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A Boundary value technique for solving singularly perturbed, fixed end‐point optimal control problems
Author(s) -
Kadalbajoo Mohan K.,
Singh Arindama
Publication year - 1988
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660090407
Subject(s) - mathematics , fixed point , boundary value problem , value (mathematics) , quadratic equation , fixed point theorem , mathematical analysis , boundary (topology) , point (geometry) , geometry , statistics
A method is proposed to solve fixed end‐point, linear optimal control problems with quadratic cost and singularly perturbed state. After translating the problem into a two‐point boundary value problem, we choose two points t 1 , t 2 ϵ [ t 0 , t f ] and let τ = ( t‐t 0 )/ϵ and σ = ( t f ‐ t )/ϵ. The τ‐scaled, original and σ‐scaled boundary value problems are then solved on the intervals [ t 0 , t 1 ], [ t 1 , t 2 ] and [ t 2 , t f ] respectively. A test example is solved to illustrate the method.