Open AccessTheory and applications of optimal control problems with multiple time-delays
Author(s) -
Laurenz Göllmann,
Helmut Maurer
Publication year - 2014
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2014.10.413
Subject(s) - optimal control , pontryagin's minimum principle , discretization , lagrange multiplier , mathematics , maximum principle , mathematical optimization , state (computer science) , control (management) , type (biology) , control theory (sociology) , nonlinear system , control variable , separation principle , computer science , algorithm , mathematical analysis , ecology , statistics , physics , quantum mechanics , artificial intelligence , biology , state observer
International audienceIn this paper we study optimal control problems with multiple time delays in control and state and mixed type control-state constraints. We derive necessary optimality conditions in the form of a Pontryagin type Minimum Principle. A discretization method is presented by which the delayed control problem is transformed into a nonlinear programming problem. It is shown that the associated Lagrange multipliers provide a consistent numerical approximation for the adjoint variables of the delayed optimal control problem. We illustrate the theory and numerical approach on an analytical example and an optimal control model from immunology