Re: Re: Re: ricatti & set of ODE solution.
- To: mathgroup at smc.vnet.net
- Subject: [mg41737] Re: [mg41716] Re: [mg41692] Re: [mg41676] ricatti & set of ODE solution.
- From: Arda Kutlu <e130559 at metu.edu.tr>
- Date: Tue, 3 Jun 2003 07:13:19 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
> I'm still not understanding the nature of your system. It sounds as
if
> you have a system of 1st order differential equations with initial
> values at t=0 (?) and final values at t=2. That kind of problem is
> simply not well posed. Or do you have second order equations?
allright. here is the question. ricatti part only.
R=r*IdentityMatrix[4]
r is a value to be found or chosen.
Q=q*IdentityMatrix[4]
q is also a value to be chosen.
ricatti equation.
M(K) --> matrix of K 4x4
Mprime(K) is the time derivative of K.
Mprime(K)= -M(K).Transpose[A].M(K)-Q+M(K).B.R.Transpose[B].M(K)
where
A={{0,1,0,0},
{0,0,0,0},
{0,0,0,1},
{0,0,0,0}}
B={{0,0},
{0.116, (-0.116)},
{0, 0},
{(-0.116), 1.366}}
first order nonlinear differential set.
and boundary .
K(2)=H
value of K at 2 seconds when the proceses ends.
H=h*IdentityMatrix[4]
again h is a value to be chosen.
As you can see here i only know/chose the final value of K. And I need
to find K. Possible numerical solution to this problem is shooting
method, but due to the last term in ricatti the ode is non-linear and
the method doesn't work.
I am supposed to find values of K in 0 2 seconds interval with a small
increment. Or better K(t).
it is well possed. Just the problem is i don't know the initial values
but final values.
These were for ricatti solution.
If u are interested in optimization or this problem i can send you the
problem and my solution (my solution using the other way - set of odes
-with semi-numerical solution, symbolic solution looks like not
possible with today's pc).