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A double window state observer for detection and isolation of abrupt changes in parameters

Jędrzej Byrski, Witold Byrski (2016)

International Journal of Applied Mathematics and Computer Science

The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of...

A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators

Qi Lü (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This result is a consequence of a new pointwise and weighted estimate for Laplace-Beltrami operators, a construction of some nonnegative function with arbitrary given critical point location in the manifold, and also two interpolation results for solutions of elliptic equations with lateral...

A variable structure observer for the control of robot manipulators

Abdelkader Abdessameud, Mohamed Khelfi (2006)

International Journal of Applied Mathematics and Computer Science

This paper deals with the application of a variable structure observer developed for a class of nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The analyzed approach to observer design proposes a simple design methodology for systems having completely observable linear parts and bounded nonlinearities andor uncertainties. This observer is basically the conventional Luenberger observer with an additional switching term that is used to guarantee robustness...

Adaptive compensators for perturbed positive real infinite-dimensional systems

Ruth Curtain, Michael Demetriou, Kazufumi Ito (2003)

International Journal of Applied Mathematics and Computer Science

The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of...

An approach to the analysis of observability and controllability in nonlinear systems via linear methods

Alexey Zhirabok, Alexey Shumsky (2012)

International Journal of Applied Mathematics and Computer Science

The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,...

An asymptotic state observer for a class of nonlinear delay systems

Alfredo Germani, Costanzo Manes, Pierdomenico Pepe (2001)

Kybernetika

The problem of state reconstruction from input and output measurements for nonlinear time delay systems is studied in this paper and a state observer is proposed that is easy to implement and, under suitable assumptions on the system and on the input function, gives exponential observation error decay. The proposed observer is itself a delay system and can be classified as an identity observer, in that it is such that if at a given time instant the system and observer states coincide, on a suitable...

An H sliding mode observer for Takagi-Sugeno nonlinear systems with simultaneous actuator and sensor faults

Ali Ben Brahim, Slim Dhahri, Fayçal Ben Hmida, Anis Sellami (2015)

International Journal of Applied Mathematics and Computer Science

This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi-Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two...

An Ingham type proof for a two-grid observability theorem

Michel Mehrenberger, Paola Loreti (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1 D -wave equation for a time T > 2 2 ; this time, if the observation is made in ( - T / 2 , T / 2 ) , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I 338 (2004) 413–418]. Our proof follows an Ingham type approach.

An Ingham type proof for a two-grid observability theorem

Paola Loreti, Michel Mehrenberger (2007)

ESAIM: Control, Optimisation and Calculus of Variations

Here, we prove the uniform observability of a two-grid method for the semi-discretization of the 1D-wave equation for a time T > 2 2 ; this time, if the observation is made in ( - T / 2 , T / 2 ) , is optimal and this result improves an earlier work of Negreanu and Zuazua [C. R. Acad. Sci. Paris Sér. I338 (2004) 413–418]. Our proof follows an Ingham type approach.

An observability estimate for parabolic equations from a measurable set in time and its applications

Kim Dang Phung, Gengsheng Wang (2013)

Journal of the European Mathematical Society

This paper presents a new observability estimate for parabolic equations in Ω × ( 0 , T ) , where Ω is a convex domain. The observation region is restricted over a product set of an open nonempty subset of Ω and a subset of positive measure in ( 0 , T ) . This estimate is derived with the aid of a quantitative unique continuation at one point in time. Applications to the bang-bang property for norm and time optimal control problems are provided.

An observability problem for a class of uncertain-parameter linear dynamic systems

Krzysztof Oprzędkiewicz (2005)

International Journal of Applied Mathematics and Computer Science

An observability problem for a class of linear, uncertain-parameter, time-invariant dynamic SISO systems is discussed. The class of systems under consideration is described by a finite dimensional state-space equation with an interval diagonal state matrix, known control and output matrices and a two-dimensional uncertain parameter space. For the system considered a simple geometric interpretation of the system spectrum can be given. The geometric interpretation of the system spectrum is the base...

An SFDI observer-based scheme for a general aviation aircraft

Marco Ariola, Massimiliano Mattei, Immacolata Notaro, Federico Corraro, Adolfo Sollazzo (2015)

International Journal of Applied Mathematics and Computer Science

The problem of detecting and isolating sensor faults (sensor fault detection and isolation-SFDI) on a general aviation aircraft, in the presence of external disturbances, is considered. The proposed approach consists of an extended Kalman observer applied to an augmented aircraft plant, where some integrators are added to the output variables subject to faults. The output of the integrators should be ideally zero in the absence of model uncertainties, external disturbances and sensor faults. A threshold-based...

Analyse régionale des systèmes distribués

A. El Jai (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Le but de cet article est de montrer l’état de l’art dans l’analyse des systèmes distribués lorsque l’on examine certains concepts à partir de considérations régionales. Autrement dit, à partir de la donnée d’un système dynamique défini sur un domaine Ω , on ne s’intéresse à sa contrôlabilité, à son observabilité, à sa stabilité, ... que sur une région privilégiée ω , ω Ω . Partant de concepts classiques, on développe leur adaptation au cas régional. On développe ensuite des concepts régionaux propres...

Analyse régionale des systèmes distribués

A. El Jai (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Le but de cet article est de montrer l'état de l'art dans l'analyse des systèmes distribués lorsque l'on examine certains concepts à partir de considérations régionales. Autrement dit, à partir de la donnée d'un système dynamique défini sur un domaine Ω, on ne s'intéresse à sa contrôlabilité, à son observabilité, à sa stabilité, ... que sur une région privilégiée ω, ω Ω . Partant de concepts classiques, on développe leur adaptation au cas régional. On développe ensuite des concepts régionaux...

Bilateral polynomial equations with unimodular right-hand-side matrices

Tadeusz Kaczorek (2003)

International Journal of Applied Mathematics and Computer Science

Necessary and sufficient conditions are established for the existence of a solution to some bilateral polynomial matrix equations with unimodular right-hand-side matrices. A procedure for the computation of the solution is derived and illustrated by a numerical example. Two examples of applications of bilateral polynomial matrix equations are presented.

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