John,
This is a dynamic optimization problem, some time also called optimal control problem. If you do not know much about optimal control theory, you can use a direct optimization approach.
Firstly, you can choose a sampling time, h to discrete the problem, so that T = hN. Then the problem can be approaximated as
L = sum_{k=0}^N (AR(k)  x(k))h (1)
R(k+1) = R(k) + (ax(k)b)R(k)h, k=0,...,N1 (2)
You can set both R(k) and x(k), k=0, ..., N are variables to be optimized. Equation (1) is the cost function, whilst (2) as the equality constraints. This problem should be solvable using fmincon.
HTH
Yi Cao
John <johnadams986@gmail.com> wrote in message <482873190.182844.1266013894815.JavaMail.root@gallium.mathforum.org>...
> I am trying to optimize a function of the following form:
>
> L = Int(t=0,t=T)[ARx)dt]
>
> i.e. I am trying to find the optimum x(t) that minimizes L over all admissible x(t)s. R is related to x using a relation:
>
> dR/dt = axR  bR, where a and b are system parameters.
>
> I was trying to use fminbnd and fminsearch but I keep getting some errors regarding functions. Can someone please help me with this?
