Parameter estimation of ordinary differential equations
Parameter estimation of ordinary differential equations
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DOI：
10.1093/imanum/drh016
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发表时间：
2005-04-01
影响因子：
2.1
通讯作者：
Prvan, T
中科院分区：
文献类型：
--
作者：
Li, ZF;Osborne, MR;Prvan, T
本文提出了一种新的常微分方程参数估计算法。在这里,我们证明了(1)在非平凡二分类的情况下，结合正交循环约简的同时方法可以将估计问题简化为受固定数量的等式约束的优化问题，而不需要结构信息来设计稳定嵌入；(2)在假设模型不正确或不正确的情况下，应该使用估计问题的拉格朗日函数的Hessian信息的牛顿近似只有数量有限的样本数据可用。提出了一种新的算法，该算法不仅使用了顺序二次规划（SQP）高斯-牛顿近似，而且还包含了SQP牛顿近似以及何时使用该近似的测试。这种复合方法放宽了SQP高斯-牛顿近似假设模型必须正确和样本数据集必须足够大的限制。该算法已在两个标准问题上进行了测试。
This paper addresses the development of a new algorithm for parameter estimation of ordinary differential equations. Here, we show that (1) the simultaneous approach combined with orthogonal cyclic reduction can be used to reduce the estimation problem to an optimization problem subject to a fixed number of equality constraints without the need for structural information to devise a stable embedding in the case of non-trivial dichotomy and (2) the Newton approximation of the Hessian information of the Lagrangian function of the estimation problem should be used in cases where hypothesized models are incorrect or only a limited amount of sample data is available. A new algorithm is proposed which includes the use of the sequential quadratic programming (SQP) Gauss-Newton approximation but also encompasses the SQP Newton approximation along with tests of when to use this approximation. This composite approach relaxes the restrictions on the SQP Gauss-Newton approximation that the hypothesized model should be correct and the sample data set large enough. This new algorithm has been tested on two standard problems.