Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two
Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two
复制标题
指数二微分代数方程最优控制问题的局部极小值原理
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
M. Gerdts
中科院分区：
文献类型：
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作者：
M. Gerdts
根据局部最小值原理的必要条件，推导出指数-2微分代数方程，纯状态约束，混合控制状态约束的最优控制问题。微分代数方程是微分方程和代数方程的复合系统，在实际应用中经常出现。局部极小值原理是基于一般无限优化问题的必要最优性条件。考虑中的最优控制问题的特殊结构被利用，并使我们能够获得更多的正规表示所涉及的乘数。一个额外的Mangasarian-Fromowitz约束资格的最优控制问题，确保了局部最小值的规律性。本文最后给出了一个示例。
Necessary conditions in terms of a local minimum principle are derived for optimal control problems subject to index-2 differential-algebraic equations, pure state constraints, and mixed control-state constraints. Differential-algebraic equations are composite systems of differential equations and algebraic equations, which arise frequently in practical applications. The local minimum principle is based on the necessary optimality conditions for general infinite optimization problems. The special structure of the optimal control problem under consideration is exploited and allows us to obtain more regular representations for the multipliers involved. An additional Mangasarian-Fromowitz-like constraint qualification for the optimal control problem ensures the regularity of a local minimum. An illustrative example completes the article.