  Splitting and projection-type algorithms have been applied to many
optimization problems due to their simplicity and efficiency, but the
application of these algorithms to optimal control is less common. In this
paper we utilize the Douglas--Rachford (DR) algorithm to solve
control-constrained minimum-energy optimal control problems. Instead of the
traditional approach where one discretizes the problem and solves it using
large-scale finite-dimensional numerical optimization techniques we split the
problem in two subproblems and use the DR algorithm to find an optimal point in
the intersection of the solution sets of these two subproblems hence giving a
solution to the original problem. We derive general expressions for the
projections and propose a numerical approach. We obtain analytic closed-form
expressions for the projectors of pure, under-, critically- and over-damped
harmonic oscillators. We illustrate the working of our approach to solving not
only these example problems but also a challenging machine tool manipulator
problem. Through numerical case studies, we explore and propose desirable
ranges of values of an algorithmic parameter which yield smaller number of
iterations.
