MaplePrimes - answers and comments on Question, Solve state-space system

Reference

Markiyan Hirnyk — Mon, 21 Jan 2013 22:42:44 Z

See

http://www.mapleprimes.com/questions/37864-Sovle-A-Differential-Equation-Of-Matrix-S

, where a similar question was asked and answered. This link can be found by the "matrix equation" search in MaplePrimes at the top of this page.

MatrixExponential

Preben Alsholm — Mon, 21 Jan 2013 22:53:01 Z

You may want to try MatrixExponential because it is so seemingly simple:

restart;
A:=ImportMatrix("G:/MapleDiverse/MaplePrimes/A-1.txt"):
C:=ImportMatrix("G:/MapleDiverse/MaplePrimes/C.txt"):
Y0:=ImportMatrix("G:/MapleDiverse/MaplePrimes/Y0.txt"):
Digits:=15:
E:=LinearAlgebra:-MatrixExponential(A,t):
simplify(fnormal~(eval(E,t=0),8)); #Just a check: Should be the identity matrix
#Considering you previously posted question I assume you may accept the following as X(0) (?):
X0:=LinearAlgebra:-LeastSquares(C,convert(Y0,Vector));
#The solution:
X:=E.X0:
plot([seq(Re(X[i]),i=1..5)],t=0..0.1); #Just to see something.

Numerical solution

Preben Alsholm — Tue, 22 Jan 2013 00:35:36 Z

Suppose you have found an acceptable initial vector X0 (see my other answer).
Then a numerical solution could be found like this:
X:= < seq(x[i](t),i=1..7 )>;
#The ode system
sys:=convert(diff~(X,t)=~A.X,set);
#The initial conditions:
ics:=convert(eval(X,t=0)=~X0,set);
#The numerical solution:
res:=dsolve(sys union ics,numeric);
plots:-odeplot(res,[seq([t,x[i](t)],i=1..7)],0..0.1);

Output Error

STHence — Tue, 22 Jan 2013 02:28:11 Z

Thanks you Preben,

Your idea is great, but there is the large error of the output at the beginning (t from 0 to 0.1).

Can we solve the state space form without finding the initial values of the state X?

X0 unknown

Preben Alsholm — Tue, 22 Jan 2013 07:09:35 Z

@STHence If X(0) is not known, but is just

X0:= <seq(x0[i],i=1..7)>;

then you can still compute E.X0, but then you are faced with having to solve Y = C.X w.r.t. X0 in some "best" way.

Professional Code

STHence — Tue, 22 Jan 2013 11:35:08 Z

I really appreciate your help @Preben Alsholm .

Your code is short and professional.

However, there are errors in the inital values of the output Y that is solved in Maple.