Banded Null Basis and ADMM for Embedded MPC*. Issue 1 (July 2017)

• Record Type: Journal Article
• Authors: Dang, Thuy V; Ling, Keck Voon; Maciejowski, Jan
• Is Part Of: IFAC-PapersOnLine. Volume 50:Issue 1(2017)
• Page Start: 13170
• Page End: 13175
• Publication Date: 2017-07
• Subjects: Banded null basis -- ADMM -- embedded MPC -- structured matrices -- sparse QP; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2017.08.2172
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: 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.