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System identification is a method of identifying or measuring the mathematical model of a system from measurements of the system inputs and outputs. The applications of system identification include any system where the inputs and outputs can be measured and include industrial processes, control systems, economic data, biology and the life sciences, medicine, social systems and many more.
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1] [2] Nonlinear problems are of interest to engineers, biologists, [3] [4] [5] physicists, [6] [7] mathematicians, and many other scientists since most systems are inherently nonlinear in nature. [8]
The function F is some nonlinear function, such as a polynomial. F can be a neural network, a wavelet network, a sigmoid network and so on. To test for non-linearity in a time series, the BDS test (Brock-Dechert-Scheinkman test) developed for econometrics can be used.
Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of dynamical systems with inputs, and how to modify the output by changes in the input using feedback ...
It is based on quasi-linearization, which is the approximation of the non-linear system under investigation by a linear time-invariant (LTI) transfer function that depends on the amplitude of the input waveform. By definition, a transfer function of a true LTI system cannot depend on the amplitude of the input function because an LTI system is ...
where () is the state, (), …, are the inputs. The approach involves transforming a nonlinear control system into an equivalent linear control system through a change of variables and a suitable control input.
With a suitable choice of how the states of this subset of oscillators depends on the input, the observables of the rest of the oscillators can become nonlinear functions of the input suitable for reservoir computing; indeed, thanks to the properties of these functions, even universal reservoir computing becomes possible by combining the ...
One example of nonlinear filters is the (generalized directional distance rational hybrid filter (GDDRHF) [1]) for multidimensional signal processing.This filter is a two-stage type hybrid filter: 1) the stage norm criteria and angular distance criteria to produce three output vectors with respect to the shape models; 2) the stage performs vector rational operation on the above three output ...