Optimal control of constrained time lag systems: Necessary conditions and numerical treatment |
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| Authors: | Laurenz Göllmann Daniela Kern Helmut Maurer |
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| Institution: | 1. Münster University of Applied Sciences, Stegerwaldstrasse 39, D-48565 Steinfurt, Germany;2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany;3. Institut für Numerische und Angewandte Mathematik, UniversitätMünster, Einsteinstrasse 62, D-48149 Münster, Germany |
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| Abstract: | 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) |
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