New optimality conditions for nonsmooth control problems

Autor(es)

de Oliveira, Valeriano Antunes ^[1] ; Silva, Geraldo Nunes ^[1]

Afiliação do(s) autor(es)

^[1] UNESP Univ Estadual Paulista, Dept Matemat Aplicada, Inst Biociencias Letras & Ciencias Exatas, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Global Optimization; v. 57, n. 4, p. 1465-1484, DEC 2013.
• Citações Web of Science: 3

Resumo

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. (AU)

• Processo FAPESP: 09/18643-0 - Controle ótimo de sistemas não lineares
• Beneficiário: Geraldo Nunes Silva
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 11/01977-2 - Contribuições em teoria de controle ótimo
• Beneficiário: Valeriano Antunes de Oliveira
• Modalidade de apoio: Auxílio à Pesquisa - Regular