MINIMIZE symbolic function P

X(t) = sym('x',[6 2])
syms t
syms X(t) t t0 tf N
a = diff(X(t),t)
b=a'
f=b*a
int( f,t, t0,tf)
P = symsum(f,t,0,N)

I need to minimize this symbolic (matrix) function P

Constraints:-

1.) P ∈ {0,1}

2.)P'*P=eye(M)

3.) t ∈ [t0, tf ]

4.) N=6

Answer 1

[Walter Roberson]

syms t t0 tf
N = 6;
M = 2;
x = sym('x',[6 M]);
X(t) = str2sym(string(x) + "(t)");
a = diff(X(t), t);
b = a';
f = b*a;
f_int = int(f, t, t0, tf);  %I do not know what this is for
temp = arrayfun(@(idx) subs(f(idx),t,1:N), 1:M.^2, 'uniform', 0);
P = reshape(sum(cat(1,temp{:}),2), M, M);

f is 2 x 2 because you are multiplying (6x2)' * (6x2) so (2x6) * (6x2) so 2x2 result.

You then symsum() the 2 x 2 over 6 different times (and it is pretty strange to choose integer times 1 through 6 when you have a constraint about t ∈ [t0, tf ] ). You would be getting a 2 x 2 result.

You then talk about P'*P, which is going to be (2x2).' * (2x2) which is (2x2)*(2x2) which is going to give a 2x2 result. That cannot possibly be eye(6)

So P will be either 2 x 2 (following your mathematics) or something x 6 (following your eye(6)). Either way, it is multi-valued, and then one has to ask what it means to minimize a multi-valued function.

[madhan ravi]

sir Walter in your code you mentioned ttt{:} I guess that’s a typo for temp{:}

[Walter Roberson]

Ah, you are right, I was using ttt in my testing and changed to temp for posting.

[Vanshika Singh]

Sir, basically i am trying to solve this equation-

here N=6

ie. summation of the Function P from 1 to 6

and integral is from t0 to tf

and X(t) is 6x2 matrix, whose all elements are time-dependent.

CONSTRAINTS-

[Vanshika Singh]

please help me in minimizing P