This article is aimed to study the modeling problems of combinational signals or periodic signals. To overcome the computation complexity of modeling the signals with plenty of characteristic parameters, a parameter separation scheme is developed based on the different characteristic of the signals to be modeled. For the purpose of achieving high-accuracy performance and reducing complexity, two multi-innovation gradient-based iterative (MIGI) subalgorithms are presented by means of gradient search. In terms of the phenomenon that the coupling parameters lead to the inability of algorithms, a separable synchronous (SS) interactive estimation method is proposed to eliminate the coupling parameters and perform the signal modeling algorithm in accordance with the hierarchical principle. By means of simulation experiments, the proposed SS iterative signal modeling algorithm based on the moving batch data is used for estimating a power signal with three sine waves and a periodic square wave signal. The results demonstrate the effectiveness of the proposed method for modeling the combinational signals with multiple frequencies and other periodic signals. Since the proposed method combines real-time data sampling and iterative estimation, it can be used for on-line identification.

This letter presents a state estimation algorithm for linear discrete-time systems with state-delay. In order to overcome the difficulty that the traditional Kalman filter cannot estimate the states of the systems with state-delay, a state estimation strategy is developed by combining the auxiliary model with the delta operator. Then, by constructing and minimizing the covariance matrix of the state reconstruction errors, a delta operator state estimation algorithm is derived and it can fulfill effective state estimation for the linear discrete-time system with state-delay. Moreover, the convergence proof is provided by means of stochastic stability theory. Finally, the experimental results demonstrate that the developed state estimation method is effective.

A nonlinear general predictive controller (NLGPC) is described which is based on the use of a Hammerstein model within a recursive control algorithm. A key contribution of the paper is the use of a novel, one-step simple root solving procedure for the Hammerstein model, this being a fundamental part of the overall tuning algorithm. A comparison is made between NLGPC and nonlinear deadbeat control (NLDBC) using the same one-step nonlinear components, in order to investigate NLGPC advantages and disadvantages.