Re: Re: ricatti & set of ODE solution.
- To: mathgroup at smc.vnet.net
- Subject: [mg41716] Re: [mg41692] Re: [mg41676] ricatti & set of ODE solution.
- From: Arda Kutlu <e130559 at metu.edu.tr>
- Date: Mon, 2 Jun 2003 04:35:23 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello Dr. Selwyn Hollis
To make something make clear i want to explain something. I am working
on a lecture's project which is optimization of a planer robot arm
with 2 DOF. And the performance measurement is in tracking type.
There are two basic approaches (as far as i know) to solve.
And one contains ricatti solution. The other is the solution of set of
odes.
For ricatti part yes, ricatti is in that form. But I have matrix
ricatti form so not one nonlinear equation I have set of them. And I
know the boundary condition at the final time (t=2 seconds). I know
how to compute ricatti equations which goes to infinity. What if the
time is fixed or certain is it possible to compute with mathematica?
I obtained equation and tried to solve using numerical approach,
shooting method. Due to the nature of the shooting method, simply it
didn't work out in solution of this type of equations.
And for ODE solution I will try it (thread) and you are right I
shouldn't define x in vector form.
Thanks.
Arda Kutlu @ metu
-------------------
> Hello Arda,
>
> > here are the questions that i can't solve with mathematica.
> > 1) i need to solve ricatti equation which ends at 2nd second, is
it
> > possible to solve with mathematica.
>
> Not sure what you mean by "ends at 2nd second." What is typically
> called a Riccati equation is one of the form x'[t] == a[t] +
b[t]x[t] +
> c[t]x[t]^2. Mathematica can solve some, but certainly not all,
> equations of this type.
>
> > 2) when solving set of ode i get error msgs.
> > as i run these commands basicly to get solution:
> >
> > x[t_]={{x1[t]},{x2[t]}}
> > at same where in the solution i get x'[t] in terms of x[t] and run
> > sol=DSolve[{x'[t]==something,x[0]==somethingelse},x[t],t]
> > and get error msg as x1[t] is not a function.
>
> Is there a reason why you have x[t_]:={{x1[t]},{x2[t]}} instead of
> x[t_]:={x1[t], x2[t]}? If so use Thread and Flatten:
>
> sol = DSolve[Thread/@{x'[t] == something, x[0] == somethingelse},
> Flatten[x[t]], t]
>
> Otherwise just use Thread.
>
> -----
> Selwyn Hollis
> http://www.math.armstrong.edu/faculty/hollis
>