| 保证路径约束严格满足的鲁棒动态优化 |
| Robust dynamic optimization with guaranteed rigorous satisfaction of path constraints |
| 摘要点击 8 全文点击 0 投稿时间：2024-04-17 修订日期：2025-03-17 |
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| 中文关键词 未知参数；非线性系统；路径约束；鲁棒动态优化 |
| 英文关键词 unknown parameters, nonlinear systems, path constraints, robust dynamic optimization |
| 基金项目 国家自然科学基金项目（面上项目，重点项目，重大项目） |
| 作者 | 单位 | 邮编 | | 周琬璐 | 东北大学 | 110819 | | 李欢 | 东北大学 | | | 付俊* | 东北大学 | 110819 |
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| 中文摘要 |
| 针对具有未知参数的非线性系统提出一种可以保证路径约束严格满足的鲁棒动态优化算法. 首先, 将连续的控制输入用有限个分段常值函数来近似, 然后将近似后的控制输入与未知参数向量作为动态优化问题的共同决策变量. 其次, 基于半无穷规划(semi-infinite program, SIP)能够描述具有有限维决策变量但约束是无限维的动态优化问题的思想, 通过限制路径约束的右端并且将路径约束强制在有限多个时间点上取值来构造原问题的近似动态规划. 然后, 经过迭代使近似问题不断逼近原问题, 从而设计了一种能够在有限步迭代内获得保证路径约束严格满足的最优控制输入和最优参数估计的鲁棒动态优化算法. 最后, 数值示例验证了该动态优化算法能够保证系统在存在未知参数的情形下的最优性和鲁棒性. |
| 英文摘要 |
| A robust dynamic optimization method is proposed for path-constrained nonlinear systems with unknown parameters while guaranteeing rigorous satisfaction of path constraints. First, the continuous control input is approximated by finite piecewise constant functions, and then the approximated control input and the unknown parameter vector are taken as the common decision variables. Second, based on the semi-infinite programming(SIP) technique, which can describe dynamic optimization with finite-dimensional decision variables but infinite-dimensional constraints, by restricting the right-hand of the path constraints and enforcing the path constraints at finite time points, an approximate dynamic programming is constructed. Then, a robust dynamic optimization algorithm is designed which can obtain the optimal control input and the optimal parameter estimation by iteratively approximating the original problem. Finally, a numerical example shows that the designed algorithm can ensure the optimality and robustness of the system with unknown parameters. |
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