). L'ensemble des résultats confirme la faisabilité et l'intérêt d'une commande LQG pour un instrument d'OA ou d'OAGC.

Adaptive Optics (AO), which enables to correct in real time wavefront deformation induced by atmospheric turbulence, faces a fundamental limitation: anisoplanatism. To counter it, the concept of Wide-Field AO (WFAO) has been proposed. Turbulence is measured in several directions of the field of view, using natural and laser guide stars, and its impact on images is mitigated by a control based on tomographic reconstruction. The Linear Quadratic Gaussian (LQG) approach is well-suited to AO control design in both WFAO and classical AO. LQG enables to estimate and predict the phase with a Kalman filter based on spatial and temporal priors. State-space models and associated controls are laid out. The first on-sky implementation of LQG control on all modes, in classical and multi-object AO, is presented on the CANARY pathfinder. These results have been obtained with identification of tip-tilt models and vibration filtering, which constitutes the first on-sky implementation of this strategy. Spatial priors on the phase in the volume are identified using the LEARN algorithm. Data from the stereoSCIDAR profilometer were also used. Comparisons are provided with integral AO control in standard AO, showing significant gain in performance with LQG. Comparisons with the static reconstructor APPLY (regularized least-squares) in multi-object AO show a gain in performance with LQG in some cases (especially in high-noise conditions). Results confirm feasibility and relevance of LQG control for AO or WFAO instruments.; L'optique adaptative (OA), qui permet de corriger en temps-réel les déformations du front d'onde induites par la turbulence atmosphérique, connaît une limitation fondamentale : l'anisoplanétisme. Pour y remédier, le concept d'OA grand champ (OAGC) a été proposé. La turbulence est mesurée dans plusieurs directions du champ de vue à l'aide d'étoiles guide naturelles et laser, et son impact corrigé sur les images par une commande basée sur une reconstruction tomographique. L'approche linéaire quadratique gaussienne (LQG) est bien adaptée à la conception de lois de commande en OAGC comme en OA classique. Elle permet d'estimer et de prédire la phase à l'aide d'un filtre de Kalman basé sur des a priori spatiaux et temporels. Les modèles d'état et commandes associées sont détaillés. On présente la première mise en œuvre sur le ciel d'une commande LQG sur tous les modes, en OA classique et multi-objet, à l'aide du démonstrateur CANARY. Ces résultats sont obtenus avec identification du modèle de tip-tilt et filtrage des vibrations, ce qui constitue la première mise en œuvre ciel de cette stratégie. Les a priori spatiaux de la phase en volume sont identifiés par la méthode LEARN. Des données issues du profilomètre stereoSCIDAR ont aussi été utilisées. Des comparaisons sont proposées avec une commande intégrateur en OA classique, avec un gain significatif en performances pour le LQG. Les comparaisons avec le reconstructeur statique APPLY (moindres carrés régularisés) en OA multi-objet mettent en évidence un gain du LQG dans certains cas (fort bruit en particulier). L'ensemble des résultats confirme la faisabilité et l'intérêt d'une commande LQG pour un instrument d'OA ou d'OAGC.

This paper introduces a novel multi-view deconvolution technique for 3-D images. An optimal Kalman-based minimum variance restoration algorithm is allowed to combine a series of image samples acquired from different viewing directions. The extended algorithm is based on the definition of a stochastic state-space representation of the image, which embeds the description of blurring effects and noise disturbances. The consistency of this model gives guarantee for high restoration performances. The extension to the data fusion is obtained by suitably including the multi-view acquisition procedure within the representation. The final algorithm results to be effective for improving the resolution and the isotropy of the estimated image, as shown by the reported numerical results.

The class of multivariate L\'{e}vy-driven autoregressive moving average (MCARMA) processes, the continuous-time analogs of the classical vector ARMA processes, is shown to be equivalent to the class of continuous-time state space models. The linear innovations of the weak ARMA process arising from sampling an MCARMA process at an equidistant grid are proved to be exponentially completely regular ($\beta$-mixing) under a mild continuity assumption on the driving L\'{e}vy process. It is verified that this continuity assumption is satisfied in most practically relevant situations, including the case where the driving L\'{e}vy process has a non-singular Gaussian component, is compound Poisson with an absolutely continuous jump size distribution or has an infinite L\'{e}vy measure admitting a density around zero., Comment: Published in at http://dx.doi.org/10.3150/10-BEJ329 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

This paper extends the ordinary quasi-likelihood estimator for stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck (OU) processes to vector processes. Despite the fact that multivariate modeling of asset returns is essential for portfolio optimization and risk management -- major areas of financial analysis -- the literature on multivariate modeling of asset prices in continuous time is sparse, both with regard to theoretical and applied results. This paper uses non-Gaussian OU-processes as building blocks for multivariate models for high frequency financial data. The OU framework allows exact discrete time transition equations that can be represented on a linear state space form. We show that a computationally feasible quasi-likelihood function can be constructed by means of the Kalman filter also in the case of high-dimensional vector processes. The framework is applied to Euro/NOK and US Dollar/NOK exchange rate data for the period 2.1.1989-4.2.2010.

International audience; In this article, we study the behaviour of the RLC cells for the four configurations that we presented earlier in Abi Zeid Daou et al. (2009a). An electric circuit is used in order to study the fractional behaviour and the robustness of these RLC operators and compare their responses to the behaviour of the fractance which is an ideal fractional operator (Moreau et al., 2003). This analysis is conducted for both natural and forced responses. In more details, the initial conditions of the capacitors and inductances are neglected in the first case and they are taken into consideration in the second one. The number of initial conditions is related to the number of RLC cells used. The robustness of all arrangements is analysed by varying the unsteady parameter value which is represented by an inductance in the electrical circuit. This inductance represents a different variable parameter in each field of application. For example, in the hydropneumatic domain, this inductance refers to the mass of the vehicle as the mass has the main influence on the dynamics and the robustness when designing the active suspension (Moreau et al., 2001). A conclusion will sum up the results for all four arrangements and a confirmation that the phase constancy and the robustness are present in both modes.

This paper extends the ordinary quasi-likelihood estimator for stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck (OU) processes to vector processes. Despite the fact that multivariate modeling of asset returns is essential for portfolio optimization and risk management -- major areas of financial analysis -- the literature on multivariate modeling of asset prices in continuous time is sparse, both with regard to theoretical and applied results. This paper uses non-Gaussian OU-processes as building blocks for multivariate models for high frequency financial data. The OU framework allows exact discrete time transition equations that can be represented on a linear state space form. We show that a computationally feasible quasi-likelihood function can be constructed by means of the Kalman filter also in the case of high-dimensional vector processes. The framework is applied to Euro/NOK and US Dollar/NOK exchange rate data for the period 2.1.1989-4.2.2010. Financial support from the Norwegian Research Council ("Finansmarkedsfondet") is gratefully acknowledged.

The concept of Internally Positive Realization (IPR) of a system generalizes the idea of realization of a generic transfer function through combination of positive filters: an IPR is a positive state space representation, endowed with input, state and output transformations, that realizes the dynamics of a given generic (i.e. with no positivity constraint) system. Techniques for the construction of IPRs of discrete-time linear systems are available in the literature. This paper presents a method for the construction of IPRs for continuous-time systems, and provides a theoretical characterization of the stability of the resulting realization. The results presented are relevant in the field of positive continuous-time systems, like compartmental systems and for the implementation of analog filters using VLSI distributed RC interconnects.

This work deals with the physical modelling of acoustic tubes for digital simulation in real-time. The main application is the sound synthesis of wind instruments, with a realistic model, a modular method and a low-cost digital implementation. The acoustic model of "Webster-Lokshin", used in this work, is an unidimensional model which takes into account the "curvature" of the profile and the "visco-thermal losses" at the wall. With this acoustic model, we obtain a framework for simulation which is compatible with the "Waveguides" approach: a tube is then represented by a system with delays and closed loops, involving several sub-systems without internal delay. A difficulty is the presence of infinite-dimensional sub-systems which behave as infinite sums of first or second order systems. First, they are approximated by finite-dimensional systems, then their "state-space representation" in the discrete time domain is determined. Finally, using standard tools of automatic control, these representations facilitate the connection of acoustic elements and reduce the computational complexity of the digital simulation. In this work, an analysis of the stability and passivity of this approach is described. For some particular cases of tubes, a problem occurs: even if the input/output relations of the tube are stable, some sub-systems have an infinity of singularities which produce internal instabilities in the system. We present an explanation of this phenomenon and to solve this problem, a new decomposition into sub-systems is performed., Ce travail porte sur la modélisation physique des tubes acoustiques pour la simulation numérique en temps-réel. Le but principal est la synthèse sonore d'instruments à vent, avec un modèle réaliste, une méthode modulaire et une implémentation numérique faible coût. Le modèle acoustique de "Webster-Lokshin", utilisé ici, est un modèle à 1 dimension prenant en compte à la fois la "courbure" du profil et les "pertes visco-thermiques" à la paroi. Pour ce modèle acoustique, une structure de simulation compatible avec l'approche des "Guides d'Ondes" est obtenue : un tube y est représenté par un système bouclé, avec retards, faisant intervenir plusieurs sous-systèmes sans retard interne. Une difficulté est la présence de sous-systèmes de dimension infinie qui se comportent comme des sommes infinies de systèmes du premier ou du second ordre. Dans un premier temps, ils sont approximés par des systèmes de dimension finie, puis leur "représentation d'état" à temps discret est obtenue. Enfin, en utilisant des outils standard de l'automatique, ces représentations nous permettent de faciliter la connexion d'éléments acoustiques et de réduire les coûts de calcul de la simulation numérique. Dans ce travail, l'étude de la stabilité et de la passivité est faite. Pour des cas paticuliers de tubes, un problème survient : même si les relations entrées/sorties du tube sont stables, certains sous-systèmes internes possèdent une infinité de singularités à l'origine d'instabilités internes. Nous présentons une explication de ce phénomène et ceci nous amène à proposer une nouvelle décomposition en sous-systèmes pour lever ce problème.

This paper deals with digital waveguide modeling of wind instruments. It presents the application of state-space representations to the acoustic model of Webster-Lokshin. This acoustic model describes the propagation of longitudinal waves in axisymmetric acoustic pipes with a varying cross-section, visco-thermal losses at the walls, and without assuming planar or spherical waves. Moreover, three types of discontinuities of the shape can be taken into account (radius, slope and curvature), which can lead to a good fit of the original shape of pipe. The purpose of this work is to build low-cost digital simulations in the time domain, based on the Webster-Lokshin model. First, decomposing a resonator into independent elementary parts and isolating delay operators lead to a network of input/output systems and delays, of Kelly-Lochbaum network type. Second, for a systematic assembling of elements, their state-space representations are derived in discrete time. Then, standard tools of automatic control are used to reduce the complexity of digital simulations in time domain. In order to validate the method, simulations are presented and compared with measurements.

Using state space techniques we study a "myopic" order-up-to policy. The policy is myopic because it is optimal at minimising local inventory holding and shortage costs. In particular we study the bullwhip effect produced by the replenishment policy reacting to a stochastic ARMA(l,l) demand processes. We reveal that bullwhip is fundamentally caused by the co-variance between the inventory level and the demand forecast. We go on to highlight the impact of a simple control engineering inspired bullwhip reduction technique, a proportional controller in the inventory feedback loop. Although it can be shown this approach is always able to remove bullwhip, we expose that it is not possible to arbitrarily "tune" the proportional controller, without knowing in advance the likely structure of the demand process. We conclude with an investigation of trade-offs and optimisations in the order and inventory variance (and their sum) produced by our policy. (c) 2006 Elsevier B.V. All rights reserved.

A 'proportional' order-up-to policy reacting to ARMA demand is analyzed using stochastic optimal control theory. This policy is compared with a full-state-feedback order-up-to policy. Necessary conditions for an optimum of a weighted sum of the inventory and the ordering variances for both policies are formulated. Based on this a relatively simple expression for the 'full-state' policy is derived. The comparison between the two policies demonstrates that the 'intuitively' designed proportional policy does not fulfill the objective of controlling both the inventory and ordering variance for all parameter values of the demand model as well as the full-state-feedback policy. The full-state-feedback policy outperforms the proportional policy in several aspects. (c) 2006 Elsevier Ltd. All rights reserved.

We consider multi-resolution time series models and their application to high-frequency financial data. An individual transaction share price of a specific firm is subject to market microstructure noise. Therefore, we propose trading duration time weighted averages over given time intervals. Averages over long intervals lead to a coarse resolution and averaging over shorter intervals lead to a finer resolution. Arranging sub-intervals of given lengths on scales with coarse to fine resolution imply a structure which can be represented as a directed acyclic graph. Time series models are then formulated using this graph structure. It is shown that these models have a linear state space representation which allows for efficient computation of the likelihood needed in parameter estimation and for a straightforward treatment of missing observations. Application of these models to the log transaction prices of the IBM shares traded at the New York Stock Exchange from February until October 2002 show that the corresponding one-step prediction errors are heavy tailed and therefore a specific variance term is allowed to follow a fiEGARCH specification, improving the tail behavior and leading to a better fit.

Due to nodes mobility and environmental changes in mobile ad-hoc networks, the ad-hoc channel is time varying and subject to fading. As a consequence of these variations, the statistical characteristics of the received signal vary continuously, giving rise to a Doppler power spectral density (DPSD) which varies from one observation instant to the next. As a result, the traditional models can no longer capture and track complex time variations in the propagation environment. These time variations compel us to introduce more advanced dynamical models in order to capture higher order dynamics of the ad-hoc channel. A stochastic ad-hoc short term fading channel model, in which the evolution of the dynamical channel is described by a stochastic state space representation, is derived. The parameters of the stochastic state space model are determined by approximating the band limited DPSD. Inphase and quadrature components of the ad-hoc channel are derived. Numerical results show that link performance for ad-hoc case is worse than cellular case, but the performance gap shrinks with increased mobility. © 2006 IEEE. 3 1277 1282

Polynomial phase signals (PPS) have found use in many area of engineering such as in radar and communication. The main problem is to estimate the parameters of such signals. Many research works have been conducted in the last decade and led to the development of various algorithms based on different mathematical tools such as time-frequency, subspace methods, High order statistics and Kalman filtering. Though, these methods have proven to perform well in estimating the signal parameters, they assume that the noise is Gaussian. The research work presented in the thesis deals with the analysis of PPS in non Gaussian environment. In this context, the noise is considered to have either an alpha-stable distribution, or epsilon-contaminated model. Three approaches of estimation are explored. The first method concerns robust time-frequency analysis of PPS, we propose to integrate the fractional lower statistics in the kernel of the polynomial phase Wigner-Ville Distribution to obtain a robust time-frequency distribution able to reveal the instantaneous frequency of the PPS. The second approach, deals with robust subspace method based on the MUSIC estimator using the covariation matrix, we propose a modified MUSIC algorithm which is able to track the values of the coefficients of the phase. Finally, using the nonlinear state space model of PPS, we explore the use of the Kalman filter for robust estimation of PPS in epsilon-contaminated noise. In this context, three types of Kalman filters are proposed: The robust extended Kalman filter, the parallel extended Kalman filter. To avoid linearization an alternative method is proposed based on parallel unscented Kalman filters.; Le sujet de la thèse porte sur l'étude des approches d'estimation des Signaux à Phase Polynomiale (SPP) noyés par un bruit non gaussien. Nous considérons deux modèles pour le bruit: le premier modèle est défini par une Somme Pondérée de Gaussiennes et le second par des distributions alpha-stables. Dans un premier temps, nous abordons les méthodes classiques d'analyse des SPP. L'utilisation des statistiques d'ordre fractionnaire permet d'obtenir des algorithmes robustes en présence de bruit impulsif; nous exploitons cette propriété pour proposer une Distribution de Wigner-Ville Polynomiale pour l'analyse des SPP. Cette nouvelle distribution, permet de mieux estimer la fréquence instantanée du SPP bruité. La deuxième partie est consacrée aux méthodes récentes d'analyse spectrale adaptées aux SPP. Nous proposons un algorithme MUSIC robuste obtenu par SVD de la matrice de covariation. Cet algorithme nous permet d'estimer les coefficients de la phase dans un plan temps-coefficient. Dans la troisième partie, une approche pour l'estimation des SPP par filtrage de Kalman est présentée. Cette approche repose sur un modèle d'état non linéaire avec un bruit d'observation non gaussien. Nous présentons trois types de filtres de Kalman robustes au bruit impulsif. Le premier, appelé filtre de Kalman étendu robuste utilise un gain de Kalman dépendant de la fonction de Huber. Aussi, nous proposons d'utiliser deux filtres de Kalman étendus (EKF) opérant en parallèle couplés via le terme d'apparition du bruit impulsif. Enfin, il est possible d'améliorer les performances d'estimation en utilisant un filtre UKF ‘unscented Kalman filter' à la place du filtre EKF.

The applicability of the Kalmann Filtering for on-line monitoring of the laser material removal process (LMRP) was studied. The study was based on the informational properties of the acoustic emission (AE) signal generated by the surface acoustic waves in the laser-material interaction zone. A periodic signature with a period of applied laser pulses was selected for characterization of the LMRP's dynamic characteristic. The system matrices of the state space representation of the model were identified that allowed calculation of Kalman filters and evaluation of the measured, estimated and predicted LMRP's characters.

Polynomial phase signals (PPS) have found use in many area of engineering such as in radar and communication. The main problem is to estimate the parameters of such signals. Many research works have been conducted in the last decade and led to the development of various algorithms based on different mathematical tools such as time-frequency, subspace methods, High order statistics and Kalman filtering. Though, these methods have proven to perform well in estimating the signal parameters, they assume that the noise is Gaussian. The research work presented in the thesis deals with the analysis of PPS in non Gaussian environment. In this context, the noise is considered to have either an alpha-stable distribution, or epsilon-contaminated model. Three approaches of estimation are explored. The first method concerns robust time-frequency analysis of PPS, we propose to integrate the fractional lower statistics in the kernel of the polynomial phase Wigner-Ville Distribution to obtain a robust time-frequency distribution able to reveal the instantaneous frequency of the PPS. The second approach, deals with robust subspace method based on the MUSIC estimator using the covariation matrix, we propose a modified MUSIC algorithm which is able to track the values of the coefficients of the phase. Finally, using the nonlinear state space model of PPS, we explore the use of the Kalman filter for robust estimation of PPS in epsilon-contaminated noise. In this context, three types of Kalman filters are proposed: The robust extended Kalman filter, the parallel extended Kalman filter. To avoid linearization an alternative method is proposed based on parallel unscented Kalman filters., Le sujet de la thèse porte sur l'étude des approches d'estimation des Signaux à Phase Polynomiale (SPP) noyés par un bruit non gaussien. Nous considérons deux modèles pour le bruit: le premier modèle est défini par une Somme Pondérée de Gaussiennes et le second par des distributions alpha-stables. Dans un premier temps, nous abordons les méthodes classiques d'analyse des SPP. L'utilisation des statistiques d'ordre fractionnaire permet d'obtenir des algorithmes robustes en présence de bruit impulsif; nous exploitons cette propriété pour proposer une Distribution de Wigner-Ville Polynomiale pour l'analyse des SPP. Cette nouvelle distribution, permet de mieux estimer la fréquence instantanée du SPP bruité. La deuxième partie est consacrée aux méthodes récentes d'analyse spectrale adaptées aux SPP. Nous proposons un algorithme MUSIC robuste obtenu par SVD de la matrice de covariation. Cet algorithme nous permet d'estimer les coefficients de la phase dans un plan temps-coefficient. Dans la troisième partie, une approche pour l'estimation des SPP par filtrage de Kalman est présentée. Cette approche repose sur un modèle d'état non linéaire avec un bruit d'observation non gaussien. Nous présentons trois types de filtres de Kalman robustes au bruit impulsif. Le premier, appelé filtre de Kalman étendu robuste utilise un gain de Kalman dépendant de la fonction de Huber. Aussi, nous proposons d'utiliser deux filtres de Kalman étendus (EKF) opérant en parallèle couplés via le terme d'apparition du bruit impulsif. Enfin, il est possible d'améliorer les performances d'estimation en utilisant un filtre UKF ‘unscented Kalman filter' à la place du filtre EKF.

The performance of stochastic optimal power control of time-varying wireless short-term flat fading channels, in which the evolution of the dynamical channel is described by a stochastic state space representation, is determined. The solution of the stochastic optimal control is obtained through path-wise optimization, which is solved by linear programming using a predictable power control strategy. The algorithm can be implemented using an iterative power control algorithm. The performance measure of the algorithm is interference or outage probability. The algorithm can be used as long as the time duration for successive adjustments of transmitter powers is less than the coherence time of the channel. Copyright © 2005 IFAC. 16 141 146

This paper deals with polynomial cointegration, i.e. with the phenomenon that linear combinations of a vector valued rational unit root process and lags of the process are of lower integration order than the process itself (for definitions see Section 2). The analysis is performed in the state space representation of rational unit root processes derived in Bauer and Wagner (2003). The state space framework is an equivalent alternative to the ARMA framework. Unit roots are allowed to occur at any point on the unit circle with arbitrary integer integration order. In the paper simple criteria for the existence of non-trivial polynomial cointegrating relationships are given. Trivial cointegrating relationships lead to the reduction of the integration order simply by appropriate differencing. The set of all polynomial cointegrating relationships is determined from simple orthogonality conditions derived directly from the state space representation. These results are important for analyzing the structure of unit root processes and their polynomial cointegrating relationships and also for the parameterization for system sets with given cointegration properties.

In this paper we develop a canonical state space representation for rational stochastic processes containing unit roots with integer integration orders at arbitrary points on the unit circle. It is shown that the state space framework, which is -- in a certain sense made precise in the paper -- equivalent to the ARMA framework, is very suitable for the analysis of unit roots and cointegration issues. The advantages become especially prominent for systems with higher integration orders at the various roots on the unit circle. A unique state space representation is constructed that clearly reveals the integration and cointegration properties. The canonical form given in the paper can be used to construct a parameterization of the class of all rational processes with a given state space unit root structure, which is defined in the paper

This paper presents a simulation study that assesses the finite sample performance of the subspace algorithm cointegration analysis developed in Bauer und Wagner (2002b). The method is formulated in the state space framework, which is equivalent to the VARMA framework, in a sense made precise in the paper. This implies applicability to VARMA processes. The paper proposes and compares six different tests for the cointegrating rank. The simulations investigate four issues: the order estimation, the size performance of the proposed tests, the accuracy of the estimation of the cointegrating space and the forecasting performance. of the state space models estimated by the proposed method. The simulations are performed on a set of trivariate processes with cointegrating ranks ranging from zero to three as well as on processes of output dimension four and cointegrating rank two. We analyze the influence of the sample size on the results as well as the sensitivity of the results with respect to stable poles approaching the unit circle. All results are compared to benchmark results obtained by applying the Johansen procedure on VAR models fitted to the data. The simulations show advantages of subspace algorithm cointegration analysis for the small sample performance of the tests for the cointegrating rank in many cases. However, we find that the accuracy of the subspace algorithm based estimation of the cointegrating space is unsatisfactory for the four-dimensional simulated systems. The forecasting performance is grosso modo comparable to the results obtained by applying the Johansen methodology on VAR approximations, although for very small sample sizes the forecasts based on VAR approximations outperform the subspace forecasts. The appendix provides critical values for the test statistics

In this paper we derive (weak) consistency and the asymptotic distribution of pseudo maximum likelihood estimates for multiple frequency I(1) processes. By multiple frequency I(1) processes we denote processes with unit roots at arbitrary points on the unit circle with the integration orders corresponding to these unit roots all equal to 1. The parameters corresponding to the cointegrating spaces at the different unit roots are estimated super-consistently and have a mixture of Brownian motions limiting distribution. All other parameters are asymptotically normally distributed and are estimated at the standard square root of T rate. The problem is formulated in the state space framework, using the canonical form and parameterization introduced by Bauer and Wagner (2002b). Therefore the analysis covers vector ARMA processes and is not restricted to autoregressive processes.

In this paper, based on the Voigt-Kelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the model's dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamilton's principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude. 'n Voigt-Kelvin saamgestelde model word in 'n nie-reglynige dinamiese oplossingsruimte gebruik om 'n soepel hanteringsrobot te ontleed. Die modellering is daartoe instaat om nie-linêre dinamiese vertoning van styfheid wat ontstaan wees sentrifugale en Corioliskragte te ontleed. Die modelvergelykings is gebaseer op die Hamiltonbeginsel. Simulasieresultate toon betekenisvolle verbetering van sisteemgedrag. Verdere ontledings handel oor strukturele demping en vibrasie-amplitude.

Dans le cadre de la modelisation des systemes dynamiques lineaires, on presente differentes formulations des equations d'etat et on analyse leur interet quant au probleme de la reduction de modele. On montre ensuite comment, a partir d'un modele de connaissance, un modele reduit peut etre obtenu par une methode originale d'identification de ses modes dominants. Cette methode est appliquee a un modele bidimensionnel (d'ordre 150), decrivant la diffusion thermique au sein d'un plancher chauffant, et comparee a d'autres techniques de reduction (Eitelberg, Marshall et agregation). Les simulations numeriques montrent que le modele identifie (d'ordre 4) donne des resultats tres satisfaisants.