Added matlab code samples.

All of these code samples currently are mis-identified in my repositories. I'm
donating them to the cause.

samples/Matlab/adapting_structural_model.m

@@ -0,0 +1,74 @@
+function [dx, y] = adapting_structural_model(t, x, u, varargin)
+%
+% Returns the time derivatives of the states and the output of the
+% structural control model with an adapting controller.
+%
+% Parameters
+% ----------
+% t : double
+%   The current time.
+% x : double, size(8, 1)
+%   The current state.
+% u : double, size(1, 1)
+%   The current input.
+% varargin : cell array
+%   m1, m2, m3, m4, b1, b2, b3, b4 : double
+%       The slope of the four gains and the offset of the four gains.
+%   aux : cell array containing a single structure
+%       The structure contains:
+%       pars : double, size(1,9)
+%           The controller parameters.
+%       timeDelay : logical
+%           If true a 1st order Pade approximation of the human's time delay
+%           is included.
+%       plantFirst : integer
+%           The number of the first plant.
+%       plantSecond : integer
+%           The number of the second plant.
+%       m : double, size(2, 1)
+%           The slope of the transfer function adaption function.
+%       b : double, size(2, 1)
+%           The offset of the transfer function adaption function.
+%
+% Returns
+% -------
+% dx : double, size(8, 1)
+%   The derivatives of the states.
+% y : double, size(1, 1)
+%   The output, theta.
+
+% MATLAB SUCKS! This is unbelievable. On the first iteration varargin is 1x2
+% and after that it is 1x9.
+%size(varargin, 2)
+
+% Unpack varargin.
+aux = varargin{end}{1};
+m = zeros(4, 1);
+b = zeros(4, 1);
+for i=1:4
+    if size(varargin, 2) == 2
+        m(i) = varargin{1}(i);
+        b(i) = varargin{1}(i + 4);
+    elseif size(varargin, 2) == 9
+        m(i) = varargin{i};
+        b(i) = varargin{i + 4};
+    else
+        display('Matlab is stupid.')
+    end
+end
+
+% First compute the gains at this time.
+aux.pars(1:4) = m .* t + b;
+% Compute the controller.
+Yp = human(aux.pars, aux.timeDelay);
+% Compute the plant and this time.
+c1 = aux.m(1) * t + aux.b(1) + 1e-10;
+c2 = aux.m(2) * t + aux.b(2) + 1e-10;
+Yc = parallel(c1 * plant(aux.plantFirst), c2 * plant(aux.plantSecond));
+% Compute the closed loop system.
+Ys = feedback(Yp * Yc, 1);
+% Convert to state space.
+[A, B, C, D] = tf2ss(Ys.num{1}, Ys.den{1});
+% Compute the derivatives of the states and the outputs.
+dx = A * x + B * u;
+y = C * x + D * u;