Stochastic contraction based online estimation of second order wiener system

Wiener system is a block oriented model, having a linear time-invariant dynamic system followed by a memory-less nonlinearity. To design a stochastic estimator for online estimation of Wiener system of second order, this paper utilizes differential mean value theorem and the results of stochastic contraction theory. The asymptotic convergence of proposed estimator is derived by using contraction theory related to semi-contracting systems. The boundedness and convergence of the parameter and state estimates have been shown analytically. The introduced method has potentials to estimate accurately states and parameters of Wiener model simultaneously from the noisy output of the system and unknown structure of nonlinearity. Numerical simulation of the stochastic estimator is presented to justify the claim by considering the two examples of the real world system with an additive measurement noise.