Error in my MATLAB code

Hello,

when I try to simulate the code:

% Define the communication topology
L = [1 -1  0 0;
    0  0  0 0;
    0 -1  1 0;
    0  0 -1 1];

% Define the coupling strengths
c = [0.1; 0.15; 0.15; 0.2];

% Define the initial conditions
x0 = [0.1   0.2;
    0.25 -0.05;
    0.1  -0.15;
    -0.25  0.3];

% Define the state space equations
A = zeros(8,8);
B = zeros(8,4);
C = [1 0 0 0;
    0 1 0 0];

for i = 1:4
    % Define the state equations for agent i
    A((2*i-1):(2*i), (2*i-1):(2*i)) = [1/(1+x0(i,1)^2) 1;
        -c(i)*cos(x0(i,1)-x0(i,2))*exp(-(x0(i,1))^2+(x0(i,2))^4) -c(i)*sin(x0(i,1)-x0(i,2))*exp(-(x0(i,1))^2+(x0(i,2))^4)];
    
    % Define the input equation for agent i
    B((2*i-1):(2*i), i) = [0; 1];
    
    % Define the coupling equations for agent i
    for j = 1:4
        if L(i,j) == 1
            A((2*i-1):(2*i), (2*j-1):(2*j)) = [-1 0;
                0 -1];
        elseif L(i,j) == -1
            A((2*i-1):(2*i), (2*j-1):(2*j)) = [1 0;
                0 1];
        end
    end
end

% Define the time span
tspan = [0 400];

% Define the initial state vector
x0_vec = reshape(x0', [8,1]);

% Define the weighting matrices Q and R
Q = eye(8);
R = eye(4);

% Compute the optimal feedback gain matrix K using LQR control
[K,~,~] = lqr(A,B,Q,R);

% Define the reference signal
yd = @(t) sin(t);

size(A)

ans = 1×2

8 8

size(B)

ans = 1×2

8 4

size(K)

ans = 1×2

4 8

% Simulate the closed-loop system with LQR control and reference signal
[t,x] = ode45(@(t,x) (A-B*K)*x + B*yd(t), tspan, x0_vec);

Error using odearguments
@(T,X)(A-B*K)*X+B*YD(T) must return a column vector.

Error in ode45 (line 107)
odearguments(odeIsFuncHandle,odeTreatAsMFile, solver_name, ode, tspan, y0, options, varargin);

% Reshape the output vector x into a matrix
x = reshape(x, [size(x,1), 2, 4]);

% Plot the results
figure;
for i = 1:4
    subplot(2,2,i);
    plot(t, squeeze(x(:,1,i)), t, yd(t), 'g--');
    xlim([0 400]);
    title(['Agent ', num2str(i)]);
    xlabel('Time');
    ylabel('State');
    legend('x_1', 'y_d');
end

figure;
for i = 1:4
    subplot(2,2,i);
    plot(t, squeeze(x(:,2,i)), t, yd(t), 'g--');
    xlim([0 400]);
    title(['Agent ', num2str(i)]);
    xlabel('Time');
    ylabel('State');
    legend('x_2', 'y_d');
end

it give me the following error:

Error using odearguments (line 93)

@(T,X)(A-B*K)*X+B*YD(T) must return a column vector.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in New_Model22 (line 59)

[t,x] = ode45(@(t,x) (A-B*K)*x + B*yd(t), tspan, x0_vec);

can anyone help me?

Thanks

Answer 1

[Torsten]

Explicitly listing the sizes of the matrices involved (see above), I come to the conclusion that yd(t) must be a 4x1 column vector instead of a 1x1 scalar.

[Mostafa Sallam]

Any notes to apply this answer will be appretiated.

[Torsten]

We don't know what your equations represent.

It's up to you to define yd(t) appropriately as a function that returns a 4x1 vector, e.g.

yd = @(t) sin(t)*ones(size(B,2),1)

[Mostafa Sallam]

Thanks so much