Local optimization of dynamic programs with guaranteed satisfaction of path constraints
Local optimization of dynamic programs with guaranteed satisfaction of path constraints
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DOI：
10.1016/j.automatica.2015.09.013
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Jun Fu;Johannes M. M. Faust-Johannes-M.-M.-Faust-33587732;B. Chachuat;A. Mitsos
中科院分区：
文献类型：
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作者：
Jun Fu;Johannes M. M. Faust-Johannes-M.-M.-Faust-33587732;B. Chachuat;A. Mitsos
针对可行路约束动态规划(PCDP)问题，提出了一种在有限次迭代内找到满足KKT条件的可行点的算法。该算法通过限制路径约束的右侧并在有限多个时间点强制实施路径约束来迭代逼近PCDP。本文的主要贡献是将Mitsos(2011)提出的半无限规划(SIP)算法应用于PCDP。证明了该算法在满足一阶KKT条件的PCDP满足一定容差的保证可行点的情况下是有限终止的。主要的假设是：(I)如果该问题确实可行，则在每次迭代中生成所构造的逼近于PCDP的KKT点的非线性规划(NLP)局部求解器的可用性；(Ii)PCDP的Slate点的存在，该点也满足PCDP的一阶KKT条件到指定的容差；(Iii)所有KKT乘子关于所有迭代都是非负的且一致有界。通过两个算例分析了该算法的性能。
An algorithm is proposed for locating a feasible point satisfying the KKT conditions to a specified tolerance of feasible inequality-path-constrained dynamic programs (PCDP) within a finite number of iterations. The algorithm is based on iteratively approximating the PCDP by restricting the right-hand side of the path constraints and enforcing the path constraints at finitely many time points. The main contribution of this article is an adaptation of the semi-infinite program (SIP) algorithm proposed in Mitsos (2011) to PCDP. It is proved that the algorithm terminates finitely with a guaranteed feasible point which satisfies the first-order KKT conditions of the PCDP to a specified tolerance. The main assumptions are: (i) availability of a nonlinear program (NLP) local solver that generates a KKT point of the constructed approximation to PCDP at each iteration if this problem is indeed feasible; (ii) existence of a Slater point of the PCDP that also satisfies the first-order KKT conditions of the PCDP to a specified tolerance; (iii) all KKT multipliers are nonnegative and uniformly bounded with respect to all iterations. The performance of the algorithm is analyzed through two numerical case studies.