2025/06/13 by Yilin Zou, Zou, Yilin, Fanghua Jiang +1
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2506.11537
openalex publication_date 2025/06/13 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28
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.