Approximate inverses in preconditioned fast dual gradient methods for MPC

摘要

This paper considers the usage of approximate inverses in a preconditioned fast dual proximal gradient method for Model Predictive Control (MPC). We show that for a dualization of the dynamic constraints, the dense preconditioner is an exponentially off-diagonally decaying matrix. By approximating the preconditioner by a banded matrix, the computational cost per iteration can be decreased, while early numerical tests indicate that the number of iterations is almost unaffected in cases where the off-diagonal decay is rapid.