Mixed-integer optimal control under minimum dwell time constraints

• 成果类型: Article
• 署名作者: Zeile, Clemens; Robuschi, Nicolo; Sager, Sebastian
• 署名单位: Otto von Guericke University; Polytechnic University of Milan
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01533-x
• 发表日期: 2021
• 页码: 653-694
• 关键词: Switched systems; implementation; algorithm

摘要

Tailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to epsilon-optimality by solving one continuous nonlinear program and one mixed-integer linear program (MILP). Within this work, we analyze the integrality gap of MIOCPs under MDT constraints by providing tight upper bounds on the MILP subproblem. We suggest different rounding schemes for constructing MDT feasible control solutions, e.g., we propose a modification of Sum Up Rounding. A numerical study supplements the theoretical results and compares objective values of integer feasible and relaxed solutions.