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International audience; For Prediction Error Identication, there are two main ingredients to get a consistent estimate: one of them is the data informativity with respect to (w.r.t.) the considered model structure. One common criterion used for the informativity is the positive deniteness of the input density spectral power (DSP) matrix at all frequencies. This criterion is not appropriate for multisine excitation but can be used for ltered white noise excitation for many identication problems. However, this criterion is not necessary and its application for some identication problems might not be possible. In this paper, we propose a necessary and sucient condition for the data informativity in the case of multiple-inputs single-output (MISO) nite impulse response (FIR) model structure in open-loop.

International audience; In this paper we consider the problem of identifying piecewise affine approximations of nonlinear dynamic systems directly from input-output measurements. This requires estimating a partition of the regression space and an associated set of affine time-invariant models. By relying on a generic Voronoi type of partition, the proposed approach treats these two tasks jointly via the minimization of an appropriate objective function formed as a weighted sum of errors related to all submodels. We minimize this objective function with respect to both the weights and the parameters (describing the partition and the affine submodels) under some heuristic constraint on the weights. It is later observed that the proposed method attempts indeed to optimize a sum (over the available dataset) of harmonic means. The final estimation algorithm consists in solving iteratively a sequence of convex optimization problems. Numerical experiments tend to suggest that the new method exhibits some nice properties: regular convergence and good estimation performance.

International audience; In this paper, we consider the problem of designing the least costly experiment that leads to a sufficiently accurate estimate of one module in a network of locally controlled systems. A module in such a network can be identified by exciting the corresponding local closed loop system. Such an excitation signal will not only perturb the input/output of the to-be-identified module, but also other modules due to the interconnection. Consequently, the cost of the identification can be expressed as the sum of the influence of the excitation signal on the inputs and outputs of all locally controlled systems. We develop a methodology to design the spectrum of the excitation signal in such a way that this cost is minimized while guaranteeing a certain accuracy for the identified model. We also propose an alternative identification configuration which can further reduce the propagation of the excitation signal to other modules and we make steps to robustify this optimal experiment design problem with respect to the cost of the identification.

In this paper we are interested in the incremental stability of piecewise-affine (PWA) systems. We present conditions to compute an upper bound on the incremental ℒ2-gain based on dissipativity analysis. These conditions are expressed as linear matrix inequalities (LMI) allowing the construction of a continuous piecewise quadratic storage function. It is also shown that these conditions imply incremental asymptotic stability of the system. The result is illustrated with numerical examples.

International audience; Identifying switched linear models directly from input-output measurements only is known to be a non-trivial identification problem. When switched state-space models are considered in a general setting and both the continuous state and the discrete mode are unmeasured, the problem proves to be a much harder realization problem. The present paper describes a method for identifying discrete-time switched linear state-space models from input-state-output measurements. While the discrete mode is unknown, we assume here that the continuous state is measured along with the input and output signals. Given a finite collection of such measured data, we propose a sparsity-inducing optimization approach for estimating the matrices associated with each submodel.

This paper addresses the problem of driving the state of a linear discrete-time system to zero in minimum time. The inputs are constrained to lie in a bounded and convex set. The solution presented in the paper is based on the observation that the state sequence induced by the minimum-time control sequence is the sparsest possible state sequence over a certain finite horizon. That is, the desired state sequence must contain as many zero vectors as possible, all those zeros corresponding to the highest values of the time index. Hence, by taking advantage of some recent developments in sparse optimization theory, we propose a numerical solution. We show in simulation that the proposed method can effectively solve the minimum-time problem even for multi-inputs linear discrete-time systems.

We consider the problem of identifying a switched nonlinear system from a finite collection of input-output data. The constituent subsystems of such a switched system are all nonlinear systems. We model each individual subsystem as a sparse expansion over a dictionary of elementary nonlinear smooth functions shaped by the whole available dataset. Estimating the switched model from data is a doubly challenging problem. First one needs, without any knowledge of the parameters, to decide which subsystem is active at which time instant. Second, the representation of each nonlinear subsystem over the considered basis shall be performed in a high dimensional space. We tackle both tasks simultaneously by sparse optimization. More specifically, we view the switched nonlinear system identification problem as the problem of minimizing the l 0 norm of an error vector. We subsequently relax it into an l 1 convex minimization problem for which powerful numerical tools exist.

The analysis of digital video content is of fundamental importance for efficient browsing, indexing and retrieval of video database in order to facilitate user's access to relevant data. An essential first step is the parsing of the video content into visually-coherent segments, called shots. In this paper we propose an efficient approach for shot change detection and shot modeling based on a new Switched AutoRegressive (SAR) model identification technique. We make the assumption that pixel intensities of all the frames obey a SAR model where each linear sub-model of the SAR model corresponds to a shot and each discrete state corresponds to a different event in the video. Finally, experimental results on three different video sequences show the performance and the feasibility of the proposed approach.

The modeling of nonlinear real-life systems subject to parameters variation is a major research problem. In this paper, a weighted combination of multiple local models is proposed to represent the dynamics of an open channel system. The multimodelling strategy followed consists in the determination of a finite number of models along with appropriate weights functions. The families of Gaussian and Boolean weights functions are particularly studied and compared in various aspects on an application example. For the purpose of supervision, the approach of composite linear local models appears to be an interesting alternative to the use of Saint Venant partial differential equations. The efficiency of the multimodelling methods is shown by simulation within the framework of a dam-gallery system.