Solving Riccati differential equation with time variable matrix

Given: differential equation -P(t)AP(t) + Q(t) = dP(t)

A is known and constant Q is known for all time steps

Now I want to solve this equation to get P. How can i achieve this by using solver like ode45? I do not know how to include the time variable matrix Q in the solving algorithm.

Thanks in advance

Answer 1

[Orion]

Hi,

look example3 in ode45

your Q is the same as g in this example

[Stephan]

Thank you.

In example3 in ode45 the function g(t) can be exactly specified with g(t)= 3*sin(t-0.25) right? In my problem I do not have such functional relation for Q. Consider Q to be a matrix containing measured data gathered by observing a system for a while.

[Stephan]

So i have to interpolate the Matrix like they did in step g = interp1(gt,g,t); % Interpolate the data set (gt,g) at time t

[Orion]

it shoudn't change anything, even if you don't have a formula.

you have a vector Q (n sample), and you just use this vector.

[Stephan]

ok thank you.

If there are further problems, I will write them down here :)