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What is Riccati equation and what is its applications?

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Roshdy

Roshdy

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Riccati equation

Dear all
what is Riccati equation and what is its applications
 

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?
 

    Roshdy

    Roshdy

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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.
 

    Roshdy

    Roshdy

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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)
 

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