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Optimal singular control for systems involving parameters
Author(s) -
Popescu Mihai
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700374
Subject(s) - singular point of a curve , mathematics , affine transformation , optimal control , singular solution , differential (mechanical device) , singular control , trajectory , manifold (fluid mechanics) , point (geometry) , class (philosophy) , variation (astronomy) , control theory (sociology) , control (management) , mathematical optimization , mathematical analysis , computer science , pure mathematics , geometry , physics , engineering , mechanical engineering , astronomy , artificial intelligence , astrophysics , thermodynamics
Abstract What we shall take into consideration is represented by the problems of singular optimal control when the index of performance, the differential constraints and the final conditions contain parameters. What is determined is the trajectory of the neighboring extremal for the initial point perturbed at the constraints of the perturbed final manifold. The present study evaluates the variation of the command on the extremal. This one allows obtaining the second variation in the singular case. The sufficient conditions of minimum are a result of imposing the non‐negativity of the second variation. The application made analysis the optimality of the singular control for a system in the class of affine differential systems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)