This paper addresses the problem of state estimation for a class of discrete-time stochastic complex networks with a constrained and randomly varying coupling and uncertain measurements. The randomly varying coupling is governed by a Markov chain, and the capacity constraint is handled by introducing a logarithmic quantizer. The uncertainty of measurements is modeled by a multiplicative noise. An asynchronous estimator is designed to overcome the difficulty that each node cannot access to the coupling information, and an augmented estimation error system is obtained using the Kronecker product. Sufficient conditions are established, which guarantee that the estimation error system is stochastically stable and achieves the strict (Q, S, R)-γ-dissipativity. Then, the estimator gains are derived using the linear matrix inequality method. Finally, a numerical example is provided to illustrate the effectiveness of the proposed new design techniques.

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The radial basis function network-based autoregressive with exogenous inputs (RBF-ARX) models have much more linear parameters than nonlinear parameters. Taking advantage of this special structure, a variable projection algorithm is proposed to estimate the model parameters more efficiently by eliminating the linear parameters through the orthogonal projection. The proposed method not only substantially reduces the dimension of parameter space of RBF-ARX model but also results in a better-conditioned problem. In this paper, both the full Jacobian matrix of Golub and Pereyra and the Kaufman's simplification are used to test the performance of the algorithm. An example of chaotic time series modeling is presented for the numerical comparison. It clearly demonstrates that the proposed approach is computationally more efficient than the previous structured nonlinear parameter optimization method and the conventional Levenberg-Marquardt algorithm without the parameters separated. Finally, the proposed method is also applied to a simulated nonlinear single-input single-output process, a time-varying nonlinear process and a real multiinput multioutput nonlinear industrial process to illustrate its usefulness.