Lyapunov stability and adaptive regulation of a class of nonlinear nonautonomous second-order differential equations

This paper presents an adaptive regulation scheme for a class of ordinary nonlinear nonautonomous second-order differential equations which includes as particular cases a number of particular differential equations which occur in applications. The unforced reference model is proposed to be a stable differential parametrization within the general class dealt with. Therefore, some sufficient Lyapunov´s stability conditions for such a class are previously investigated which can be used, in particular, to set an appropriate reference model. The resulting closed-loop adaptive scheme is proved to be stable and it involves a parameter estimation scheme of least-squares type which is proved to possess all suitable properties