Vectorized Sparse Second-Order Forward Automatic Differentiation for Optimal Control Direct Methods
Direct collocation methods are widely used numerical techniques for solving optimal control problems. The discretization of continuous-time optimal control problems transforms them into large-scale nonlinear programming problems, which require efficient computation of first- and second-order derivatives. To achieve computational efficiency, these derivatives must be computed in sparse and vectorized form, exploiting the problem's inherent sparsity structure. This paper presents a vectorized sparse second-order forward automatic differentiation framework designed for direct collocation methods in optimal control. The method exploits the problem's sparse structure to efficiently compute derivatives across multiple mesh points. By incorporating both scalar and vector nodes within the expression graph, the approach enables effective parallelization and optimized memory access patterns while maintaining flexibility for complex problems. The methodology is demonstrated through application to a prototype optimal control problem. A complete implementation for multi-phase optimal control problems is available as an open-source package, supporting both theoretical research and practical applications.
Code (1)
Tasks
Computational EfficiencySimilar Papers 제목 키워드 기반
Parameterizing Region Covariance: An Efficient Way To Apply Sparse Codes On Second Order Statistics
Sparse representations have been successfully applied to signal processing, computer vision and machine learning. Currently there is a trend to learn sparse models directly on structure data, such as region covariance. H…
BIG-bench Machine LearningEva: A General Vectorized Approximation Framework for Second-order Optimization
Second-order optimization algorithms exhibit excellent convergence properties for training deep learning models, but often incur significant computation and memory overheads. This can result in lower training efficiency …
VENOM: A Vectorized N:M Format for Unleashing the Power of Sparse Tensor Cores
The increasing success and scaling of Deep Learning models demands higher computational efficiency and power. Sparsification can lead to both smaller models as well as higher compute efficiency, and accelerated hardware …
Computational EfficiencyLGmap: Local-to-Global Mapping Network for Online Long-Range Vectorized HD Map Construction
This report introduces the first-place winning solution for the Autonomous Grand Challenge 2024 - Mapless Driving. In this report, we introduce a novel online mapping pipeline LGmap, which adept at long-range temporal mo…
DecoderEfficient Vectorized Backpropagation Algorithms for Training Feedforward Networks Composed of Quadratic Neurons
Higher order artificial neurons whose outputs are computed by applying an activation function to a higher order multinomial function of the inputs have been considered in the past, but did not gain acceptance due to the …