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 t₁, t₂ ? t₀, t_f] and let τ = (t-t₀)/? and σ = (t_f-t)/?. The τ-scaled, original and σ-scaled boundary value problems are then solved on the intervals t₀, t₁], t₁, t₂] and t₂, t_f] respectively. A test example is solved to illustrate the method.