Artigo
On some extension of optimal control theory
Registro en:
European Journal of Control, v. 20, p. 284-291, 2014.
0947-3580
9527284964541341
3638688119433520
Autor
Karamzin, Dmitry Yu [UNESP]
Oliveira, Valeriano A. de [UNESP]
Pereira, F.L.
Silva, Geraldo Nunes [UNESP]
Resumen
Some problems of Calculus of Variations do not have solutions in the class of classic continuous and smooth arcs. This suggests the need of a relaxation or extension of the problem ensuring the existence of a solution in some enlarged class of arcs. This work aims at the development of an extension for a more general optimal control problem with nonlinear control dynamics in which the control function takes values in some closed, but not necessarily bounded, set. To achieve this goal, we exploit the approach of R.V. Gamkrelidze based on the generalized controls, but related to discontinuous arcs. This leads to the notion of generalized impulsive control. The proposed extension links various approaches on the issue of extension found in the literature. Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Ciência da Computação e Estatística, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto, São José do Rio Preto, RUA CRISTOVÃO CRISTOVÃO COLOMBO, 2265 (Sala 15 - DCCE), JD NAZARETH, CEP 15054000, SP, Brasil Universidade Estadual Paulista Júlio de Mesquita Filho, Departamento de Ciência da Computação e Estatística, Instituto de Biociências Letras e Ciências Exatas de São José do Rio Preto, São José do Rio Preto, RUA CRISTOVÃO CRISTOVÃO COLOMBO, 2265 (Sala 15 - DCCE), JD NAZARETH, CEP 15054000, SP, Brasil Computing Centre of RAS, Vavilova Street, 40, 119991, Moscow, Russia Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, s/n 4200-465, Porto, Portugal