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An output controllability problem for semilinear distributed hyperbolic systems

E. Zerrik, R. Larhrissi, H. Bourray (2007)

International Journal of Applied Mathematics and Computer Science

The paper aims at extending the notion of regional controllability developed for linear systems cite to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder's fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples....

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...

An SQP trust region method for solving the discrete-time linear quadratic control problem

El-Sayed M.E. Mostafa (2012)

International Journal of Applied Mathematics and Computer Science

In this paper, a sequential quadratic programming method combined with a trust region globalization strategy is analyzed and studied for solving a certain nonlinear constrained optimization problem with matrix variables. The optimization problem is derived from the infinite-horizon linear quadratic control problem for discrete-time systems when a complete set of state variables is not available. Moreover, a parametrization approach is introduced that does not require starting a feasible solution...

An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection

Hasim A. Obaid, Rachid Ouifki, Kailash C. Patidar (2013)

International Journal of Applied Mathematics and Computer Science

We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical...

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...

Analysis of a time optimal control problem related to the management of a bioreactor

Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of,...

Analysis of a time optimal control problem related to the management of a bioreactor***

Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a time optimal control problem arisen from the optimal management of a bioreactor devoted to the treatment of eutrophicated water. We formulate this realistic problem as a state-control constrained time optimal control problem. After analyzing the state system (a complex system of coupled partial differential equations with non-smooth coefficients for advection-diffusion-reaction with Michaelis-Menten kinetics, modelling the eutrophication processes) we demonstrate the existence of,...

Analysis of an on-off intermittency system with adjustable state levels

Shi-Jian Cang, Zeng-Qiang Chen, Zhu Zhi Yuan (2008)

Kybernetika

We consider a chaotic system with a double-scroll attractor proposed by Elwakil, composing with a second-order system, which has low-dimensional multiple invariant subspaces and multi-level on-off intermittency. This type of composite system always includes a skew-product structure and some invariant subspaces, which are associated with different levels of laminar phase. In order for the level of laminar phase be adjustable, we adopt a nonlinear function with saturation characteristic to tune the...

Analysis of some dual properties in discrete dynamic systems

Aleksey Zhirabok (2006)

International Journal of Applied Mathematics and Computer Science

The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.

Analysis of structural properties of Petri nets based on product incidence matrix

Guangyou Ji, Mingzhe Wang (2013)

Kybernetika

This paper presents some structural properties of a generalized Petri net (PN) with an algorithm to determine the (partial) conservativeness and (partial) consistency of the net. A product incidence matrix A = C C T or A ˜ = C T C is defined and used to further improve the relations among PNs, linear inequalities and matrix analysis. Thus, based on Cramer’s Rule, a new approach for the study of the solution of a linear system is given in terms of certain sub-determinants of the coefficient matrix and an efficient...

Analysis of the descriptor Roesser model with the use of the Drazin inverse

Tadeusz Kaczorek (2015)

International Journal of Applied Mathematics and Computer Science

A method of analysis for a class of descriptor 2D discrete-time linear systems described by the Roesser model with a regular pencil is proposed. The method is based on the transformation of the model to a special form with the use of elementary row and column operations and on the application of a Drazin inverse of matrices to handle the model. The method is illustrated with a numerical example.

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