Robust interval observer with uncertainties in the output

Bolajraf, M.; Rami, Mustapha Ait; Tadeo, Fernando

doi:10.1109/med.2010.5547617

Cited by 7 publications

(7 citation statements)

References 19 publications

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“…The previous result can be applied to a very interesting class of interval observers, which involves the following dilatation functions:

({, \begin{matrix} ψ (x) = 0.5 (x + | x |), \\ φ (x) = 0.5 (x - | x |), \end{matrix})

where | x | denotes the vector formed by the absolute values of the components of

x \in {double-struckR}^{n_{x}}

. As a result, the following dilatation observer can be viewed as an extended interval observer :

({, \begin{matrix} \dot{\overset{true¯}{θ}} & = Ã \overset{true¯}{θ} + L (y - \underset{true_}{η}) - G (y - \overset{true¯}{η}) - 0.5 R (\overset{true¯}{θ} - | \overset{true¯}{θ} |) \\ + F (\overset{true¯}{θ} - \underset{true_}{θ}) + \overset{true¯}{ξ} (t), \\ \dot{\underset{true_}{θ}} & = Ã \underset{true_}{θ} + L (y - \overset{true¯}{η}) - G (y - \underset{true_}{η}) - 0.5 R (\underset{true_}{θ} + | \underset{true_}{θ} |) \\ - F (\overset{true¯}{θ} - \underset{true_}{θ}) + \underset{true_}{ξ} (t), \\ \overset{true¯}{θ} (0) = {\overset{true¯}{x}}_{0}, \underset{true_}{θ} (0) = x \end{matrix})

…”

Section: Robust Interval Observermentioning

confidence: 99%

A robust estimation approach for uncertain systems with perturbed measurements

Bolajraf

Rami

2015

Intl J Robust & Nonlinear

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SUMMARYThis paper deals with state estimation problem for uncertain continuous-time systems. A numerical treatment is proposed for designing interval observers that ensures guaranteed upper and lower bounds on the estimated states. In order to take into account possible perturbations on the system and its outputs, a new type of interval observers is introduced. Such interval observers consist of two coupled general Luenbergertype observers that involve dilatation functions. In addition, we provide an optimality criterion in order to find optimal interval observers that lead to tight interval error estimation. The proposed existence and optimality conditions are expressed in terms of linear programming. Also, some illustrative examples are given.

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“…The previous result can be applied to a very interesting class of interval observers, which involves the following dilatation functions:

({, \begin{matrix} ψ (x) = 0.5 (x + | x |), \\ φ (x) = 0.5 (x - | x |), \end{matrix})

where | x | denotes the vector formed by the absolute values of the components of

x \in {double-struckR}^{n_{x}}

. As a result, the following dilatation observer can be viewed as an extended interval observer :

({, \begin{matrix} \dot{\overset{true¯}{θ}} & = Ã \overset{true¯}{θ} + L (y - \underset{true_}{η}) - G (y - \overset{true¯}{η}) - 0.5 R (\overset{true¯}{θ} - | \overset{true¯}{θ} |) \\ + F (\overset{true¯}{θ} - \underset{true_}{θ}) + \overset{true¯}{ξ} (t), \\ \dot{\underset{true_}{θ}} & = Ã \underset{true_}{θ} + L (y - \overset{true¯}{η}) - G (y - \underset{true_}{η}) - 0.5 R (\underset{true_}{θ} + | \underset{true_}{θ} |) \\ - F (\overset{true¯}{θ} - \underset{true_}{θ}) + \underset{true_}{ξ} (t), \\ \overset{true¯}{θ} (0) = {\overset{true¯}{x}}_{0}, \underset{true_}{θ} (0) = x \end{matrix})

…”

Section: Robust Interval Observermentioning

confidence: 99%

A robust estimation approach for uncertain systems with perturbed measurements

Bolajraf

Rami

2015

Intl J Robust & Nonlinear

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“…However, this approach suffers from a certain conservatism mainly due to the structure of Equation (36) expressing the evolution of reconstruction errors. 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%

“…Remark 4. Following the work of Bolajraf et al, 36 additional degrees of freedom can be introduced in the observer design by tuning an extra parameter, denoted by F, in the following observer definition:…”

Section: Examplementioning

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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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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“…In the light of the above discussion, the objective of this paper is to propose a neural network-based fault detection scheme and then to enhance its performance by minimizing the size of the uncertainty interval. For that purpose a quality measure called Mean Uncertainty Interval (MUI) [38][39][40] is employed. Finally, it should be noted that the proposed approach does not estimate the fault but it provides a binary evaluation if there is the fault or not.…”

Section: Related Work: Active and Passive Approaches To Fault Detectionmentioning

confidence: 99%

Towards Enhanced Performance of Neural-Network-Based Fault Detection Using an Sequential D-Optimum Experimental Design

Mrugalska

2018

Applied Sciences

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Increasing expectations of industrial system reliability require development of more effective and robust fault diagnosis methods. The paper presents a framework for quality improvement on the neural model applied for fault detection purposes. In particular, the proposed approach starts with an adaptation of the modified quasi-outer-bounding algorithm towards non-linear neural network models. Subsequently, its convergence is proven using quadratic boundedness paradigm. The obtained algorithm is then equipped with the sequential D-optimum experimental design mechanism allowing gradual reduction of the neural model uncertainty. Finally, an emerging robust fault detection framework on the basis of the neural network uncertainty description as the adaptive thresholds is proposed.

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Robust interval observer with uncertainties in the output

Cited by 7 publications

References 19 publications

A robust estimation approach for uncertain systems with perturbed measurements

A robust estimation approach for uncertain systems with perturbed measurements

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

Towards Enhanced Performance of Neural-Network-Based Fault Detection Using an Sequential D-Optimum Experimental Design

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