I understand that you seek guidance to separate state and unknown parameters in adaptive control using MATLAB. Using Symbolic Toolbox can simplify the process of separating the dynamics into a linear vector and a matrix based on measured states. Here's a general approach to solving this problem using MATLAB's symbolic toolbox:
STEP 1: Define the symbolic variables representing the states and parameters in your system
STEP 2: Define the dynamics of the system using the symbolic variables.
STEP 3: Use the symbolic expressions you have to formulate the product Y*a as a function of the symbolic variables.
STEP 4: To separate Y and a, you can use MATLAB's symbolic manipulation functions such as `solve` or `mldivide`.
STEP 5: Once you have obtained the separate expressions for Y and a, you can use them to implement the adaptation law and proceed with your adaptive control algorithm.
Have a look at the following code snippet to use MATLAB's Symbolic Toolbox to separate 'Y' and 'a':
% Define symbolic variables
syms q dq ddq m1 m2 I1 I2
% Define the dynamics
H = ...;
C = ...;
D = ...;
% Formulate Y*a
Y_times_a = ...;
% Separate Y and a
Y = solve(Y_times_a == ..., Y);
a = solve(Y_times_a == ..., a);
I hope this helps.
