On parameter identification for ordinary differential equations (Q1114356)

For the vector initial value problem \(\dot x(t)=f(t,x,a)\), \(x(0)=x_ 0\) when the data are noisy the associated regularized parameter identification problem is formulated as follows: Given noisy observations \(z(t)=x(t)+\delta(t),\) \((0\leq t\leq T)\) of the state x(t) \((0\leq t\leq P)\), determine the parameter vector \(a\in R^ m\) minimizing the functional \(J_{\alpha}(a)=\| x-z\|_{Z^ 2}+\alpha /2\| a-\bar a\|^ 2_{R^ m}.\) For minimizing \(J_{\alpha}(a)\) the gradient method and Gauss-Newton method are examined. An application to a inverse problem of the water movement is considered.