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9. Reduced-Order Identification of Aeroelastic Systems with Constrained and Imposed Poles

Author

Hugo Fournier, Paolo Massioni, Minh Tu Pham, Laurent Bako, and Robin Vernay

Subjects
Space and Planetary Science, Control and Systems Engineering, Applied Mathematics, Aerospace Engineering, Electrical and Electronic Engineering
Abstract

This work investigates the identification of reduced-order state-space models from aeroelastic simulations of the interaction of a built-in structural finite element model and a linear aerodynamic model using unsteady potential theory. The objective is to propose and compare different new frequency-based identification methods operating on frequency response associated to the inputs and outputs of interest. The first methods considered are the Loewner interpolation method and a subspace algorithm. Subsequently, the paper introduces the possibility to apply stability constraints and to impose a certain number of poles estimated beforehand by the [Formula: see text] method in order to make the identified models closer to the true aeroelastic physics. To achieve this goal, new dedicated techniques are developed and subsequently validated on data generated by random state-space models of various orders, and on aeroelastic data obtained from structural and aerodynamic aircraft models.

Published
2023

13. Special Issue on Sparsity‐inducing Methods in Control Theory

Author

Laurent Bako, Yilin Mo, and Masaaki Nagahara

Subjects
Control and Systems Engineering, Mechanical Engineering, General Chemical Engineering, Biomedical Engineering, Aerospace Engineering, Electrical and Electronic Engineering, Industrial and Manufacturing Engineering
Published
2022

14. Robust Gust Load Alleviation of Flexible Aircraft Equipped with Lidar

Author

Robin Vernay, Minh Tu Pham, Paolo Massioni, Laurent Bako, Michele Colombo, Hugo Fournier, Airbus Operation S.A.S., Airbus [France], Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
ComputingMethodologies_SIMULATIONANDMODELING, Computer science, Aerospace Engineering, ComputerApplications_COMPUTERSINOTHERSYSTEMS, 02 engineering and technology, 01 natural sciences, GeneralLiterature_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 010305 fluids & plasmas, [SPI]Engineering Sciences [physics], 0203 mechanical engineering, 0103 physical sciences, Electrical and Electronic Engineering, Aerospace engineering, ComputingMilieux_MISCELLANEOUS, 020301 aerospace & aeronautics, Wing, business.industry, Applied Mathematics, Work (physics), Flight control surfaces, Aerodynamic force, Model predictive control, Lidar, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], Space and Planetary Science, Control and Systems Engineering, Actuator, business
Abstract

This work concerns the problem of gust load alleviation of a flexible aircraft by focusing on Airbus’s XRF1 aircraft concept, with a fully actuated wing. The aircraft is equipped with a lidar senso...

Published
2022

31. Analysis of the Least Sum-of-Minimums Estimator for Switched Systems

Author

Laurent Bako, Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
robustness to outliers, 0209 industrial biotechnology, Optimization problem, Systems and Control (eess.SY), 02 engineering and technology, Electrical Engineering and Systems Science - Systems and Control, [SPI.AUTO]Engineering Sciences [physics]/Automatic, data richness, 020901 industrial engineering & automation, 0203 mechanical engineering, FOS: Electrical engineering, electronic engineering, information engineering, Applied mathematics, Uniqueness, Electrical and Electronic Engineering, Finite set, system identification, Mathematics, Pointwise, 020301 aerospace & aeronautics, sparsity, Solution set, Estimator, Function (mathematics), Infimum and supremum, Computer Science Applications, Control and Systems Engineering, switched systems
Abstract

International audience; This paper considers a particular parameter estimator for switched systems and analyzes its properties. The estimator in question is defined as the map from the data set to the solution set of an optimization problem where the to-be-optimized cost function is a sum of pointwise infima over a finite set of sub-functions. This is a hard nonconvex problem. The paper studies some fundamental properties of this problem such as uniqueness of the solution or boundedness of the estimation error regardless of computational considerations. The interest of the analysis is to lay out the main influential properties of the data on the performance of this (ideal) estimator.

Published
2021

33. On the notion of persistence of excitation for linear switched systems

Author

Mihaly Petreczky, Laurent Bako, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Property (philosophy), Computer science, Markov process, Systems and Control (eess.SY), Topology, Signal, symbols.namesake, 93B15, 93B20, 93B25, 93C99, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Switched system, System identification, Mathematics - Optimization and Control, Linear system, Computer Science Applications, Realization theory, Optimization and Control (math.OC), Control and Systems Engineering, symbols, Computer Science - Systems and Control, Persistence of excitation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Persistence (discontinuity), Realization (systems), Excitation, Analysis
Abstract

International audience; The paper formulates the concept of persistence of excitation for discrete-time linear switched systems, and provides sufficient conditions for an input signal to be persistently exciting. Persistence of excitation is formulated as a property of the input signal, and it is not tied to any specific identification algorithm. The results of the paper rely on realization theory and on the notion of Markov-parameters for linear switched systems.

Published
2023

34. Data Informativity for the Identification of particular Parallel Hammerstein Systems

Author

Xavier Bombois, Federico Morelli, Kévin Colin, Laurent Bako, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Computer science, Property (programming), Data Informativity, 020208 electrical & electronic engineering, Vibrating structure gyroscope, Structure (category theory), 02 engineering and technology, Type (model theory), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Identification (information), Consistency (database systems), symbols.namesake, Nonlinear system, 020901 industrial engineering & automation, Additive white Gaussian noise, Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, symbols, Consistency, Hammerstein Systems, Algorithm, System Identication, Prediction Error Method
Abstract

International audience; To obtain a consistent estimate when performing an identication with Prediction Error, it is important that the excitation yields informative data with respect to the chosen model structure. While the characterization of this property seems to be a mature research area in the linear case, the same cannot be said for nonlinear systems. In this work, we study the data informativity for a particular type of Hammerstein systems for two commonly-used excitations: white Gaussian noise and multisine. The real life example of the MEMS gyroscope is considered.

Published
2020

36. Least Costly Identification Experiment for the Identification of One Module in a Dynamic Network

Author

Xavier Bombois, Kévin Colin, Laurent Bako, Federico Morelli, Håkan Hjalmarsson, Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), ACCESS Linnaeus Center and Department of Automatic Control, and Royal Institute of Technology [Stockholm] (KTH )

Subjects
0209 industrial biotechnology, 020901 industrial engineering & automation, Dynamic network analysis, Control and Systems Engineering, Computer science, 020208 electrical & electronic engineering, 0202 electrical engineering, electronic engineering, information engineering, Control engineering, 02 engineering and technology, Electrical and Electronic Engineering, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; In this paper we consider the design of least costly experiments for the identification of one module in a given network of locally controlled systems. The identification experiment will be designed in such a way that we obtain a sufficiently accurate model of the to-be-identified module with the smallest identification cost i.e. with the least perturbation of the network.

Published
2021

37. An interval-valued recursive estimation framework for linearly parameterized systems

Author

Laurent Bako, Seydi Ndiaye, and Eric Blanco

Subjects
History, Polymers and Plastics, General Computer Science, Control and Systems Engineering, Mechanical Engineering, FOS: Electrical engineering, electronic engineering, information engineering, Systems and Control (eess.SY), Business and International Management, Electrical and Electronic Engineering, Electrical Engineering and Systems Science - Systems and Control, Industrial and Manufacturing Engineering
Abstract

This paper proposes a recursive interval-valued estimation framework for identifying the parameters of linearly parameterized systems which may be slowly time-varying. It is assumed that the model error (which may consist in measurement noise or model mismatch or both) is unknown but lies at each time instant in a known interval. In this context, the proposed method relies on bounding the error generated by a given reference point-valued recursive estimator, for example, the well-known recursive least squares algorithm. We discuss the trade-off between computational complexity and tightness of the estimated parametric interval., 11 pages, 4 figures

Published
2022

38. Data Informativity for the Closed-Loop Identification of MISO ARX Systems

Author

Xavier Bombois, Laurent Bako, Kévin Colin, Centre National de la Recherche Scientifique (CNRS), Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
0209 industrial biotechnology, Computer science, Property (programming), Data Informativity, 020208 electrical & electronic engineering, System identification, Structure (category theory), System Identification, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Consistency (database systems), Identification (information), 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Consistency, Focus (optics), Closed loop, Prediction Error Method
Abstract

International audience; In the Prediction Error identification framework, it is crucial that the collected data are informative with respect to the chosen model structure to get a consistent estimate. In this work, we focus on the data informativity property for the identification of multi-inputs single-output ARX systems in closed-loop and we derive a necessary and sufficient condition to verify if a given multisine external excitation combined with the feedback introduced by the controller yields informative data with respect to the chosen model structure.

Published
2021

39. Incremental L2-gain stability of piecewise-affine systems with piecewise-polynomial storage functions

Author

Paolo Massioni, Laurent Bako, Sérgio Waitman, and Gérard Scorletti

Subjects
0209 industrial biotechnology, Polynomial, 020208 electrical & electronic engineering, Explained sum of squares, 02 engineering and technology, Linear matrix, Stability (probability), Upper and lower bounds, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, Piecewise, Applied mathematics, Piecewise affine, Electrical and Electronic Engineering, Mathematics
Abstract

This paper concerns the incremental L2-gain stability of piecewise-affine (PWA) systems. We propose sufficient conditions derived from dissipativity theory to compute an upper bound on the incremental L2-gain. This is achieved by constructing piecewise-polynomial storage functions through the use of sum of squares (SOS) relaxations. The constraints are expressed as linear matrix inequalities (LMIs), which can be solved numerically in an efficient way. The proposed conditions are verified to be less conservative than previous results found in the literature by means of a numerical example.

Published
2019

40. Interval-valued state estimation for linear systems: The tightest estimator and its relaxations

Author

Vincent Andrieu, Laurent Bako, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire d'automatique et de génie des procédés (LAGEP), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-École Supérieure Chimie Physique Électronique de Lyon-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
0209 industrial biotechnology, Mathematical optimization, Computational complexity theory, Intersection (set theory), Computer science, 020208 electrical & electronic engineering, Interval estimation, Linear system, SIGNAL (programming language), Estimator, 02 engineering and technology, State (functional analysis), Expression (mathematics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering
Abstract

International audience; This paper discusses an interval-valued state estimation framework for linear dynamic systems. In particular, we derive an expression of the tightest possible interval estimator in the sense that it is the intersection of all interval-valued estimators for the system of interest. However, from a numerical implementation perspective, this estimator might suffer from a high complexity, at least in the general setting. Therefore, practical implementation might require some over-approximations which would yield a good trade-off between computational complexity and tightness. We discuss a number of such over-approximations. We also consider the general estimation scenario when the system parameters, the initial state, the input signal and the measurement are all uncertain.

Published
2019

41. Robust optimal identification experiment design for multisine excitation

Author

Xavier Bombois, Håkan Hjalmarsson, Laurent Bako, Federico Morelli, Kévin Colin, Centre National de la Recherche Scientifique (CNRS), Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), ACCESS Linnaeus Center and Department of Automatic Control, and Royal Institute of Technology [Stockholm] (KTH )

Subjects
0209 industrial biotechnology, Optimization problem, Computer science, Design of experiments, 020208 electrical & electronic engineering, Spectrum (functional analysis), 02 engineering and technology, Signal, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), Constraint (information theory), Identification (information), 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Convex optimization, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering
Abstract

International audience; In least costly experiment design, the optimal spectrum of an identification experiment is determined in such a way that the cost of the experiment is minimized under some accuracy constraint on the identified parameter vector. Like all optimal experiment design problems, this optimization problem depends on the unknown true system, which is generally replaced by an initial estimate. One important consequence of this is that we can underestimate the actual cost of the experiment and that the accuracy of the identified model can be lower than desired. Here, based on an a-priori uncertainty set for the true system, we propose a convex optimization approach that allows to prevent these issues from happening. We do this when the to-be-determined spectrum is the one of a multisine signal. 1 Introduction We consider in this paper the problem of optimally designing the spectrum Φ u of the excitation signal u of an open-loop identification experiment. By optimal spectrum , we here mean the spectrum yielding the smallest experiment cost while guaranteeing that the accuracy of the identified parameter vector of the plant transfer function is larger than a given threshold. We thus consider the least costly experiment design framework [5], but the approach can easily be adapted to other (dual) frameworks [10,17,13]. The experiment cost J can be defined as a linear combination of the power of the exci-tation signal u and of the power of the part of the output signal induced by u. The experiment cost will therefore be a function of the spectrum Φ u , but also of the unknown true parameter vector θ 0 (we therefore denote the cost as J (θ 0 , Φ u)). Likewise, the accuracy constraint will also depend on θ 0 and on Φ u since the classical accuracy constraints are of the type P −1 (θ 0 , Φ u) ≥ R adm where P (θ 0 , Φ u) is the covariance matrix of the to-be-identified parameter vector (which depends on θ 0 and Φ u) and R adm a matrix reflecting the desired accuracy. The dependency of the optimal spectrum Φ u,opt on the unknown true parameter vector θ 0 is the so-called chicken-and-egg issue encountered in optimal experiment design. This issue is generally circumvented by replacing θ 0 by

Published
2021

42. Closed-loop Identification of MIMO Systems in the Prediction Error Framework: Data Informativity Analysis

Author

Kévin Colin, Laurent Bako, Federico Morelli, Xavier Bombois, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
0209 industrial biotechnology, Work (thermodynamics), Computer science, Property (programming), 020208 electrical & electronic engineering, System identification, Structure (category theory), System Identification, Closed-loop Identification, 02 engineering and technology, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Identification (information), Consistency (database systems), 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, MIMO Systems, 0202 electrical engineering, electronic engineering, information engineering, Consistency, Electrical and Electronic Engineering, Focus (optics), Algorithm, Prediction Error Methods
Abstract

In the Prediction Error identification framework, it is essential that the experiment yields informative data with respect to the chosen model structure to get a consistent estimate. In this work, we focus on the data informativity property for the identification of multi-inputs multi-outputs systems in closed-loop and we derive conditions to verify if a given external excitation combined with the feedback introduced by the controller yields informative data with respect to the chosen model structure. This study covers the case of multiple-inputs multiple-outputs model structures that are natural generalizations of the classical single-input single-output model structures used in Prediction Error identification and the classical types of external excitation vectors, i.e., vectors whose elements are either multisine or filtered white noises.

Published
2020

43. Minimality and identifiability of discrete‐time switched autoregressive exogenous systems

Author

Mihaly Petreczky, K.M.D. Motchon, Stéphane Lecoeuche, Laurent Bako, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Ecole nationale supérieure Mines-Télécom Lille Douai (IMT Lille Douai), Institut Mines-Télécom [Paris] (IMT), Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 (CRESTIC), Université de Reims Champagne-Ardenne (URCA), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL], Ecole nationale supérieure Mines-Télécom Lille Douai [IMT Lille Douai], and Centre de Recherche en Sciences et Technologies de l'Information et de la Communication - EA 3804 [CRESTIC]

Subjects
0209 industrial biotechnology, Computer science, General Chemical Engineering, Biomedical Engineering, Aerospace Engineering, 02 engineering and technology, 01 natural sciences, Industrial and Manufacturing Engineering, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], 0101 mathematics, Electrical and Electronic Engineering, Switched ARX systems, ComputingMilieux_MISCELLANEOUS, system identification, Mechanical Engineering, 010102 general mathematics, System identification, hybrid systems, identifiability, Discrete time and continuous time, Autoregressive model, Control and Systems Engineering, Hybrid system, Identifiability, minimality
Abstract

International audience; The paper studies the problem of minimality and identifiability for Switched Auto-Regressive eXogenous (abbreviated by SARX) systems. We propose formal definitions of the concepts of identifiability and minimality for SARX models. Based on these formalizations, we derive conditions for minimality and identifiability of SARX systems. In particular, we show that polynomially parameterized SARX systems are generically identifiable.

Published
2020

44. Analysis of pulse width modulation controlled systems based on a piecewise affine description

Author

Laurent Bako, Alexandre Trofino, Paolo Massioni, Gérard Scorletti, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC)

Subjects
Semidefinite programming, 0209 industrial biotechnology, Computer science, Mechanical Engineering, General Chemical Engineering, Biomedical Engineering, Aerospace Engineering, 02 engineering and technology, Invariant (physics), Instability, Industrial and Manufacturing Engineering, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Exponential stability, Discrete time and continuous time, Control and Systems Engineering, Control theory, Hybrid system, 0202 electrical engineering, electronic engineering, information engineering, Piecewise, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Pulse-width modulation
Abstract

International audience; The problem of assuring the asymptotic stability of a pulse width modulation (PMW) control scheme is a classical topic in control engineering, where a continuous‐time control signal is approximated by a piecewise constant signal. This paper proposes a general framework that either shows the local asymptotic stability of the closed‐loop PWM system or proves the convergence of the state to an invariant set, which is the case in the presence of limit cycles. The proposed method is based on a piecewise affine representation of the closed‐loop system in discrete time, and it uses semidefinite programming both to find a Lyapunov‐like function and to determine an estimate of the region of attraction. This is an important feature since the desired continuous‐time control action at some instants may be larger than the magnitude of the PWM signals, leading to saturation of the applied control action, a well‐known source of performance degradation and even instability. Two academic examples of applications are shown, in the domain of spacecraft positioning control and electric direct current (DC) motor servoing.

Published
2020

45. Stability of uncertain piecewise-affine systems with parametric dependence

Author

Laurent Bako, Gérard Scorletti, Paolo Massioni, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
Lyapunov stability, Lyapunov function, 0209 industrial biotechnology, Polynomial, Hybrid systems, Computer science, 020208 electrical & electronic engineering, Linear matrix inequalities, 02 engineering and technology, Function (mathematics), Piecewise-affine systems, Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control and Systems Engineering, Hybrid system, 0202 electrical engineering, electronic engineering, information engineering, symbols, Applied mathematics, Variable (mathematics), Parametric statistics
Abstract

International audience; This paper proposes a numerical approach to the stability analysis for a class of piecewise-affine systems with (possibly time-varying) parameter-dependent cells and dynamics. This class of model aims at allowing a better modelling of time-varying or parameter-varying nonlinearities of physical phenomena such as dry friction. We form the stability certification problem as the one of finding a Lyapunov function that is parameterised as a polynomial function of the variable parameter. The application of the well-known Lyapunov stability theorem together with the use of the generalised S-procedure reduces the problem to checking whether a certain set of matrices has the sum-of-squares property. The latter can be solved using well-documented numerical solvers, and we provide two examples of successful applications at the end of the paper.

Published
2020

46. On the resilience of a class of Correntropy-based state estimators

Author

Laurent Bako, Alexandre Kircher, Mohamed Benallouch, Eric Blanco, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), LabECAM, and ECAM Lyon (ECAM Lyon)

Subjects
0209 industrial biotechnology, Class (set theory), Optimization problem, Maximum Correntropy Criterion (MCC), Generalization, Computer science, Cyber-physical systems, 020208 electrical & electronic engineering, Estimator, Observable, 02 engineering and technology, State (functional analysis), optimal estimation, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Noise, 020901 industrial engineering & automation, Control and Systems Engineering, Bounded function, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Secure state estimation
Abstract

International audience; This paper deals with the analysis of a class of offline state estimators for LTI discrete-time systems in the presence of an arbitrary measurement noise which can potentially take any value. The considered class of estimators is defined as the solution of an optimization problem involving a performance function which can be interpreted as a generalization of cost functions used in the Maximum Correntropy Criterion. The conclusion of the analysis is that if the system is observable enough, then the considered class of estimators is resilient, which means that the obtained estimation error is independent from the highest values of the measurement noise. In the case of systems with a bounded process noise, the considered class of estimators provides a bounded estimation error under the appropriate conditions despite not being designed for this scenario.

Published
2020

47. Analysis of resilience for a State Estimator for Linear Systems

Author

Mohamed Benallouch, Alexandre Kircher, Anton Korniienko, Laurent Bako, Eric Blanco, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), LabECAM, and ECAM Lyon (ECAM Lyon)

Subjects
0209 industrial biotechnology, sensor attacks, Computer science, Cyber-physical systems, Linear system, outliers, Estimator, 020206 networking & telecommunications, 02 engineering and technology, Expression (mathematics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Noise, 020901 industrial engineering & automation, Control theory, Bounded function, resilient estimators, 0202 electrical engineering, electronic engineering, information engineering, Observability, Resilience (network), Extreme value theory, Secure state estimation
Abstract

International audience; This paper proposes to analyze the resilient properties of a specific state estimator for LTI discrete-time systems. The dynamic equation of the system is assumed to be affected by a bounded process noise. As to the available measurements, they are potentially corrupted by a noise of both dense and impulsive natures. In this setting, we define an estimator as the map which associates to the measurements, the minimizing set of an appropriate (convex) performance function. It is then shown that the proposed estimator enjoys the property of resilience, that is, it induces an estimation error which, under certain conditions, is independent of the extreme values of the (impulsive) measurement noise. Therefore, the estimation error may be bounded while the measurement noise is virtually unbounded. Moreover, the expression of the bound depends explicitly on the degree of observability of the system being observed and on the considered performance function. Finally, a few simulation results are provided to illustrate the resilience property.

Published
2020

48. Data Informativity for the Open-Loop Identification of MIMO Systems in the Prediction Error Framework

Author

Federico Morelli, Laurent Bako, Xavier Bombois, Kévin Colin, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Centre for Digital Systems (CERI SN), Ecole nationale supérieure Mines-Télécom Lille Douai (IMT Lille Douai), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
0209 industrial biotechnology, Property (programming), Computer science, Mean squared prediction error, 020208 electrical & electronic engineering, Data informativity, Open-loop controller, Structure (category theory), System Identification, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Identification (information), 020901 industrial engineering & automation, Control and Systems Engineering, MIMO Systems, 0202 electrical engineering, electronic engineering, information engineering, Consistency, Electrical and Electronic Engineering, Algorithm, Prediction Error Methods, Mimo systems
Abstract

International audience; In Prediction Error identification, to obtain a consistent estimate of the true system, it is crucial that the input excitation yields informative data with respect to the chosen model structure. We consider in this paper the data informativity property for the identification of a Multiple-Input Multiple-Output system in open loop and we derive conditions to check whether a given input vector will yield informative data with respect to the chosen model structure. We do that for the classical model structures used in prediction-error identification and for the classical types of input vectors, i.e., input vectors whose elements are either multisines or filtered white noises.

Published
2020

49. Data Informativity for the Identification of MISO FIR Systems with Filtered White Noise Excitation

Author

Laurent Bako, Xavier Bombois, Federico Morelli, Kévin Colin, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Centre for Digital Systems (CERI SN), Ecole nationale supérieure Mines-Télécom Lille Douai (IMT Lille Douai), and Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)

Subjects
0209 industrial biotechnology, Finite impulse response, 020208 electrical & electronic engineering, Structure (category theory), Spectral density, White noise excitation, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Identification (information), Matrix (mathematics), 020901 industrial engineering & automation, Positive definiteness, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Identifiability, Algorithm, Mathematics
Abstract

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.

Published
2019

50. Optimal Experiment Design for the Identification of One Module in the Interconnection of Locally Controlled Systems

Author

Laurent Bako, Kévin Colin, Xja Bombois, Håkan Hjalmarsson, Federico Morelli, Ampère, Département Méthodes pour l'Ingénierie des Systèmes (MIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Centre National de la Recherche Scientifique (CNRS), Division of Decision and Control Systems - School of Electrical Engineering and Computer Science, Royal Institute of Technology [Stockholm] (KTH ), ACCESS Linnaeus Center and Department of Automatic Control, and Morelli, Federico

Subjects
0209 industrial biotechnology, Interconnection, Excitation signal, Computer science, Design of experiments, 020208 electrical & electronic engineering, Spectrum (functional analysis), 02 engineering and technology, local closed loop system, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Identification (information), [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, excitation signal, optimal experiment design problem, locally controlled systems, Closed loop
Abstract

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.

Published
2019

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