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Thread Subject:
Riccati Equation in Backwards time.

Subject: Riccati Equation in Backwards time.

From: Faraz Afzal

Date: 4 Mar, 2009 19:25:03

Message: 1 of 1

Hello Genius' Around,

I was wondering if someone can help me solve this Riccati differential in backward time.

dX/dt = -XA - A'X - D'QD + XB(R^-1)B'X

Just to make things clear I will write in words what i state above..

X dot = (minus X into A) - ( A transpose into X) - (D transpose into Q into D) + (X into B into R inverse into B transpose into U).....

My Matrices are such as
with g = 9.81 and c = 10

A = [ 0 1 0 0 0 ; 0 0 -g 0 1 ; 0 0 0 1 0 ; 0 0 0 -1/c 0 ; 0 0 0 0 -20]
B = [0 0 ; 0 0 ; 0 0 ; 1/c 0 ; 0 20]
D = [1 0 0 0 0 ; 0 0 0 0 1]
Q = [0.005 0 ; 0 1]
R = [1 0 ; 0 4]

my initial conditions are (which in fact are the final time i would say Tf) as this

U (Tf) = [ 0.01 0 0 0 0 ; 0 0 0 0 0 ; 0 0 0 0 0 ; 0 0 0 0 0 ; 0 0 0 0 2]

I hope i have given a lot of things here.... the left are steps of time which u can take and suggest by yourself...... that make look plot beautiful i mean....

I hope this kind of solution is possible with MATLAB...

Looking forward towards your help..

Regards,
Faraz

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