# What is Riccati equation and what is its applications?

1. ## Riccati equation

Dear all
what is Riccati equation and what is its applications

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2. ## 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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3. ## 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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4. ## 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)

5. ## 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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