Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters

We consider the problem of asymptotic reconstruction of the state and parameter values for dynamical systems that cannot be transformed into the canonical adaptive observer form. A solution to this problem is proposed for a class of systems for which the unknowns are allowed to be nonlinearly parameterized functions of state and time. Going beyond asymptotic Lyapunov stability, we provide for this class of systems a reconstruction technique, based on the concepts of weakly attracting sets, non-uniform convergence, and Poisson stability.