dynamics_final.m

function dstate = dynamics_final(t, state, x_hat, m_true, k_p, k_d, gamma)
    x = state(1:2); v = state(3:4);
    m_hat = state(5); f_hat = state(6); d_hat = state(7);

    % Reference Trajectory
    xd = [10*t; 10*t]; xdd = [10; 10];
    z = x - xd; dz = v - xdd;

    % DEAD-ZONE: Stop adaptation if error is negligible to prevent drift
    if norm(z) < 1e-3, z = [0;0]; end

    % Control input (Crucial: Use x_hat for control)
    u = m_hat * (0 - k_p*(x_hat - xd) - k_d*dz) + f_hat*norm(v) + d_hat;

    % Physical System
    dx = v;
    dv = (u - 0.5*v + 0.5*sin(t)) / m_true;

    % Adaptation Laws with Clamping
    dm_hat = -gamma(1) * (z' * [0;0]);
    if (m_hat < 0.1 && dm_hat < 0) || (m_hat > 10 && dm_hat > 0), dm_hat = 0; end % Clamp mass

    df_hat = -gamma(2) * (z' * v);
    dd_hat = -gamma(3) * sum(z);

    dstate = [dx; dv; dm_hat; df_hat; dd_hat];
end