System identification nonlinear

Wu, X., and Cinar, A. (1996). An adaptive robust M-estimator for nonparametric nonlinear system identification. J. Proc. Control 6, 233-239. 

System Identification Techniques. In system identification, the (nonlinear) resi pnses of the outputs of a system to the input signals are approximated by a linear model. The parameters in this linear model are determined by minimizing a criterion function that is based on some difference between the input-output data and the responses predictedv by the model. Several model structures can be chosen and depending on this structure, different criteria can be used (l ,IX) System identification is mainly used as a technique to determine models from measured input-output data of processes, but can also be used to determine compact models for complex physical models The input-output data is then obtained from simulations of the physical model. 

To determine the state space model with system Identification, responses of the nonlinear model to positive and negative steps on the Inputs as depicted in Figure 4 were used. Amplitudes were 20 kW for P,, . 4 1/s for and. 035 1/s for Q. The sample interval for the discrete-time model was chosen to be 18 minutes. The software described In ( 2 ) was used for the estimation of the ARX model, the singular value analysis and the estimation of the approximate... 

Response of vr to a step of +20 kW on P, obtained with the nonlinear model, system identification and method of lines... 

J Sjoberg, Q Zhang, L Ljung, A Benveniste, B Delyon, P Glorennec, H Hjalmarsson, and A Juditsky. Nonlinear black-box modeling in system identification A unified overview. Automatica, 31(12) 1691-1721, 1995. 

However, this method is not applicable to all situations. Figure 3.8 d shows that detecting the input/output characteristics at several points is not sufficient to calibrate sensitivity and offset errors if there are nonlinear effects involved. Here, a complete system identification might be necessary, depending on the order of the effects. Calibration of this kind of error is possible in theory, but not practicable, considering the expense in time and money. 

Nelles, O. Nonlinear System Identification From Classical Approaches to Neural Networks and Fuzzy Models-, Springer Berlin, 2001. 

The multiple convolutions of the Volterra model involve kernel functions fc,(mi,..., m,) which constitute the descriptors of the system nonlinear dynamics. Consequently, the system identification task is to obtain estimates of these kernels from input-output data. These kernel functions are symmetric with respect to their arguments. 

Shi, J. and Sun, H.H. 1990. Nonlinear system identification for cascade block model an application to electrode polarization impedance. IEEE Trans. Biomed. Eng. 37 574. 

Nelles, O. (f.OOT). Nonlinear System Identification. Springer, Berlin. 

The free parameters of the model are fitted to experimental data (the 0-I-D-P-fluorescence rise of dark-adapted tobacco leaves) by means of the multiple shooting algorithm PARFIT as developed by Bock [2] for parameter identification in systems of nonlinear differential equations. We use a multiple experiment structure for measurements at different light intensities. The initial trajectory and the results are shown in Figs. 2 and 3. 

Cifuentes, A.O. 6c Iwan, W.D. 1989. Nonlinear system identification based on modeling of restoring force behavioi Soil Dynamics and Earthquake Engineering, 8, 2-8. 

Jayakumar, P. Beck, J.L. 1988. System identification using nonlinear structural models. H.G. Natke, J.T.P. Yao eds. Structural safety evaluation based on system identification approaches, Vieweg and Sons. 

Having successfully implemented conventional MRAC techniques, the next logical step was to try to incorporate the MRAC techniques into a neural network-based adaptive control system. The ability of multilayered neural networks to approximate linear as well as nonlinear functions is well documented and has foimd extensive application in the area of system identification and adaptive control. The noise-rejection properties of neural networks makes them particularly useful in smart structure applications. Adaptive control schemes require only limited a priori knowledge about the system to be controlled. The methodology also involves identification of the plant model, followed by adaptation of the controller parameters based on a continuously updated plant model. These properties of adaptive control methods makes neural networks ideally suited for both identification and control aspects [7-11]. 

Although the focus of this chapter will be on linear model identification, a cursory investigation of nonlinear approaches will be presented in order to provide a complete overview of system identification. 

Although in many circumstances linear system identification can provide a sufficiently good model of the system for the intended purpose, it is occasionally necessary to consider nonlinear system identification. 

Nonlinear system identification attempts to fit a nonlinear model to the given data. However, since there is a large number of potential nonlinear models that could be fit, nonlinear identification simplifies the available functions. Instead of choosing any arbitrary function, a basis function, k(x), is selected. The basis function can also be called the generating function or the mother function. Then, the goal becomes to fit the following model to the data... 

Instead of fitting a fully nonlinear model, another approach to nonlinear system identification is to partition the nonUnearities from the linear component A common application of this approach is the Wiener-Hammerstein model. A Wiener-Hammerstein model is a generalisation of the Hammerstein model, where non-linearities are assumed cmly to be in the input and the Wiener model, where nonlinearities are assumed only to be in the output, which allows nonlinearities to be present in both the input and output The process model is assumed to be linear. Thus, the general form of the model can be written as... 

The objective of this experiment is to determine an appropriate model for the water level in Tank 1 assuming that the splits are fixed, but the flow rate from the two pumps can vary. Design an appropriate experiment and analyse the results. Perform both linear and nonlinear system identification and compare the resulting models. Which one would be preferred ... 

This section presents three examples that show how to implement various forms of regression analysis in MATLAB. The topics considered are linear regression, nonlinear regression, and system identification. AH examples are based on real data obtained from experiments. Appropriate MATLAB code, as well as the final results, is provided so that the reader can modify these examples to fit their particular needs. 

The identification of the models involves the repeated solving of large systems of nonlinear differential or partial derivatives equations, for the necessity of sensitivity analysis and optimization processes. These goals could be betto reached by using more efficient algorithms (progresses in this way are expected) or supercomputers (some works are in progress in this Une). 

Researchers are beginning to develop nonlinear system-identification and feedback control algorithms that offer stable, controlled flight some distance beyond the nominal steady flight envelope (Tang et al., 2009). Such systems could make it feasible for an autonomous system to discover this more expansive envelope (Choi et al., 2010) and continue stable operation despite anomalies... 

The problem posed in Eq. (51) involves the solution of a system of nonlinear equations. The identification of all multiple global solutions requires the use of a deterministic global optimization method, as outlined in Section n.B. The application of this method to protein systems will be described fully in Section IV.B. 

The examples presented below employ linear system identification techniques in which superposition and scaling are assumed. These enable conversion between the frequency and time-domain models. Nonlinearities in conducting polymers can arise from significant potential-dependent ionic and electronic conductivities, for example. In cases where nonlinearities are significant, it may nevertheless be appropriate to apply linear techniques over certain ranges of voltage, strain, or charge state where response is effectively linear. 

Since the complexity of the physiologic system identification problem rivals its importance, we begin by demarcating those areas where effective methods and tools currently exist. The selection among candidate models is made on the basis of the following key functional characteristics (1) static or dynamic (2) linear or nonlinear (3) stationary or nonstationary (4) deterministic or stochastic (5) single or multiple inputs and/or outputs (6) lumped or distributed. These classification criteria do not constitute an exhaustive list but cover most cases of current interest. Furthermore, it is critical to remember that contaminating noise (be it systemic or measurement-related) is always present in an actual study, and... 

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