Pitfalls in parameter estimation for delay differential equations

被引:19
作者
Baker, C
Paul, CAH
机构
[1] Mathematics Department, Victoria University of Manchester
关键词
parameter estimation; delay differential equations; derivative discontinuities;
D O I
10.1137/S1064827595287201
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Given a set of data {U(gamma(i)) approximate to u(gamma(i);p*)} corresponding to the delay differential equation u'(t;p) = f(t,u(t;p),u(alpha(t;p);p);p) for t greater than or equal to t(0)(p), u(t;p) = Psi(t;p) for t less than or equal to t(0)(p), the basic problem addressed here is that of calculating the vector p* epsilon R(n). (We also consider neutral differential equations.) Most approaches to parameter estimation calculate p* by minimizing a suitable objective function that is assumed by the minimization algorithm to be sufficiently smooth. In this paper, we use the derivative discontinuity tracking theory for delay differential equations to analyze how jumps can arise in the derivatives of a natural objective function. These jumps can occur when estimating parameters in lag functions and estimating the position of the initial point, and as such are not expected to occur in parameter estimation problems for ordinary differential equations.
引用
收藏
页码:305 / 314
页数:10
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