GPU-Accelerated Dual Gradient-Projection Algorithm for Embedded Linear Model Predictive Control

This work considers the dual gradient-projection algorithm (GPAD), a lightweight quadratic programming (QP) solver for real-time embedded model predictive control (MPC) applications, and investigates the use of massively parallel processors in expediting its computation. Furthermore, we expand on the initial parallel implementation by taking into consideration the advantages that come with ELLPACK (ELL) matrix compression, using the GPU's shared memory, and caching our constants of interest. Our findings demonstrate that storing linear time-invariant (LTI) matrices in constant memory, combined with coalesced memory accesses, significantly reduces computation time, achieving a 38.9x speedup compared to the CPU implementation. Reduction and warp-level tiling introduce further timing improvements.