Re: differentiate control model

From: Fredrik Axelsson (frax0795_at_student.uu.se)
Date: 01/22/05 

Date: Sat, 22 Jan 2005 22:15:06 +0000

Jim,

You are absolutely right. Do you think it is safe to assume that

dx/da=Int(-x dt)

dx/da=0 t=0

As I see it, the initial value of the state, x, is not affected by the
parameters.

Best Regards,

Fredrik Axelsson

Jimbo wrote:
> Fredrik,
>
> You have assumed that x = x(a), this is why you need to fully
> differentiate your differential eqn and then integrate to get the
> partial you want. You also need to recognize that h = h(x,u) = h(x(a),
> u). To convence yourself, perturb a = a + d where d is small. You
> will still integrate Eq. (1) but also
>
> x_dot_perturbed = -(a+d)*x_perturbed + b*u + e*h(x_perturbed,u).
>
> Then at any time of interest you get an approximate solution for
>
> dx/da = (x_perturbed - x)/d
>
> Use this result to compare with the eariler result.
>
> Regards
>
> Jim Turner
> Manager, Business Development
> Dynacs Military and Defense
> 1300 Hercules, Suite 210
> Houston, TX 77058
> 281-226-5213
>