On identification of parallel block-cascade nonlinear models

In this study, a Wiener-type neural network (WNN) is derived for identification and control of single-input and single-output (SISO) nonlinear systems. The nonlinear system is identified by the WNN, which consists of a linear dynamic block in cascade with a nonlinear static gain. The Lipschitz criteria for model order determination and back propagation for the adjustment of weights in the network are presented. Using the parameters of the Wiener model, the analytical expressions used in the controller, generalized predictive control (GPC) is modified every time step, to handle the nonlinear dynamics of the controlled variable. Finally, the proposed WNN-based GPC algorithm is tested in simulation on several nonlinear plants with different degrees of nonlinearity. Simulation results show that WNN identification approach has better accuracy, in comparison to other neural network identifiers. The WNN-based GPC has better control performance, in comparison to standard GPC.

Hammerstein–Wiener models constitute a significant class of block-structured dynamic models, as they approximate process nonlinearities on the basis of input–output data without requiring identification of a full nonlinear process model. Optimization problems with Hammerstein–Wiener models embedded are nonconvex, and thus local optimization methods may obtain suboptimal solutions. In this work, we develop a deterministic global optimization strategy that exploits the specific structure of Hammerstein–Wiener models to extend existing theory on global optimization of systems with linear dynamics. At first, we discuss alternative formulations of the dynamic optimization problem with Hammerstein–Wiener models embedded, demonstrating that careful selection of the optimization variables of the problem can offer significant numerical advantages to the solution approach. Then, we develop convex relaxations for the proposed optimization problem and discuss implementation aspects to obtain the global solution focusing on a control parametrization technique. Finally, we apply our optimization strategy to case studies comprising both offline and online dynamic optimization problems. The results confirm an improved computational performance of the proposed solution approach over alternative options not exploiting the linear dynamics for all considered examples. They also underline the tractability of deterministic global dynamic optimization when using few control intervals in online applications like nonlinear model predictive control.

Identification of continuous-time nonlinear systems: The nonlinear difference equation with moving average noise (NDEMA) framework

The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W) model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.

Identification and adaptive neural network control of a DC motor system with dead-zone characteristics

Wiener systems consist of a linear dynamic block in cascade with static nonlinearity. One of the challenging issues in the identification of a process noise disturbed Wiener system is that the influence of noise is difficult to eliminate. For Wiener systems with process noise, traditional algorithms will result in biased estimates. To solve this problem, a novel recursive Bayesian algorithm based on variable knot spline approximation is proposed in this paper. First, a spline function is taken to approximate the inverse function of the nonlinear part, which can achieve excellent extrapolation and eliminate oscillatory behaviors. A knot selection method is then presented to achieve accurate estimates. Furthermore, a knot variation strategy to improve the accuracy of the spline approximation is described. Finally, the proposed algorithm is validated through a numerical simulation.

Most contemporary battery models are series-models based on electrochemical principles. Describing the charge/discharge efficiency of a battery is a complex issue and of major importance in the design of control systems in future cars (combined 42 V and 14 V systems). Not only does battery efficiency strongly depend on current levels, it also varies greatly with frequency. In this paper a parallel equivalent model is introduced to get a good grip on this matter. A general description of efficiency as a function of frequency, current level and initial voltage is presented. The parallel model regards the battery as a system with multiple parallel buffers and yields a different perspective on the energy distribution and distribution of losses in a battery. Furthermore, dynamic behavior is easily explained. Depending on the spectral load and required accuracy, it is possible to simplify the parallel model. Identification techniques for both linear and nonlinear model identification are presented. It appears that the nonlinear parallel model is not capable of modeling the battery for the full frequency range. However, the identification techniques can be modified to apply to other model structures as well.

International audience

Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.

Limit distributions for the maxima of stationary Gaussian processes

On the Identification of Non Linear Models of Unmanned Underwater Vehicles

Higher-order cyclostationarity-based methods for identifying volterra systems by input–output noisy measurements

Presently, the problem of parameter estimation is addressed for a more general nonlinear model. In this respect, the proposed nonlinear system is composed of the parallel connection of linear and nonlinear blocks. The interconnected structure of linear and nonlinear blocks systems leads to a highly nonlinear problem involving several unknown parameters and inaccessible internal signals. In this parameter estimation method, the linear and nonlinear block parameters are estimated in one stage by using simple a sine signal or multi-cosine wave.

Correlation analysis-based parameter learning of Hammerstein nonlinear systems with output noise

Block-oriented nonlinear systems have attracted a considerable attention for their flexible structure and practicability. This study proposes a novel multi-innovation stochastic gradient (MISG) algorithm to address the identification problem in input nonlinear systems. This involves applying the inexact line search strategy to determine an appropriate convergence factor at each recursive step. The proposed algorithm tracks the nonlinear system dynamics faster than the conventional MISG algorithm. It is therefore suitable for online identification and can be applied to nonlinear time-varying systems. The concept of auxiliary model identification is also adopted for dealing with unmeasurable variables. The effectiveness of the proposed algorithm is verified through simulated examples.