Parallel Dynamic Programming for Conic Linear Quadratic Control

2026-06-23

AI Summary

This work addresses the limited real-time scalability of traditional linear-quadratic (LQ) control, which relies on sequential dynamic programming and cannot exploit the parallel processing capabilities of modern multi-core CPUs. To overcome this bottleneck, the authors propose a novel time-parallel method that, for the first time, integrates the Riccati recursion with the alternating direction method of multipliers (ADMM). By decomposing the time domain, the approach partitions constrained optimal control problems—specifically those with conic constraints—into smaller LQ subproblems that can be solved in parallel. Each subproblem is efficiently handled via dynamic programming. The resulting framework breaks the serial dependency inherent in classical solvers and achieves up to a 5× speedup on multi-core CPUs in two real-world scenarios, demonstrating significant gains in computational efficiency without compromising solution accuracy.

Abstract

Linear Quadratic (LQ) control problems are at the heart of linear control theory and Model Predictive Control (MPC). While performant, standard approaches to solving such problems are inherently serial, limiting real-time scalability despite the parallel computing power available on modern multi-core CPUs. Contributing to addressing this challenge and motivated by ``divide and conquer'' strategies, we present a parallel-in-time approach that solves computationally demanding conic optimal control problems through the use of the alternating direction method of multipliers (ADMM). In particular, we formulate the inner primal update of ADMM as an LQ problem and split the reformulated problem along the time horizon. This enables us to derive a variant of the Riccati recursion using dynamic programming to solve each subproblem in parallel. Numerical benchmarks on two real-world applications demonstrate as much as a 5x speedup compared to existing related approaches on multi-core CPU hardware.

Problem

• Linear Quadratic Control
• Parallel Computing
• Real-time Scalability
• Conic Optimization
• Model Predictive Control

Innovation

• parallel-in-time
• ADMM
• Riccati recursion
• dynamic programming
• conic LQ control