Cooperative controls for air traffic management

A. Marigo; Benedetto Piccoli

doi:10.3934/cpaa.2003.2.355

Article Contents

2003, Volume 2, Issue 3: 355-369. Doi: 10.3934/cpaa.2003.2.355

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Cooperative controls for air traffic management

A. Marigo^1, and
Benedetto Piccoli^2,

1.
Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico 137, 00161 ROMA
2.
Viale del Policlinico 137, I-00161 Roma

Received: November 30, 2002

Revised: March 31, 2003

Published: August 2003

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Abstract

We consider a model of cooperative control system, that is a system where different controls act with non conflictual purposes. For example one control is chosen in order to minimize some cost while another is designed for safety purposes. In our main application, a model of Air Traffic Management, one control minimizes the travel time while the other is applied to avoid crashes in a free flight environment.
The mathematical difficulties arise because of the use of two discontinuous feedbacks at the same time. We consider stratified feedbacks and solutions in Krasowskii sense. Two refinements of this concept are given to guarantee existence and good behavior of solutions.

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Mathematics Subject Classification: 49J15, 49N35, 34A36.

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