New Architectures for Hierarchical Predictive Control

We analyze the structure of the Euler-Lagrange (EL) conditions of a long-horizon optimal control problem. The analysis reveals that the conditions can be solved by using block Gauss-Seidel (GS) schemes. We prove that such schemes can be implemented in the primal space by solving sequences of short-horizon optimal control problems. This analysis also reveals that a traditional receding-horizon (RH) scheme is equivalent to performing a single GS sweep. We have also found that we can use adjoint information from a coarse long-horizon problem to construct terminal penalties that correct the policies of the RH scheme. We observe that this scheme can be interpreted as a hierarchical controller in which a coarse high-level controller transfers long-horizon information to a low-level, short-horizon controller of fine resolution. The results open the door to a new family of hierarchical control architectures that can handle multiple time scales systematically.