Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Modeling and Optimization of Control Problems on GPUs

Alexis Montoison, Jean-Baptiste Caillau

TL;DR

The paper addresses the challenge of solving large-scale sparse nonlinear OCPs by building an end-to-end GPU-first workflow in Julia. It discretizes continuous dynamics via direct transcription, compiles the resulting sparse NLPs into SIMD-enabled GPU kernels, and solves them on NVIDIA GPUs using MadNLP.jl and cuDSS. The approach delivers substantial speed-ups over CPU-based toolchains on benchmark problems like the Goddard rocket and quadrotor, demonstrating scalable performance for real-time or large-scale applications. This work enables high-performance, portable optimal control computation in robotics, aerospace, and related fields, with a clear path toward multi-GPU and differentiable programming integration.

Abstract

We present a fully Julia-based, GPU-accelerated workflow for solving large-scale sparse nonlinear optimal control problems. Continuous-time dynamics are modeled and then discretized via direct transcription with \texttt{OptimalControl.jl} into structured sparse nonlinear programs. These programs are compiled into GPU kernels using \texttt{ExaModels.jl}, leveraging SIMD parallelism for fast evaluation of objectives, constraints, gradients, Jacobians and Hessians. The resulting sparse problems are solved entirely on GPU using the interior-point solver \texttt{MadNLP.jl} and the GPU sparse linear solver cuDSS, yielding significant speed-ups over CPU-based approaches.

Modeling and Optimization of Control Problems on GPUs

TL;DR

The paper addresses the challenge of solving large-scale sparse nonlinear OCPs by building an end-to-end GPU-first workflow in Julia. It discretizes continuous dynamics via direct transcription, compiles the resulting sparse NLPs into SIMD-enabled GPU kernels, and solves them on NVIDIA GPUs using MadNLP.jl and cuDSS. The approach delivers substantial speed-ups over CPU-based toolchains on benchmark problems like the Goddard rocket and quadrotor, demonstrating scalable performance for real-time or large-scale applications. This work enables high-performance, portable optimal control computation in robotics, aerospace, and related fields, with a clear path toward multi-GPU and differentiable programming integration.

Abstract

We present a fully Julia-based, GPU-accelerated workflow for solving large-scale sparse nonlinear optimal control problems. Continuous-time dynamics are modeled and then discretized via direct transcription with \texttt{OptimalControl.jl} into structured sparse nonlinear programs. These programs are compiled into GPU kernels using \texttt{ExaModels.jl}, leveraging SIMD parallelism for fast evaluation of objectives, constraints, gradients, Jacobians and Hessians. The resulting sparse problems are solved entirely on GPU using the interior-point solver \texttt{MadNLP.jl} and the GPU sparse linear solver cuDSS, yielding significant speed-ups over CPU-based approaches.

Paper Structure

This paper contains 11 sections, 9 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Background and limitations
  3. SIMD parallelism in direct optimal control
  4. A Julia-based GPU optimization stack
  5. From optimal control models to SIMD abstraction
  6. Orchestrating model derivatives and sparse GPU linear solvers
  7. Benchmark problems
  8. Discussion
  9. Supplementary material
  10. Descriptions of the control problems used for the benchmark
  11. GPU detailed configurations and results

Figures (4)

  • Figure 7.1: Goddard problem, A100 solve. The grid size ranges from to $N = 1e2$ to $N = 1e5$.
  • Figure 7.2: Goddard problem, H100 solve. The grid size ranges from to $N = 1e2$ to $N = 2e5$.
  • Figure 7.3: Quadrotor problem, A100 solve. The grid size ranges from to $N = 1e2$ to $N = 1e5$.
  • Figure 7.4: Quadrotor problem, H100 solve. The grid size ranges from to $N = 1e2$ to $N = 2e5$.