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We consider the local order estimation of nonlinear autoregressive systems with exogenous inputs (NARX), which may have different local dimensions at different points. By minimizing the kernel-based local information criterion introduced in this paper, the strongly consistent estimates for the local orders of the NARX system at points of interest are obtained. The modification of the criterion and a simple procedure of searching the minimum of the criterion, are also discussed. The theoretical results derived here are tested by simulation examples. [ABSTRACT FROM AUTHOR]

The problem of distributed identification of linear stochastic system with unknown coefficient θ ∗ over time-varying networks is considered. For estimating θ ∗ , each agent in the network can only access the input and the binary-valued output of the local system. Compared with the existing works on distributed optimization and estimation, the binary-valued local output observation considered in the paper makes the problem challenging. By assuming that the agent in the network can communicate with its adjacent neighbors, a stochastic approximation-based distributed identification algorithm is proposed, and the consensus and convergence of the estimates are established. Finally, a numerical example is given showing that the simulation results are consistent with the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper considers the recursive identification of errors-in-variables Wiener–Hammerstein system, which is composed of a static nonlinearity sandwiched by two linear dynamic subsystems. Both the system input and output are observed with additive noises being ARMA processes with unknown coefficients. By the stochastic approximation algorithms incorporated with the deconvolution kernel functions, the coefficients of the linear subsystems and the values of the nonlinear function are recursively estimated. All the estimates are proved to converge to the true values with probability one. A simulation example is given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the recursive identification of errors-in-variables (EIV) Wiener systems composed of a linear dynamic system followed by a static nonlinearity. Both the system input and output are observed with additive noises being ARMA processes with unknown coefficients. By a stochastic approximation incorporated with the deconvolution kernel functions, the recursive algorithms are proposed for estimating the coefficients of the linear subsystem and for the values of the nonlinear function. All the estimates are proved to converge to the true values with probability one. A simulation example is given to verify the theoretical analysis. [Copyright &y& Elsevier]

Abstract: The iterative learning control (ILC) is constructed for the discrete-time large scale systems. Each subsystem is affine nonlinear and its observation equation is with noise. Subsystems are nonlinearly connected via the large state vector of the whole system. The possibility of data missing, and communication delay is taken into account. It is proved that ILC given in the paper with probability one converges to the optimal one minimizing the tracking error. The simulation results are consistent with theoretical analysis. [Copyright &y& Elsevier]

Abstract: A weighted least squares (WLS) based adaptive tracker is designed for a class of Hammerstein systems. It is proved that the tracking error is asymptotically minimized. Incorporating with the diminishing excitation technique, the minimality of the tracking error and strong consistency of the estimates for parameters of the system are simultaneously achieved. Numerical examples are given and the simulation results are consistent with the theoretical analysis. [Copyright &y& Elsevier]

Abstract: The recursive algorithm is given for estimating matrix coefficients of the multivariate errors-in-variables (EIV) systems. It is shown that under mild conditions the estimate given by the algorithm converges to a limit belonging to the solution set of the Yule–Walker equation satisfied by the true coefficients of the system. The sufficient conditions guaranteeing the uniqueness of the solution to the Yule–Walker equation are given. In this case the estimate provided by the recursive algorithm is strongly consistent. [Copyright &y& Elsevier]

Abstract: The paper concerns identification of the Wiener system consisting of a linear subsystem followed by a static nonlinearity with no invertibility and structure assumption. Recursive estimates are given for coefficients of the linear subsystem and for the value at any fixed . The main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values. This probably is the first strong consistency result for this kind of Wiener systems. A numerical example is given, which justifies the theoretical analysis. [Copyright &y& Elsevier]

Abstract: For the single-input-single-output (SISO) errors-in-variables system it is assumed that the system input is an ARMA process and that the driven noise of the system input and the observation noise are jointly Gaussian. The two-dimensional observation made on system input and output is represented as a two-dimensional (2D) ARMA system of minimum phase driven by a sequence of 2D i.i.d. Gaussian random vectors (innovation representation). It is shown that the resulting ARMA system is identifiable, i.e., its coefficients are uniquely defined under reasonable conditions. Recursive algorithms are proposed for estimating coefficients of the ARMA representation including those contained in the original SISO system. The estimates are proved to be convergent to the true values with probability one and the convergence rate is derived as well. The theoretical results are justified by numerical simulation. [Copyright &y& Elsevier]

This work is devoted to the study of a class of recursive algorithms for blind channel identification. Using weak convergence methods, the convergence of the algorithm is obtained and the rate of convergence is ascertained. The technique discussed can also be used in the analysis of rates of convergence for decreasing step-size algorithms. [Copyright &y& Elsevier]