State and Parameter Estimation for Systems in Non-canonical Adaptive Observer Form

We consider the problem of state and parameter reconstruction for uncertain dynamical systems that cannot be transformed into the canonical adaptive observer form. The uncertainties are allowed to be both linearly and nonlinearly parameterized functions of state and time. We provide a technique that allows successful reconstruction of uncertain state and parameters for a broad range of dynamical systems that belong to this class. In contrast to conventional approaches our technique is based on the concepts of weakly attracting sets, and non-uniform convergence and Poisson stability rather than the notion of Lyapunov stability. Relevance of the proposed approach to the domains of control and system identification is illustrated with examples.