Interval observer design for Linear Parameter-Varying systems subject to component faults

Lamouchi, Rihab; Amairi, Messaoud; Raïssi, Tarek; Aoun, Mohamed

doi:10.1109/med.2016.7536019

Cited by 19 publications

(9 citation statements)

References 19 publications

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“…Indeed, in (36) and thus in (38), the dependence between the variables x k and |x k | is not taken into account. According to (21), the magnitude of the lower and upper bounds of the state estimate can be expressed as a multimodel expression based on…”

Section: Theorem 2 Systemmentioning

confidence: 99%

“…The second approach 9-13 consists in explicitly building an interval observer from the interval model of the system. Then, solving the interval state equations of the observer, the upper and lower bounds of the state variable estimates are provided.Studies on systems with bounded uncertain parameters can be found in several areas of automatic control such as stability analysis, 14,15 state estimation, 8,16,17 synthesis of iterative learning control law, 18 system diagnosis, 19,20 components fault detection, 21,22 data analysis, 23 model sensitivity analysis, 24 regression with abnormal values, 25 and classification. 26 Roughly speaking, uncertainties in the measures and in the parameters are handled in two main ways.…”

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confidence: 99%

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State estimation of system with bounded uncertain parameters: Interval multimodel approach

Ichalal

Marx

Maquin

et al. 2018

Adaptive Control & Signal

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The objective of this study is the analysis of dynamic systems represented by a multimodel expression with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires the consideration of all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment.This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger-type observer, fed with the system measurements. KEYWORDSbounded uncertainties, interval observers, multimodel technique, uncertain systems INTRODUCTIONAs widely known, one of the main difficulties in system simulation, control, or estimation is dealing with uncertainties. These uncertainties may affect the input or output signals of the system (eg, unknown input, disturbance, measurement noises, etc) as well as the system model itself (eg, nonmodeled dynamics, unknown parameter, etc). The uncertainties may also be of different natures: total lack of information (unknown value of a parameter) or partial knowledge (upper and lower bounds, statistical properties, etc). This paper deals with systems with uncertain parameters.Even a low magnitude change in some parameters may have a significant impact on the system behavior and, namely, on the system state trajectory. Uncertain parameters can be considered from two main points of view: the stochastic and the deterministic ones. In the first approach, the uncertain parameters are assumed to be the results of random process realizations. It then needs to choose the probability density functions and their parameters describing the system's uncertain parameters. In the deterministic approach, no statistical models of the parameters are assumed to be available, and only the upper and lower bounds of the parameter values are known. This approach, also known as the interval approach, is adopted in this paper.The search for trajectories, which are solutions of differential inclusions, 1 were the starting point of the large amount of works on stability, stabilization, and state estimation. In the latter topic, our communication follows the pioneering work of Gouzé et al, 2 which proposed the synthesis of the interval-type observer to reconstruct the system state 480 ;32:480-493. ICHALAL ET AL. 481from measurements of inputs and outputs. Since then, many results were published on designing observers adapted to nonlinear systems with uncertain but bounded parameters. [3][4][5][6] The model-based state estimation techniques in the context of bounded uncertainties can be classified into two categories. The first one is ba...

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Section: Theorem 2 Systemmentioning

confidence: 99%

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confidence: 99%

State estimation of system with bounded uncertain parameters: Interval multimodel approach

Ichalal

Marx

Maquin

et al. 2018

Adaptive Control & Signal

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“…Theorem 1. The switched observer (9) is a switched UIO for system (8) if and only if the following conditions are satisfied:…”

Section: Vehicle Fault Detectionmentioning

confidence: 99%

“…In this paper, zonotopes are used to provide the interval enclosing the unknown true residual vector. The advantage of using zonotopes is that monotonicity property is no longer needed as in [8], [9], [11] allowing to consider the whole set of possible trajectories. The zonotope-based approaches in fault detection has already been investigated in the literature, see for instance [5], [7].…”

Section: Introductionmentioning

confidence: 99%

Robust Fault Detection for Vehicle Lateral Dynamics: A Zonotope-based Set-membership Approach

Ifqir¹,

Puig²,

Ait-Oufroukh³

et al. 2018

2018 21st International Conference on Intelligent Transportation Systems (ITSC)

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In this work, a model-based fault detection layout for vehicle lateral dynamics system is presented. The major focus in this study is on the handling of model uncertainties and unknown inputs. In fact, the vehicle lateral model is affected by several parameter variations such as longitudinal velocity, cornering stiffnesses coefficients and unknown inputs like wind gust disturbances. Cornering stiffness parameters variation is considered to be unknown but bounded with known compact set. Their effect is addressed by generating intervals for the residuals based on the zonotope representation of all possible values. The developed fault detection procedure has been tested using real driving data acquired from a prototype vehicle.

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“…According to the interval observers theory, the uncertainties are assumed to be unknown but bounded with a priori known bounds. In the literature, interval observers are applied to several classes of nonlinear systems [27], [23], discrete-time systems [22], [6] and linear systems [10], [17].…”

Section: Introductionmentioning

confidence: 99%

Interval estimation for continuous-time switched linear systems

Ethabet¹,

Rabehi²,

Efimov³

et al. 2018

Automatica

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This paper deals with the design of interval observers for switched linear systems (SLS), a class of hybrid systems. Under the assumption that the disturbances and the measurement noise are bounded, upper and lower bounds for the state are calculated. New conditions of cooperativity in discrete-time instants are firstly proposed. Then, some techniques for interval estimation are developed in continuous-time. It is shown that it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable via some change of coordinates under arbitrary switching sequences. The performances of the developed techniques are illustrated through numerical examples.

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Interval observer design for Linear Parameter-Varying systems subject to component faults

Cited by 19 publications

References 19 publications

State estimation of system with bounded uncertain parameters: Interval multimodel approach

State estimation of system with bounded uncertain parameters: Interval multimodel approach

Robust Fault Detection for Vehicle Lateral Dynamics: A Zonotope-based Set-membership Approach

Interval estimation for continuous-time switched linear systems

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