Solving Dynamic Optimization Problems to a Specified Accuracy: An Alternating Approach Using Integrated Residuals

• 成果类型: Article
• 署名作者: Nie, Yuanbo; Kerrigan, Eric C.
• 署名单位: Imperial College London; Imperial College London; Imperial College London
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3144131
• 发表日期: 2023
• 页码: 548-555
• 关键词: dynamic optimization; estimation; nonlinear model predictive control (MPC); optimal control; System identification

摘要

We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct collocation, the new approach alternates between minimizing and constraining the squared norm of the dynamic constraint residuals integrated along the whole solution trajectories. As a result, the method can obtain solutions of higher accuracy for the same mesh compared to direct collocation methods, enables a flexible tradeoff between solution accuracy and optimality, and provides reliable solutions for challenging problems, including those with singular arcs and high-index differential algebraic equations.