Adaptive control of nonlinear dynamical systems using a model reference approach (Q1415642)

The paper contains a review of linear model reference adaptive control designed by hyperstability and Lyapunov techniques. The system reads \[ \dot{x}_{e}=A_mx_e + B\Phi^Tw-d(t),\quad \Phi=k_e-k, \] \[ k(t)=C_1y_ew+C_2\int_{t_0}^{t}y_e(\tau)w(\tau)\,d\tau \] and \(y_e=Cx_e\); the coefficients \(C_1\) and \(C_2\) are to be chosen in order to obtain a stable system. The same kind of problem is reviewed for a nonlinear system \[ \dot{x}=f_1(x,t) + g_1(u,t),\qquad \dot{x}_m =F_2(x,t) + g_2(r(t),t), \] where the second equation means the reference model description. This case is solved by feedback linearization and by applying afterwards the previous approach. An application of chaotic motion control is given.