On the identification of nonlinear dynamical systems

Two classes of nonlinear dynamical systems driven by independent noise on which linear discrete-time scalar measurements are performed also in the presence of additive independent noise are considered. The evolution operators for these classes are described, respectively, by algebraic and trigonometric polynomials in the state variables. Such polynomials frequently appear in equations describing physical systems. On the assumption that certain moments of the noise sources are known, a framework is developed which leads to convergent stochastic approximation algorithms for the identification of system parameters.