Cyqlone: A Parallel, High-Performance Linear Solver for Optimal Control

TL;DR

Cyqlone is a high-performance, parallel linear solver tailored for optimal control problems, enabling real-time solutions for long horizons by leveraging multi-level parallelism and vectorization techniques.

Contribution

The paper introduces Cyqlone, a novel parallel linear solver that unifies multiple algorithms to minimize computations and maximize hardware utilization for optimal control.

Findings

Scales logarithmically with horizon length given sufficient parallelism

Outperforms traditional solvers like BLAS and BLASFEO on small matrices

Achieves order-of-magnitude speedups over HPIPM

Abstract

We present Cyqlone, a solver for linear systems with a stage-wise optimal control structure that fully exploits the various levels of parallelism available in modern hardware. Cyqlone unifies algorithms based on the sequential Riccati recursion, parallel Schur complement methods, and cyclic reduction methods, thereby minimizing the required number of floating-point operations, while allowing parallelization across a configurable number of processors. Given sufficient parallelism, the solver run time scales with the logarithm of the horizon length (in contrast to the linear scaling of sequential Riccati-based methods), enabling real-time solution of long-horizon problems. Beyond multithreading on multi-core processors, implementations of Cyqlone can also leverage vectorization using batched linear algebra routines. Such batched routines exploit data parallelism using single instruction, multiple data (SIMD) operations, and expose a higher degree of instruction-level parallelism than their non-batched counterparts. This enables them to significantly outperform BLAS and BLASFEO for the small matrices that arise in optimal control. Building on this high-performance linear solver, we develop CyQPALM, a parallel and optimal-control-specific variant of the QPALM quadratic programming solver. It combines the parallel and vectorized linear algebra operations from Cyqlone with a parallel line search and parallel factorization updates, resulting in order-of-magnitude speedups over the state-of-the-art HPIPM solver. Open-source C++ implementations of Cyqlone and CyQPALM are available at https://github.com/kul-optec/cyqlone