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

Abstract

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