Benoît Marx

Bio: Benoît Marx is an academic researcher from University of Lorraine. The author has contributed to research in topics: Observer (quantum physics) & Nonlinear system. The author has an hindex of 27, co-authored 122 publications receiving 2204 citations. Previous affiliations of Benoît Marx include Nancy-Université & Centre national de la recherche scientifique.

Design of observers for TakagiߝSugeno descriptor systems with unknown inputs and application to fault diagnosis

Abstract: This paper presents a method for state-estimation of Takagi-Sugeno descriptor systems (TSDS) affected by unknown inputs (UI). For ease of implementation's sake, the proposed observers are not in descriptor form but in usual form. Sufficient existence conditions of the unknown input observers are given and strict linear matrix inequalities (LMI) are solved to determine the gain of the observers. If the perfect unknown input decoupling is not possible, the UI observer is designed in order to minimise the L2-gain from the UI to the state estimation error. The two previous objectives can be mixed in order to decouple the estimation to a subset of the UI, while attenuating the L2 gain from the other UI to the estimation. The proposed UI observers are used for robust fault diagnosis. Fault diagnosis for TSDS is performed by designing a bank of observers. A simple decision logic and thresholds setting allow to determine the occurring fault. The results are established for both the continuous and the discrete time cases. The proposed method is illustrated by a numerical example.

Brief paper: state estimation of Takagi-Sugeno systems with unmeasurable premise variables

Abstract: This study is dedicated to the design of observers for non-linear systems described by Takagi–Sugeno (T–S) multiple models with unmeasurable premise variables. Furthermore, this T–S structure can represent a larger class of non-linear systems compared to the T–S systems with measurable premise variables. Considering the state of the system as a premise variable allows one to exactly represent the non-linear systems described by the general form x=f(x, u). Unfortunately, the developed methods for estimating the state of T–S systems with measured premise variable are not directly applicable for the systems that use the state as a premise variable. In the present paper, firstly, the design of observers for T–S systems with unmeasurable premise variable is proposed and sufficient convergence conditions are established by Lyapunov stability analysis. The linear matrix inequality (LMI) formalism is used in order to express the convergence conditions of the state estimation error in terms of LMI and to obtain the gains of the observer. Secondly, the proposed method is extended in order to attenuate energy-bounded unknown inputs such as disturbances. An academic example is proposed to compare some existing methods and the proposed one.

Unknown Input Observers for Switched Nonlinear Discrete Time Descriptor Systems

Abstract: In this paper, a linear matrix inequality technique for the state estimation of discrete-time, nonlinear switched descriptor systems is developed. The considered systems are composed of linear and nonlinear parts. An observer giving a perfect unknown input decoupled state estimation is proposed. Sufficient conditions of global convergence of observers are proposed. Numerical examples are given to illustrate this method.

Simultaneous state and unknown inputs estimation with PI and PMI observers for Takagi Sugeno model with unmeasurable premise variables

Abstract: In this paper, a proportional integral (PI) and a proportional multiple integral observer (PMI) are proposed in order to estimate the state and the unknown inputs of nonlinear systems described by a Takagi-Sugeno model with unmeasurable premise variables. This work is an extension to nonlinear systems of the PI and PMI observers developed for linear systems. The state estimation error is written as a perturbed system. First, the convergence conditions of the state estimation errors between the system and each observer are given in LMI (Linear Matrix Inequality) formulation. Secondly, a comparison between the two observers is made through an academic example.

Controllability of structural brain networks.

Abstract: Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function.

Controllability Metrics, Limitations and Algorithms for Complex Networks

Abstract: This paper studies the problem of controlling complex networks, i.e., the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem, 1) we propose a metric to quantify the difficulty of the control problem as a function of the required control energy, 2) we derive bounds based on the system dynamics (network topology and weights) to characterize the tradeoff between the control energy and the number of control nodes, and 3) we propose an open-loop control strategy with performance guarantees. In our strategy, we select control nodes by relying on network partitioning, and we design the control input by leveraging optimal and distributed control techniques. Our findings show several control limitations and properties. For instance, for Schur stable and symmetric networks: 1) if the number of control nodes is constant, then the control energy increases exponentially with the number of network nodes; 2) if the number of control nodes is a fixed fraction of the network nodes, then certain networks can be controlled with constant energy independently of the network dimension; and 3) clustered networks may be easier to control because, for sufficiently many control nodes, the control energy depends only on the controllability properties of the clusters and on their coupling strength. We validate our results with examples from power networks, social networks and epidemics spreading.

Nonlinear System Identification

Abstract: This chapter contains sections titled: Historical Review Supervised Multilayer Networks Unsupervised Neural Networks: Kohonen Network Unsupervised Networks: Adaptive Resonance Theory Network Model Validation Summary References Recommended Exercises

Disturbance Observer for Estimating Higher Order Disturbances in Time Series Expansion

Abstract: In the note, a generalized disturbance observer capable of estimating higher order disturbances in the time series expansion is newly proposed. Initiated from a constant disturbance observer, we extend it systematically to cope with ramp disturbance and general order disturbances. The generalized form for disturbance observer exhibits the novel structure incorporating the system model and integrals. To be practical, the noisy measurement and the performance in the frequency domain are addressed. In addition, for a class of linear systems, an output-based disturbance observer of reduce order is newly derived from the proposed full state disturbance observer, and its potential applicability will be demonstrated by an example.

Unknown Input Observer-Based Robust Fault Estimation for Systems Corrupted by Partially Decoupled Disturbances

Abstract: Robust fault estimation plays an important role in real-time monitoring, diagnosis, and fault-tolerance control. Accordingly, this paper aims to develop an effective fault estimation technique to simultaneously estimate the system states and the concerned faults, while minimizing the influences from process/sensor disturbances. Specifically, an augmented system is constructed by forming an augmented state vector composed of the system states and the concerned faults. Next, an unknown input observer (UIO) is designed for the augmented system by decoupling the partial disturbances and attenuating the disturbances that cannot be decoupled, leading to a simultaneous estimate of the system states and the concerned faults. In order to be close to the practical engineering situations, the process disturbances in this study are assumed not to be completely decoupled. In the first part of this paper, the existence condition of such an UIO is proposed to facilitate the fault estimation for linear systems subjected to process disturbances. In the second part, robust fault estimation techniques are addressed for Lipschitz nonlinear systems subjected to both process and sensor disturbances. The proposed technique is finally illustrated by the simulation studies of a three-shaft gas turbine engine and a single-link flexible joint robot.