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Equivalent formulation and numerical analysis of a fire confinement problem

Alberto Bressan, Tao Wang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion $\dot{x}$ ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂ $ℝ^{2}$ . In this paper we show that the search for blocking strategies...

Evaluation of the reachability subspace of general form polynomial matrix descriptions (PMDs)

George F. Fragulis, Antonis I. G. Vardulakis (1994)

Kybernetika

Exact controllability in short time for the wave equation

V. Komornik (1989)

Annales de l'I.H.P. Analyse non linéaire

Exact controllability of the Euler-Bernoulli equation with $L_{2}(\Sigma)$ -control only in the Dirichlet Boundary condition

I. Lasiecka, R. Triggiani (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The paper studies the problem of exact controllability of the Euler- Bernoulli equation in a cylinder $\Omega\times\left[0,T\right]$ of $\mathbb{R}^{n+1}$ , via boundary controls acting on its lateral surface.

Exact controllability of the linear elasticity system with evolutive Ventcel conditions. (Contrôlabilité exacte d'un problème avec conditions de Ventcel évolutives pour le système linéaire de l'élasticité.)

Heminna, Amar (2001)

Portugaliae Mathematica. Nova Série

Existence theorems for some optimal control problems

V. Janković (1981)

Matematički Vesnik

External reachability (reachability with pole assignment by p. d. feedback) for implicit descriptions

Moisés Bonilla Estrada, Michel Malabre (1993)

Kybernetika

Externally and internally positive time-varying linear systems

Tadeusz Kaczorek (2001)

International Journal of Applied Mathematics and Computer Science

The notions of externally and internally positive time-varying linear systems are introduced. Necessary and sufficient conditions for the external and internal positivities of time-varying linear systems are established. Moreover, sufficient conditions for the reachability of internally positive time-varying linear systems are presented.

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