Lyapunov stability and adaptive regulation of a class of nonlinear nonautonomous second-order differential equations (Q1851034)

For a class of ordinary nonlinear, nonautonomous second-order differential equations, an adaptive regulation scheme is introduced. The class of equations under consideration contains a number of particular cases with practical applications. Some sufficient Lyapunov stability conditions for the investigated class are presented, which can be used in particular to set an appropriate reference model. The resulting closed-loop adaptive scheme is proved. This scheme involves a parameter estimation scheme of least-square type with all suitable properties in term of estimates, boundedness and asymptotic convergence of estimates to a finite limit as well as time-integrability of the squared adaptation error.