By P.P. Kanjilal
This e-book is ready prediction and regulate of methods which might be expressed by means of discrete-time versions (i.e. the features differ indirectly with time). the purpose of the ebook is to supply a unified and accomplished insurance of the rules, views and strategies of adaptive prediction, that is utilized by scientists and researchers in a wide selection of disciplines
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Extra info for Adaptive prediction and predictive control
The three types of models studied are: (1) models based on Group Method of Data Handling (GMDH), (2) neural network models, and (3) models based on singular value decomposition with or without nonlinear transformation. All these models have hierarchical stages or layers, where each stage incorporates simple elements of nonlinearity. Since most processes contain a certain degree of nonlinearity, these models are applicable for nonlinear as well as nearly linear (and nearly periodic) processes. Typical processes that can be modelled are multi-input single output processes like the economic inflation process, quasiperiodic processes like the yearly averaged sunspot series etc.
Since coswt = cos(c<>t±2ir) and sinwt = sin(a>t±2n), cosa>ot « cos(wot+2im)f n = ±1, ±2, ... 1 A continuous-time having period length T. • periodic signal f(t) 38 Chapter 2 Process Models Similarly, sina>ot « sinwo(t+nT). 1b) Hence it should be possible to represent f(t) in terms of the sinusoidal functions. The Fourier series Consider the infinite series a0 + (a1coswot+b1sinwot) + (a2cos2wot + b2sin2wot) + ... + (anCosnWot+bnSinnc^t) + ... , na>o, produces a periodic signal with period T, where T « 2n/u>0.
1b) Hence it should be possible to represent f(t) in terms of the sinusoidal functions. The Fourier series Consider the infinite series a0 + (a1coswot+b1sinwot) + (a2cos2wot + b2sin2wot) + ... + (anCosnWot+bnSinnc^t) + ... , na>o, produces a periodic signal with period T, where T « 2n/u>0. Here the zero frequency represents the constant component or the mean value. The converse of this result also holds as follows. , na>o: 00 f(t) • ao + £(ancosnwot+bnsinnwot). 2) The magnitudes of the coefficients aj and bj define the pattern of the function f(t).