Re: Re: Re: ricatti & set of ODE solution.
- To: mathgroup at smc.vnet.net
- Subject: [mg41730] Re: [mg41716] Re: [mg41692] Re: [mg41676] ricatti & set of ODE solution.
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Tue, 3 Jun 2003 07:13:11 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On Monday, June 2, 2003, at 04:35 AM, Arda Kutlu wrote:
> 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.
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?
>
> 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
>>
>