  We present a hierarchical computation approach for solving finite-time
optimal control problems using operator splitting methods. The first split is
performed over the time index and leads to as many subproblems as the length of
the prediction horizon. Each subproblem is solved in parallel and further split
into three by separating the objective from the equality and inequality
constraints respectively, such that an analytic solution can be achieved for
each subproblem. The proposed solution approach leads to a nested decomposition
scheme, which is highly parallelizable. We present a numerical comparison with
standard state-of-the-art solvers, and provide analytic solutions to several
elements of the algorithm, which enhances its applicability in fast large-scale
applications.
