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Unbounded viscosity solutions of hybrid control systems

Guy Barles, Sheetal Dharmatti, Mythily Ramaswamy (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study a hybrid control system in which both discrete and continuous controls are involved. The discrete controls act on the system at a given set interface. The state of the system is changed discontinuously when the trajectory hits predefined sets, namely, an autonomous jump set A or a controlled jump set C where controller can choose to jump or not. At each jump, trajectory can move to a different Euclidean space. We allow the cost functionals to be unbounded with certain growth and hence...

Uncertain input data problems and the worst scenario method

Ivan Hlaváček (2007)

Applications of Mathematics

An introduction to the worst scenario method is given. We start with an example and a general abstract scheme. An analysis of the method both on the continuous and approximate levels is discussed. We show a possible incorporation of the method into the fuzzy set theory. Finally, we present a survey of applications published during the last decade.

Uncertainty models of vision sensors in mobile robot positioning

Piotr Skrzypczyński (2005)

International Journal of Applied Mathematics and Computer Science

This paper discusses how uncertainty models of vision-based positioning sensors can be used to support the planning and optimization of positioning actions for mobile robots. Two sensor types are considered: a global vision with overhead cameras, and an on-board camera observing artificial landmarks. The developed sensor models are applied to optimize robot positioning actions in a distributed system of mobile robots and monitoring sensors, and to plan the sequence of actions for a robot cooperating...

Une nouvelle transformation des réseaux de Petri généralisés : l’abstraction généralisée

Christophe Haro, Patrick Martineau, Christian Proust (2004)

RAIRO - Operations Research - Recherche Opérationnelle

Cet article introduit une nouvelle transformation des réseaux de Petri généralisés appelée l’abstraction généralisée. C’est une réduction dont nous montrons qu’elle conserve les invariants du réseau de départ et les propriétés structurelles les plus importantes. Une fonction de transformation de marquages nous permet d’introduire l’étude de la conservation des propriétés comportementales.

Une nouvelle transformation des réseaux de Petri généralisés : L'abstraction généralisée

Christophe Haro, Patrick Martineau, Christian Proust (2010)

RAIRO - Operations Research

Cet article introduit une nouvelle transformation des réseaux de Petri généralisés appelée l'abstraction généralisée. C'est une réduction dont nous montrons qu'elle conserve les invariants du réseau de départ et les propriétés structurelles les plus importantes. Une fonction de transformation de marquages nous permet d'introduire l'étude de la conservation des propriétés comportementales.

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

Uniform controllability of the linear one dimensional Schrödinger equation with vanishing viscosity

Sorin Micu, Ionel Rovenţa (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

Uniform exponential stability for linear discrete time systems with stochastic perturbations in Hilbert spaces

Viorica Mariela Ungureanu (2004)

Bollettino dell'Unione Matematica Italiana

In this paper we study the exponential and uniform exponential stability problem for linear discrete time-varying systems with independent stochastic perturbations. We give two representations of the solutions of the discussed systems and we use them to obtain necessary and sufficient conditions for the two types of stability. A deterministic characterization of the uniform exponential stability, in terms of Lyapunov equations are given.

Unifying approach to observer-filter design

Václav Černý (2009)

Kybernetika

The paper examines similarities between observer design as introduced in Automatic Control Theory and filter design as established in Signal Processing. It is shown in the paper that there are obvious connections between them in spite of different aims for their design. Therefore, it is prospective to make them be compatible from the structural point of view. Introduced error invariance and error convergence properties of both of them are unifying tools for their design. Lyapunov's stability theory,...

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