I would like to generate symbolic expressions representing the computations involved in a snippet of code (shown below), while simultaneously computing the actual numeric values used to solve the problem.
Let's say A is a 2x2 matrix, B is a 1x2 vector, Q is a 2x2 matrix, and R is a 1x1:
b = 100;
m = 1500;
A = [0 1; 0 -b/m];
B = [0 1/m]';
Q = 2*eye(length(A));
R = 2*eye(size(B,2));
I would like both the numeric solution for K, and the symoblic expressions representing the solution to K. For example,
K = [0 , -0.0125] and
K = [- A11*((B11*Q11)/(R11 + B11*(B11*Q11 + B21*Q21) + B21*(B11*Q12 + B21*Q22)) ...., - A12*((B11*Q11)/(R11 + B11*(B11*Q11 + B21*Q21) + B21*(B11*Q12 + B21*Q22)) ...]
function [ K ] = dlqr_finite( A, B, Q, R, N )
P = cell(1, N);
K = cell(1, N);
P{N+1} = Q;
n = N+1;
while n > 1
P{n-1} = Q + (A.'*P{n}*A) - (A.'*P{n}*B)*(R+B.'*P{n}*B)^-1*(B.'*P{n}*A);
K{n-1} = -1*(R+B.'*P{n}*B)^-1*(B.'*P{n}*A);
n = n-1;
end
end
What is the easiest way to achieve these simultaneously?
