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This is my code

clear; close; clc;

syms a1_head a2_head b hstar

%Parameter Massa

m1 = 8095; % massa train set 1 dalam kg

m2 = 8500; % massa train set 2 dalam kg

g = 10;

c_0_1 = 0.01176;

c_1_1 = 0.00077616;

c_2_1 = 4.48 ;

c_0_2 = 0.01176 ;

c_1_2 = 0.00077616;

c_2_2 = 4.48;

v_0 = 300;

hstar = 120;

a_1 = -1./m1.*(c_1_1 + 2.*c_2_1.*v_0);

a_2 = -1./m2.*(c_1_2 + 2.*c_2_2.*v_0);

a_1_head = 1-(a_1.*hstar);

a_2_head = 1-(a_2.*hstar);

b = 1;

% Model data

A = sym(zeros(4,4));

A(1,2) = a_1_head;

A(3,2) = (a_2_head) - 1; A(3,4) = a_2_head;

display(A);

B = sym(zeros(4,2));

B(1,1) = -b*hstar;

B(2,1) = b;

B(3,2) = -b*hstar ;

B(4,1) = -b; B(4,2) = b;

display(B);

% Q and R matrices for ARE

Q = sym(eye(4)); display(Q);

R = sym(zeros(2,2)); R(1,:) = [1 2]; R(2,:) = [2 3]; display(R);

% Matrix S to find

svar = sym('s',[1 16]);

S = [svar(1:4); svar(5:8); svar(9:12); svar(13:16)];

S(2,1) = svar(2);

S(2,2) = svar(1);

S(2,4) = svar(2);

S(3,1) = svar(3);

S(3,2) = svar(7);

S(3,3) = svar(1);

S(4,1) = svar(4);

S(4,2) = svar(2);

S(4,3) = svar(12);

S(4,4) = svar(1);

display(S);

% LHS of ARE: A'*S + S*A' - S*B*Rinv*B'*S

left_ARE = transpose(A)*S + S*A - S*B*inv(R)*transpose(B)*S;

display(left_ARE);

% RHS of ARE: -Q

right_ARE = -Q;

display(right_ARE);

% subs(left_ARE,{s1, s2, s3}, {1, 5, 10})

% Find S in ARE

syms s1 s2 s3 s4 s7 s12

[Sol_S] = solve(left_ARE == right_ARE,s1,s2,s3,s4,s7,s12,'Real',true,'returnconditions',true)

The result like this

Sol_S =

struct with fields:

s1: [0×1 sym]

s2: [0×1 sym]

s3: [0×1 sym]

s4: [0×1 sym]

s7: [0×1 sym]

s12: [0×1 sym]

I want to find my value s using this code

D = [s1 s2 s3 s4 s7 s12];

D = [S.s1 S.s2 S.s3 S.s4 S.s7 S.s12];

But it said

Error using sym/subsref

Too many output arguments.

Error in ARE (line 78)

D = [S.s1 S.s2 S.s3 S.s4 S.s7 S.s12];

Ameer Hamza
on 11 Jun 2020

The values of S are stored in the struct returned by solve(). The actual value of the symbolic variable does not change. So the correct syntax is

D = [Sol_S.s1 Sol_S.s2 Sol_S.s3 Sol_S.s4 Sol_S.s7 Sol_S.s12];

However, the result shows

Sol_S =

struct with fields:

s1: [0×1 sym]

s2: [0×1 sym]

s3: [0×1 sym]

s4: [0×1 sym]

s7: [0×1 sym]

s12: [0×1 sym]

that MATLAB is not able to find a solution. It is probably the case that a solution does not exist. Also, note that there are 16 equations and only 6 variables, so I guess the system is over-determined.

Ameer Hamza
on 11 Jun 2020

In this case, I think the equation is unsolvable for these particular matrices A, B, Q, and R.

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