A hierarchical time-splitting approach for solving finite-time optimal control problems

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 approach leads to a highly parallelizable nested decomposition scheme. We present a numerical comparison with the standard state-of-the-art solver SDPT3, and provide analytic solutions to several elements of the algorithm, which enhances its applicability in fast large-scale applications.