A Boundary value technique for solving singularly perturbed, fixed end‐point optimal control problems

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.