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Real‐Time Solution of Bi‐Level Optimal Control Problems
Author(s) -
Knauer Matthias,
Büskens Christof,
Lasch Peter
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510349
Subject(s) - jerk , optimal control , terminal (telecommunication) , trajectory , mathematical optimization , container (type theory) , position (finance) , extension (predicate logic) , control theory (sociology) , computer science , rest (music) , control (management) , state (computer science) , point (geometry) , mathematics , engineering , acceleration , algorithm , artificial intelligence , telecommunications , geometry , classical mechanics , cardiology , programming language , mechanical engineering , medicine , physics , finance , astronomy , economics
Bi‐level optimal control problems are presented as an extension to classical optimal control problems. Hereby, additional constraints for the primary problem are considered, which depend on the optimal solution of a secondary optimal control problem. A demanding problem is the numerical complexity, since at any point in time the solution of the optimal control problem as well as a complete solution of the secondary problem have to be determined. Hence we deal with two dependent variables in time. The numerical solution of the bi‐level problem is illustrated by an application of a container crane. Jerk and energy optimal trajectories with free final time are calculated under the terminal condition that the crane system comes to be at rest at a predefined location. In enlargement additional constraints are investigated to ensure that the crane system can be brought to a rest position by a safety stop at a free but admissible location in minimal time from any state of the trajectory. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)