具有自由终端时间的多目标最优控制问题可行解的存在性
Existence of the Feasible Solutions forMulti-Objective Optimal ControlProblem with Free End Time
摘要: 本文主要考虑在欧式空间中,初始状态和终端状态满足约束,具有自由终端时间的多目标最优控 制问题。 通过引入额外的状态与控制,把具有自由终端时间的多目标最优控制问题转变为有限时 间区间的多目标最优控制问题,得到了具有自由终端时间的多目标最优控制问题可行解存在性条件。
Abstract: In this paper, we mainly consider the multi-objective optimal control problem with free end time, initial state and terminal state satisfying constraints. By introducing additional state and control, we transform this problem into a control problem with fixed end time, we obtain the existence of the feasible solutions for multi-objective optimal control problem with free end time.
文章引用:洪叶. 具有自由终端时间的多目标最优控制问题可行解的存在性[J]. 理论数学, 2024, 14(5): 307-314. https://doi.org/10.12677/PM.2024.145187

参考文献

[1] Kaya, C.Y. and Maurer, H. (2023) Optimization over the Pareto Front of Nonconvex Multiobjective Optimal Control Problems. arXiv preprint arXiv: 2301.13327[CrossRef
[2] Bolzoni, L., Bonacini, E., Della Marca, R. and Groppi, M. (2019) Optimal Control of Epidemic Size and Duration with Limited Resources. Mathematical Biosciences, 315, Article 108232.[CrossRef] [PubMed]
[3] Logist, F., Van Erdeghem, P.M.M. and Van Impe, J.F. (2009) Effcient Deterministic Multiple Objective Optimal Control of (Bio)Chemical Processes. Chemical Engineering Science, 64, 2527-2538. [Google Scholar] [CrossRef
[4] Vertovec, N., Ober-Blobaum, S. and Margellos, K.(2023) Multi-Objective Low-Thrust Spacecraft Trajectory Design Using Reachability Analysis. European Journal of Control, 69, Article 100758.[CrossRef
[5] Vertovec, N., Ober-Blobaum, S. and Margellos, K. (2021) Multi-Objective Minimum Time Optimal Control for Low-Thrust Trajectory Design. 2021 European Control Conference (ECC), Delft, 29 June-2 July 2021, 1975-1980.[CrossRef
[6] 袁嘉宁. 多目标优化控制问题可行解的存在性[J]. 理论数学, 2022, 12(1): 97-102. [Google Scholar] [CrossRef