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Optimal control of constrained time lag systems: Necessary conditions and numerical treatment
Author(s) -
Göllmann Laurenz,
Kern Daniela,
Maurer Helmut
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700182
Subject(s) - discretization , optimal control , mathematics , lagrange multiplier , maximum principle , state variable , state (computer science) , mathematical optimization , constant (computer programming) , boundary value problem , lag , class (philosophy) , nonlinear system , nonlinear programming , dynamic programming , pontryagin's minimum principle , control variable , control theory (sociology) , control (management) , computer science , mathematical analysis , algorithm , computer network , statistics , physics , quantum mechanics , artificial intelligence , programming language , thermodynamics
We consider retarded optimal control problems with constant delays in state and control variables under mixed controlstate inequality constraints. First order necessary optimality conditions in the form of Pontryagin's minimum principle are presented and discussed as well as numerical methods based upon discretization techniques and nonlinear programming. The minimum principle for the considered problem class leads to a boundary value problem which is retarded in the state dynamics and advanced in the costate dynamics. It can be shown that the Lagrange multipliers associated with the programming problem provide a consistent discretization of the advanced adjoint equation for the delayed control problem. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)