Chapter 9: Mixed-Integer DAE Optimal Control Problems: Necessary Conditions and Bounds
Chapter 9: Mixed-Integer DAE Optimal Control Problems: Necessary Conditions and Bounds
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第 9 章：混合整数 DAE 最优控制问题：必要条件和界限
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
S. Sager
中科院分区：
文献类型：
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作者：
M. Gerdts;S. Sager
我们感兴趣的是动态过程的最优控制，它可以用微分代数方程(DAE)来描述，并且包含对部分或全部控制函数的整数限制。我们假设DAE系统是指数为1的。在我们的研究中，我们考虑了混合系统这一特定情况的最优性的必要条件，并得到了在算法设置中重要的下界。这两个结果推广了前人对常微分方程组的研究。有趣的是，这两个分析结果的证明都是基于构造元素，以获得从重新公式或松弛到纯连续控制函数的整数控制。这些构造性元素还可用于最优解的有效数值计算。我们通过一个具有代数变量的混合整数非线性最优控制基准问题来说明理论结果。
We are interested in the optimal control of dynamic processes that can be described by Differential Algebraic Equations (DAEs) and that include integer restrictions on some or all of the control functions. We assume the DAE system to be of index 1. In our study we consider necessary conditions of optimality for this specific case of a hybrid system and results on lower bounds that are important in an algorithmic setting. Both results generalize previous work for the case of Ordinary Differential Equations (ODE). Interestingly, the proofs for both analytical results are based on constructive elements to obtain integer controls from reformulations or relaxations to purely continuous control functions. These constructive elements can also be used for an efficient numerical calculation of optimal solutions. We illustrate the theoretical results by means of a mixed–integer nonlinear optimal control benchmark problem with algebraic variables.