Banded null basis and ADMM for embedded MPC

• Main Authors: Dang, Thuy V, Ling, Keck Voon, Maciejowski, Jan
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2018
• Subjects: DRNTU::Engineering::Electrical and electronic engineering; ADMM; Banded Null Basis
• Online Access: https://hdl.handle.net/10356/89779; http://hdl.handle.net/10220/47137
• Institution: Nanyang Technological University

In this paper, we propose an improved QP solver for embedded implementations of MPC controllers. We adopt a “reduced Hessian” approach for handling the equality constraints that arise in the well-known “banded” formulation of MPC (in which the predicted states are not eliminated). Our key observation is that a banded basis exists for the null space of the banded equality-constraint matrix, and that this leads to a QP of the same size as the “condensed” formulation of MPC problems, which is considerably smaller than the “banded” formulation. We use the Alternating Direction Method of Multipliers (ADMM) - which is known to be particularly suitable for embedded implementations - to solve this smaller QP problem. Our C implementation results for a particular MPC example (a 9-state, 3-input quadrotor) show that our proposed algorithm is about 4 times faster than an existing well-performing ADMM variant (“indirect indicator” ADMM or “iiADMM”) and 3 times faster than the well-known QP solver CVXGEN. The convergence rate and code size of the proposed ADMM variant is also comparable with iiADMM.