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26th March 2006, 23:14 #1
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Riccati equation
Dear all
what is Riccati equation and what is its applications

26th March 2006, 23:14

31st March 2006, 05:06 #2
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Riccati equation
Dear friend 
It has sadly been almost a week with no response.
My only experiences with Riccati equatiions has been to do with Kalman (and Kalman/Bucy) filters ... differential or discrete (as per the application).
Riccati had several pivotal solutions to differential equations.
Can you be more specific as to what you're studying them for?
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31st March 2006, 05:06

31st March 2006, 09:32 #3
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Re: Riccati equation
Riccati equations are specific ODEs as the following:
dy/dx=f(x) + g(x)y + h(x)y^2.
These equations usually cannot be solved by closed forms, except for very special (f(x),g(x),h(x)).
Look at this simple equation:
dy/dx=x^2 + y^2,
which is a classical Riccati equation and has to be solved numerically.
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31st March 2006, 09:32

31st March 2006, 09:58 #4
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Re: Riccati equation
Thanks all
if anyone has a documents or books with more details the help will be highly appreciated, I study the Riccati equations as a part of studing the optimization techniques(the Kalman filters is an issue)

1st April 2006, 07:01 #5
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Riccati equation
Hi,
Here is a link of differential equations book with several pages dealing with Riccati eqs.
http://www.sosmath.com/diffeq/diffeq.html
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