How to use sostools to find S matrix in ARE
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This is the parameter
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;
This is the model
% 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);
This is the Q and R matrix for LQR
% Q and R matrices for ARE
Q = [10 0 0 0;
0 10 0 0;
0 0 10 0;
0 0 0 10;
];
R = sym(zeros(2,2)); R(1,:) = [1 0]; R(2,:) = [0 1]; display(R);
This is the S matrix that I want to find the value
% 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(3,1) = svar(3);
S(3,2) = svar(7);
S(4,1) = svar(4);
S(4,2) = svar(8);
S(4,3) = svar(12);
display(S);
This is the Algebra Ricatti Equation (ARE) in LQR Control
% 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);
I want to use sostools and sedumi to find S semidifinite matrix
syms s1 s2 s3 s4 s6 s7 s8 s11 s12 s16
[Sol_s] = sosgetsol(left_ARE,right_ARE,sedumi)
disp(Sol_s)
But why there is error like this
Error using sedumi (line 232)
Should have at least (A,b) or (A,c) arguments
Error in Algebraricattieqvpa (line 75)
[Sol_s] = sosgetsol(left_ARE == right_ARE,sedumi)
my left_ARE is A*x
my right_ARE is B
but why can't get the answer?
12 Comments
Walter Roberson
on 30 Sep 2020
I do not know at the moment.
The difficulty I am having installing sedumi is probably related to my using MacOS.
Answers (0)
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