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CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

MARÍA BARBERO-LIÑÁN

INRIA (Projet CORIDA) and Institut Élie Cartan de Nancy, Université Nancy 1, BP 239, Vandœuvre-lès-Nancy, 54506, France

The author is now with Department of Mathematics and statistics, Queen's University, Kingston, ON, Canada.

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and

MIGUEL C. MUÑOZ-LECANDA

Departamento de Matemática Aplicada IV, Edificio C-3, Campus Norte UPC. C/Jordi Girona 1. E-08034 Barcelona, Spain

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https://doi.org/10.1142/S0219887809004193Cited by:8 (Source: Crossref)

Abstract

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

Keywords:

AMSC: 34A26, 49J15, 49K15, 70G45, 70H05, 70H45

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