arXiv subjects

Christophe Aubrun

Publications and source records attributed to Christophe Aubrun.

9 recordsLinked to original sources

arXiv2020

An approach to parameter identifiability for a class of nonlinear models represented in LPV form

In several model-based system maintenance problems, parameters are used to represent unknown characteristics of a component, equipment degradation, etc. This allows for modelling constant, slow-varying terms. The identifiability of these parameters is an important condition to estimate them. Linear Parameter Varying (LPV) models are being increasingly used in the industries as a bridge between linear and nonlinear models. Techniques exist that can rewrite some nonlinear models in LPV form. However, the problem of identifiability of these models is still at a nascent stage. In this paper, we propose an approach to verify identifiability of unknown parameters for LPV state-space models. It makes use of a parity-space like formulation to eliminate the states of the model. The resulting input-output-parameter equation is analysed to verify the identifiability of the original model or a subset of unknown parameters. This approach provides a framework for both continuous-time and discrete-time models and we illustrate it using examples.

math.OC↗

arXiv2017

An Adaptive Observer Design for Takagi-Sugeno type Nonlinear System

Takagi-Sugeno (T-S) type of polytopic models have been used prominently in the literature to analyze nonlinear systems. With the sector nonlinearity approach, an exact representation of a nonlinear system within a sector could be obtained in a T-S form. Hence, a number of observer design strategies have been proposed for nonlinear systems using the T-S framework. In this work, a design strategy for adaptive observers is presented for a type of T-S systems with unknown parameters. The proposed approach improves upon the existing literature in two folds: reduce the computational burden and provide an algorithmic procedure that would seamlessly connect the state estimation and parameter estimation parts of the observer design. Lyapunov approach is used for the stability analysis and the design procedure. The results are illustrated on a simulation example.

math.OC↗

arXiv2017

An adaptive observer design approach for discrete-time nonlinear systems

We discuss a design approach for nonlinear discrete-time adaptive observer. This involves transforming a nonlinear system into a quasi-LPV (Linear Parameter Varying) polytopic model in Takagi-Sugeno (T-S) form using nonlinear embedding and sector nonlinearity (SNL) transformation. We then develop a discrete-time counterpart for a joint state and parameter estimation, based on design strategies developed for continuous time models in the existing literature. The design uses a Lyapunov approach and provides an error bounded by $\mathbb{L}_2$ gain. Based on this strategy, we propose a design for adaptive observers for nonlinear systems whose T-S form can have unmeasured premise variables.

math.OC↗

arXiv2014

On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach

In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state constraints. Due to a nature of the dynamical system and the constraints, we consider a one-step receding horizon. Using inverse cumulative distribution function, we convert the probabilistic state constraints to deterministic constraints, and obtain a tractable deterministic receding horizon control problem. We consider the receding control law to have a linear state-feedback and an admissible offset term. We ensure mean square boundedness of the state variable via solving linear matrix inequalities off-line, and solve the receding horizon control problem on-line with control offset terms. We illustrate the overall approach applied on a macroeconomic system.

eess.SY↗

arXiv2014

Stochastic stability and stabilization of a class of state-dependent jump linear systems

This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state variable, and addressed the problem of stochastic stability and stabilization analysis for the proposed system. Numerically solvable sufficient conditions for the stochastic stability and stabilization of the proposed system is established in terms of linear matrix inequalities. The obtained results are illustrated in numerical examples.

eess.SY↗

arXiv2006

Comparison between Networked Control System behaviour based on CAN and Switched Ethernet networks

The distributed control systems are more and more used in many industrial applications. These systems are often referred as "Networked control systems". The goal of this paper is to show the network influence on feedback control systems. Two networks are considered: Switched Ethernet network and CAN fieldbus. The first one represents the non deterministic network and second one represents the deterministic one. Several scenarii are studied to analyse the stability of system according to different network parameters (packets losses, congestion and frame priority). The Truetime simulator is used in this work.

cs.NI↗

arXiv2006

Network calculus based FDI approach for switched Ethernet architecture

The Networked Control Systems (NCS) are complex systems which integrate information provided by several domians such as automatic control, computer science, communication network. The work presented in this paper concerns fault detection, isolation and compensation of communication network. The proposed method is based on the classical approach of Fault Detection and Isolation and Fault Tolerant Control (FDI/FTC) currently used in diagnosis. The modelling of the network to be supervised is based on both couloured petri nets and network calculus theory often used to represent and analyse the network behaviour. The goal is to implement inside network devices algorithms enabling to detect, isolate and compensate communication faults in an autonomous way.

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arXiv2006

Modelling and Simulation of Scheduling Policies Implemented in Ethernet Switch by Using Coloured Petri Nets

The objective of this paper is to propose models enabling to study the behaviour of Ethernet switch for Networked Control Systems. Two scheduler policies are analyzed: the static priority and the WRR (Weighted Round Robin). The modelling work is based on Coloured Petri Nets. A temporal validation step based on the simulation of these modelling, shows that the obtained results are near to the expected behaviour of these scheduler policies.

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arXiv2006

Control compensation based on upper bound delay in networked control systems

Recent interest in networked control systems (NCS) has instigated research in both communication networks and control. Analysis of NCSs has usually been performed from either the network or the control point of view, but not many papers exist where the analysis of both is done in the same context. In this paper an overall analysis of the networked control system is presented. First, the procedure of obtaining the upper bound delay value for packet transmission in the switched Ethernet network is presented. Next, the obtained delay estimate is utilised in delay compensation for improving the Quality of Performance (QoP) of the control systems. The presented upper bound delay algorithm applies ideas from network calculus theory. For the improvement of QoP, two delay compensation strategies, the Smith predictor based and the robust control based delay compensation strategies, are presented and compared.

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