Normal Forms of Necessary Conditions for Dynamic Optimization Problems with Pat...

• Author(s): Fernando A. C. C. Fontes ; Sofia O. Lopes
• Date: 2013
• Persistent ID: http://hdl.handle.net/10216/66939
• Origin: Repositório Aberto da Universidade do Porto
• Subject(s): Ciências Físicas; Matemática; Matemática aplicada; Investigação operacional, Ciências Físicas; Matemática; Matemática aplicada; Matemática para a engenharia, Ciências Tecnológicas; Engenharia; Engenharia de sistemas; Teoria de sistemas
• Document Type: Article
• Language: English

Description

There has been a longstanding interest in deriving conditions under which dynamic optimization problems are normal, that is, the necessary conditions of optimality (NCO) can be written with a nonzero multiplier associated with the objective function. This paper builds upon previous results on nondegenerate NCO for trajectory constrained optimal control problems to provide even stronger, normal forms of the conditions. The NCO developed may address problems with nonsmooth, less regular data. The particular case of calculus of variations problems is here explored to show a favorable comparison with existent results. Keywords Optimal control; Maximum principle; State constraints; Calculus of variations; Normality; Degeneracy; Nonsmooth analysis