Stéphane Lecoeuche

A sparse optimization approach to state observer design for switched linear systems

Abstract A new continuous state observer is derived for discrete-time linear switched systems under the assumptions that neither the continuous state nor the discrete state are known. A specificity of the proposed observer is that, in contrast to the state of the art, it does not require an explicit prior estimation of the discrete state. The key idea of the method consists in minimizing a non-smooth l 2 -norm-based weighted cost functional, constructed from the matrices of all the subsystems regardless of when each of them is active. In the light of recent development in the literature of compressed sensing, the minimized cost functional has the ability to promote sparsity in a way that makes the knowledge of the discrete mode sequence unnecessary.

Incremental and Decremental Multi-category Classification by Support Vector Machines

In this paper we propose an online multi-category support vector classifier dedicated to non-stationary environment. Our algorithm recursively discriminates between datasets of three or more classes, one sample at a time. With its incremental and decremental procedures, it can achieve an efficient update of the decision function after the incorporation/elimination of the incoming/oldest data. The key idea is to keep the KKT conditions of one single optimization problem satisfied, while adding or eliminating data. Compared to the QP approach, our classifier is able to provide accurate results. The performance of the proposed algorithm is shown on synthetic and experimental data.

The minimum-time problem for discrete-time linear systems: A non-smooth optimization approach

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.

Condition monitoring architecture for maintenance of dynamical systems with unknown failure modes

Abstract In this paper, a condition monitoring architecture for maintenance of dynamical systems with unknown failure modes is proposed. In many real applications, dysfunctional analysis techniques do not allow the determination of the complete list of failures that may impact a system. Our proposed architecture allows us to update this a priori analysis. The considered faults are slowly evolving gradual faults known also as drift. The architecture is based on dynamical clustering algorithm which leads to the detection and characterization of drifts amongst the normal operating mode and failure operating modes. The method is highlighted on a case study of a tank system.

Switched affine models for describing nonlinear systems

Abstract In this work, a recursive procedure is derived for the identification of switched affine models from input-output data. Starting from some initial values of the parameter vectors that represent the different submodels, the proposed algorithm alternates between data assignment to submodels and parameter update. At each time instant, the discrete state is determined as the index of the submodel that, in term of the prediction error, appears to have most likely generated the regressor vector observed at that instant. Given the estimated discrete state, the associated parameter vector is updated based on recursive least squares. Convergence of the whole procedure although not theoretically proved, seems to be easily achieved when enough rich data are available. Finally performance is tested through some computer simulations and the modeling of an open channel system.

Drift detection and characterization for fault diagnosis and prognosis of dynamical systems

In this paper, we present a methodology for drift detection and characterization. Our methodology is based on extracting indicators that reflect the health state of a system. It is situated in an architecture of fault diagnosis/prognosis of dynamical system that we present in this paper. A dynamical clustering algorithm is used as a major tool. The feature vectors are clustered and then the parameters of these clusters are updated as each feature vector arrives. The cluster parameters serve to compute indicators for drift detection and characterization. Then, a prognosis block uses these drift indicators to estimate the remaining useful life. The architecture is tested on a case study of a tank system with different scenarios of single and multiple faults, and with different dynamics of drift.

Multi-agent Simulation Design Driven by Real Observations and Clustering Techniques

The multi-agent simulation consists in using a set of interacting agents to reproduce the dynamics and the evolution of the phenomena that we seek to simulate. It is considered now as an alternative to classical simulations based on analytical models. But, its implementation remains difficult, particularly in terms of behaviors extraction and agents modelling. This task is usually performed by the designer who has some expertise and available observation data on the process. In this paper, we propose a novel way to make use of the observations of real world agents to model simulated agents. The modelling is based on clustering techniques. Our approach is illustrated through an example in which the behaviors of agents are extracted as trajectories and destinations from video sequences analysis. This methodology is investigated with the aim to apply it, in particular, in a retail space simulation for the evaluation of marketing strategies. This paper presents experiments of our methodology in the context of a public area modelling.

Temporal video segmentation using a switched affine models identification technique

The analysis of digital video content is of fundamental importance for efficient browsing, indexing and retrieval of video database in order to facilitate users 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.

Multimodeling vs PieceWise Affine modeling for the identification of open channel systems

Abstract The modeling of open-channel systems is a major research problem, particularly because the management of the water resource is getting critical. These systems belong to the general class of nonlinear diffusive systems. In this paper, we present a comparison between a multimodeling approach and a piecewise affine modeling approach for the identification of open channel systems. Both approaches are developed to approximate the behavior of non linear dynamical systems. Based on an a priori physical knowledge, the multimodeling method consists in the determination of a finite number of linear models along with appropriate weighting functions. Unlike the multimodeling, the piecewise affine modeling is a black-box identification approach. Given input-output data from the true system, this approach consists in (i) clustering the data according to their submodels, (ii) estimating the minimum number of submodels, (iii) estimating the parameter vector of each submodel and finally (iv) determining the regions of the regressor space where each of the submodels is valid.

Purchase Intention Based Model for a Behavioural Simulation of Sale Space

Simulation of retail space is a growing topic in the multi-agent systems community. Those systems vary depending on many issues, such as the type of store, or type of behaviour. The kind of issue that is wished to be simulated, or the type of data used to build the simulation, are other subjects of variations. Our ambition is to develop a simulator using a generic model, based on real data easy to collect. In this paper, we focus on the agent model. We develop it and make some experiments to test it.