Gérard Favier

Numerical integration approach to on-line identification of continuous-time systems

Al~traet--The problem of estimating the parameters in linear continuous differential equation models from sampled data is treated. Using a linear integral filter, we can obtain an identification model that is parametrized directly in the continuous-time model parameters. The unknown initial states of the system do not require estimation. The choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden. By applying the results from discrete-time model identification with the obtained identification model, a discrete-time parameter estimation method is developed, and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations. A simulation study is also included to confirm the theoretical results.Abstract The problem of estimating the parameters in linear continuous differential equation models from sampled data is treated. Using a linear integral filter, we can obtain an identification model that is parametrized directly in the continuous-time model parameters. The unknown initial states of the system do not require estimation. The choice of the sampling interval and the design of the linear integral filter are discussed considering the accuracy of parameter estimates and the computational burden. By applying the results from discrete-time model identification with the obtained identification model, a discrete-time parameter estimation method is developed, and the necessary condition as well as the sufficient condition on the input for consistency are explicitly derived and discussed in particular situations. A simulation study is also included to confirm the theoretical results.

PARAFAC-based unified tensor modeling for wireless communication systems with application to blind multiuser equalization

In some antenna array-based wireless communication systems the received signal is multidimensional and can be treated as a tensor (3D array) instead of a matrix (2D array). In this paper, we make use of a generalized tensor decomposition known as constrained Block-PARAFAC and propose a tensor (3D) model for the signal received by three types of wireless communication systems. The considered wireless communication systems are multiuser systems subject to frequency-selective multipath and employing multiple receiver antennas together with (i) oversampling or (ii) direct-sequence spreading or (iii) multicarrier modulation. The proposed modeling approach aims at unifying the received signal model of these systems into a single PARAFAC model. We show that the proposed model has a constrained structure, where model constraints and associated dimensions depend on each particular system. The proposed constrained Block-PARAFAC model is demonstrated by expanding the tensor using Kronecker products of canonical vectors. As an application of this model to tensor signal processing, a new tensor-based receiver is proposed for blind multiuser equalization, which combines PARAFAC-based modeling with a subspace method. Simulation results are presented to illustrate the performance of the proposed blind receiver.

Brief Optimal expansions of discrete-time Volterra models using Laguerre functions

This work is concerned with the optimization of Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of Laguerre functions associated with a given series truncation error, thus reducing the complexity of the resulting finite-dimensional representation. Fu and Dumont (IEEE Trans. Automatic Control 38(6) (1993) 934) indirectly approached this problem in the context of linear systems by minimizing an upper bound for the error resulting from the truncated Laguerre expansion of impulse response models, which are equivalent to first-order Volterra models. A generalization of the work mentioned above focusing on Volterra models of any order is presented in this paper. The main result is the derivation of analytic strict global solutions for the optimal expansion of the Volterra kernels either using an independent Laguerre basis for each kernel or using a common basis for all the kernels.

Brief Constrained robust predictive controller for uncertain processes modeled by orthonormal series functions

The present work focuses on robust predictive control (RPC) of uncertain processes and proposes a new approach based on orthonormal series function modeling. In such unstructured modeling, the output signal is described as a weighted sum of orthonormal functions that uses approximative information about the time constant of the process. Due to an efficient uncertainty representation, this kind of modeling is advantageous in the RPC context, even for constrained systems and processes with integral action. The stability of the closed-loop system is guaranteed by the setting of sufficient conditions for the selection of the controller prediction horizon. Simulation results are presented to illustrate the performance of this new RPC algorithm.

A Constrained Factor Decomposition With Application to MIMO Antenna Systems

In this paper, we formulate a new tensor decomposition herein called constrained factor (CONFAC) decomposition. It consists in decomposing a third-order tensor into a triple sum of rank-one tensor factors, where interactions involving the components of different tensor factors are allowed. The interaction pattern is controlled by three constraint matrices the columns of which are canonical vectors. Each constraint matrix is associated with a given dimension, or mode, of the tensor. The explicit use of these constraint matrices provides degrees of freedom to the CONFAC decomposition for modeling tensor signals with constrained structures which cannot be handled with the standard parallel factor (PARAFAC) decomposition. The uniqueness of this decomposition is discussed and an application to multiple-input multiple-output (MIMO) antenna systems is presented. A new transmission structure is proposed, the core of which consists of a precoder tensor decomposed as a function of the CONFAC constraint matrices. By adjusting the precoder constraint matrices, we can control the allocation of data streams and spreading codes to transmit antennas. Based on a CONFAC model of the received signal, blind symbol/code/channel recovery is possible using the alternating least squares algorithm. For illustrating this application, we evaluate the bit-error-rate (BER) performance for some configurations of the precoder constraint matrices.

Wiener-Hammerstein systems modeling using diagonal Volterra kernels coefficients

In this letter, we first present explicit relations between block-oriented nonlinear representations and Volterra models. For an identification purpose, we show that the estimation of the diagonal coefficients of the Volterra kernels associated with the considered block-oriented nonlinear structures is sufficient to recover the overall model. An alternating least squares-type algorithm is provided to carry out this model identification.

Blind channel identification algorithms based on the Parafac decomposition of cumulant tensors: The single and multiuser cases

In this paper, we exploit the symmetry properties of 4th-order cumulants to develop new blind channel identification algorithms that utilize the parallel factor (Parafac) decomposition of cumulant tensors by solving a single-step (SS) least squares (LS) problem. We first consider the case of single-input single-output (SISO) finite impulse response (FIR) channels and then we extend the results to multiple-input multiple-output (MIMO) instantaneous mixtures. Our approach is based on 4th-order output cumulants only and it is shown to hold for certain underdetermined mixtures, i.e. systems with more sources than sensors. A simplified approach using a reduced-order tensor is also discussed. Computer simulations are provided to assess the performance of the proposed algorithms in both SISO and MIMO cases, comparing them to other existing solutions. Initialization and convergence issues are also addressed.

Space-Time Multiplexing Codes: A Tensor Modeling Approach

In this paper, we present new space-time multiplexing codes (STMC) for multiple-antenna transmissions, which rely on a three-dimensional tensor modeling of the transmitted/received signals. The proposed codes combine spatial multiplexing and space-time coding by spreading a linear combination of different sub-streams of data over the space and time dimensions. We show the STMC induces a tensor structure on the transmitted/received signal that can be modeled using a trilinear tensor decomposition. Tensor modeling is exploited at the receiver for a blind decoding of the transmitted sub-streams based on linear processing and without any ambiguity. The proposed approach also provides full diversity while benefiting from the maximum multiplexing gain offered by the multiple antennas. Simulation results show that the tensor-based STMC offer remarkable performance with good diversity-multiplexing trade-off

Self-Tuning Long-Range Predictive Controllers

Abstract A new class of control methods, called long-range predictive control methods, has been recently introduced. Among these methods, Generalized Predictive Control (GPC) appears very promising for applications. In this paper some improvements of this method are presented and experimental results obtained with a real tracking system are reported.

Space-time spreading-multiplexing for MIMO wireless communication systems using the PARATUCK-2 tensor model

In this paper, we present a new space-time spreading-multiplexing model for multiple-input multiple-output (MIMO) wireless communication systems relying on a tensor modeling of the transmitted and received signals. At the transmitter, we exploit the core of a PARATUCK-2 tensor model composed of a precoding matrix and two allocation matrices that allow to control the spreading and multiplexing of the data streams across the space dimension (transmit antennas) and time-dimension (time-slots). Different MIMO schemes combining space-time multiplexing and diversity can be derived from the proposed model. The identifiability and uniqueness of the PARATUCK-2 tensor model for the received signal are discussed and subsequently exploited for a joint blind channel estimation and symbol detection. The bit-error-rate performance of different transmit schemes derived from the proposed tensor model is evaluated by means of computer simulations.