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From: Karthi on 12 Mar 2010 09:29
hi paul,
it really helps.i have one more question, i have the differential equations(state space equations)for the system and i can solve the diff equations using ode and calculate the cost function. but the parameter integral gain is in the diff equations which is to be optimized.
let me explain the problem(for example)
minimize C=integral(x1^2+x2^2)dt
where x1 and x2 state variables
the state equations looks like

dx1/dt=-x1+ki/100;
dx2/dt=-x1+x2+ki/20

here i want to find the value of ki which minimize the cost function.
From: Torsten Hennig on 11 Mar 2010 23:50
> hi paul,
> it really helps.i have one more question, i have the
> differential equations(state space equations)for the
> system and i can solve the diff equations using ode
> and calculate the cost function. but the parameter
> integral gain is in the diff equations which is to be
> optimized.
> let me explain the problem(for example)
> minimize C=integral(x1^2+x2^2)dt
> where x1 and x2 state variables
> the state equations looks like
>
> dx1/dt=-x1+ki/100;
> dx2/dt=-x1+x2+ki/20
>
> here i want to find the value of ki which minimize
> the cost function.

Define a third differential equation by
dI/dt = x1^2 + x2^2, I(0)=0.
At t = tend, I(tend) gives you
integral_{0}^{tend} (x1^2+x2^2) dt.
You see:
For a given set of parameters ki, call ODE45
from within the optimizer, integrate
(including the ODE for I) and hand
I(tend) to the optimizer.
It will then (hopefully) adjust the ki such that
the integral in question is minimized.

Best wishes
Torsten.
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