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GPU-Accelerated Pseudospectral Methods for Optimal Control Problems

I tiakina i:
I whakaputaina i:Mathematics vol. 13, no. 20 (2025), p. 3252-3267
Kaituhi matua: Zou Yilin
Ētahi atu kaituhi: Jiang Fanghua
I whakaputaina:
MDPI AG
Ngā marau:
Sparsity
Accuracy
Interplanetary trajectories
Applied mathematics
Trajectory optimization
Fourier transforms
Graphics processing units
Optimization
Effectiveness
System dynamics
Methods
Algorithms
Optimal control
Aerospace engineering
Energy consumption
Nonlinear programming
Derivatives
Computing time
Linear algebra
Robotics
Spectral methods
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Whakarāpopotonga:Pseudospectral methods are effective tools for solving optimal control problems, but they result in large-scale nonlinear programming (NLP) problems that are computationally demanding. A major bottleneck is the repeated evaluation of the objective function, system dynamics, path constraints, and their derivatives. This paper presents an approach to accelerating these computations using Graphics Processing Units (GPUs). We offload the evaluation of the NLP functions and their first and second derivatives to the GPU by developing custom CUDA kernels that exploit the parallelism in the discretized problem structure. The effectiveness of this method is demonstrated on a low-thrust interplanetary trajectory optimization problem. A comparison with a CPU implementation shows that the GPU-accelerated approach reduces the overall computational time. This work demonstrates the potential of GPU acceleration and provides a foundation for future research into fully GPU-native optimal control solvers.
ISSN:2227-7390
DOI:10.3390/math13203252
Puna:Engineering Database