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Author(s): S. O. Lopes
F. A. C. C. Fontes
Title: An overview of nondegenerate necessary conditions of optimality for optimal control problems with higher index state constraints
Issue Date: 2008
Abstract: The main purpose of necessary conditions of optimality (NCO) is, given an optimizationproblem, to select a set of candidates to minimizer. However, for some optimization problemswith constraints in particular for optimal control problems , it may happen that the NCOare unable to provide any useful information; that is, the set of candidates to minimizers thatsatisfy certain NCO coincides with the set of all admissible solutions. When this happens,we say that the degeneracy phenomenon occurs. To avoid this phenomenon, stronger formsof NCO are developed. These stronger forms can be applied when the problem satisfiesadditional hypotheses, known as constraint qualifications. In the case of optimal controlproblems with state constraints that have higher index (i.e. the first derivative of the stateconstraint with respect to time does not depend on the control), most constraint qualificationsdescribed in literature are not adequate. We note that control problems with higher index stateconstraints arise frequently in practice. An example, explored here, is a common mechanicalsystems for which there is a constraint on the position (an obstacle in the path, for example)and the control acts as a second derivative of the position (a force or acceleration) whichis a typical case arising in the area of mobile robotics. So, there is a need to develop newconstraint qualifications, involving higher derivatives of the state constraint. In this paper,we make an overview of recent constraint qualifications that allow strengthened forms of theNCO for optimal control with higher index state-constraints.
Subject: Ciências da engenharia e tecnologias
Engineering and technology
Scientific areas: Ciências da engenharia e tecnologias
Engineering and technology
Source: Proceedings of the 9th Portuguese Conference on Automatic Control - CONTROLO 2008
Document Type: Artigo em Livro de Atas de Conferência Internacional
Rights: openAccess
Appears in Collections:FEUP - Artigo em Livro de Atas de Conferência Internacional

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