American Institute of Mathematical Sciences

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September  2003, 2(3): 355-369. doi: 10.3934/cpaa.2003.2.355

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, Italy
2. 

Viale del Policlinico 137, I-00161 Roma, Italy

Received  December 2002 Revised  April 2003 Published  June 2003

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.
Keywords: optimal synthesis, discontinuous ODEs., Cooperative control.
Mathematics Subject Classification: 49J15, 49N35, 34A3.
Citation: A. Marigo, Benedetto Piccoli. Cooperative controls for air traffic management. Communications on Pure & Applied Analysis, 2003, 2 (3) : 355-369. doi: 10.3934/cpaa.2003.2.355
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