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Bridging the Gap Between Multigrid, Hierarchical, and Receding-Horizon Control

Victor M Zavala (vzavala***at***mcs.anl.gov)

Abstract: We analyze the structure of the Euler-Lagrange conditions of a lifted long-horizon optimal control problem. The analysis reveals that the conditions can be solved by using block Gauss-Seidel schemes and we prove that such schemes can be implemented by solving sequences of short-horizon problems. The analysis also reveals that a receding-horizon control scheme is equivalent to performing a single Gauss-Seidel sweep. We also derive a strategy that uses adjoint information from a coarse long-horizon problem to correct the receding-horizon scheme and we observe that this strategy can be interpreted as a hierarchical control architecture in which a high-level controller transfers long-horizon information to a low-level, short-horizon controller. Our results bridge the gap between multigrid, hierarchical, and receding-horizon control.

Keywords: Euler-Lagrange, Gauss-Seidel, multigrid, receding-horizon, hierarchical control

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 3: Infinite Dimensional Optimization (Distributed Control )


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Entry Submitted: 04/19/2015
Entry Accepted: 04/19/2015
Entry Last Modified: 11/08/2015

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