Download e-book for kindle: Dynamic Feature Space Modelling, Filtering and Self-Tuning by Pieter W. Otter

By Pieter W. Otter

ISBN-10: 3540156542

ISBN-13: 9783540156543

ISBN-10: 364245593X

ISBN-13: 9783642455933

The literature on platforms turns out to were starting to be nearly expo­ nentially over the past decade and one could query even if there's desire for an additional ebook. within the author's view, lots of the literature on 'systems' is both technical in mathematical feel or technical ifF engineering experience (with technical phrases resembling noise, filtering and so on. ) and never simply obtainable to researchers is different fields, specifically to not economists, econometricians and quantitative researchers in so­ cial sciences. this can be unlucky, simply because achievements within the particularly 'young' technology of method thought and method engineering are of impor­ tance for modelling, estimation and legislation (control) difficulties in different branches of technological know-how. nation house mode~iing; the idea that of ob­ servability and controllability; the mathematical formulations of sta­ bility; the so-called canonical varieties; prediction blunders e~timation; optimum regulate and Kalman filtering are a few examples of result of approach idea and procedure engineering which proved to achieve success in perform. a quick precis of procedure theoretical ideas is given in bankruptcy II the place an try out has been made to translate the thoughts in­ to the extra 'familiar' language utilized in econometrics and social sciences through examples. by way of interrelating ideas and effects from approach concept with these from econometrics and social sciences, the writer has tried to slim the distance among the extra technical sciences comparable to engi­ neering and social sciences and econometrics, and to give a contribution to both side.

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Additional resources for Dynamic Feature Space Modelling, Filtering and Self-Tuning Control of Stochastic Systems: A Systems Approach with Economic and Social Applications

Sample text

Realization Theory. It is not the intention to study realization theory in depth, because the theory for stochastic dynamical systems is still in motion and somewhat random, but merely to give an impression of this important concept in system theory. The problem in realization theory is to obtain a state 21 space model from input-output data, or in other words, given an input-output description, find a state space model with the same behaviour as the input-output model. L J k,j E Z, y(k) E IR P and u(k) E IRm.

It can be immediately noticed that this equation is always Lyapunov stable for every trajectory {C(i)}. Note that {C(i)} is not a equilibrium point. External Stability; BIBO Stability. A type of stability, which may be important for economic systems, is the so-called external stability or BIBO stability (~ounded Input ~ounded Qutput). Only linear time-invariant difference equations will be considered. Consider the linear discrete system Ld: y(k+l) = Ay(k) + Bu(k), k = ko ,k0 +1, ... ) such that 6 and for a11 k E [-oo,co] there is a constant ~ e(k ,y(k ) ,6) > 0 such that Ily(k)1I < e for a11 k > k • o 0 = = In other words if every bounded input produces a bounded output we have 0 33 external stability.

In order to determine the dimensions of the output and input factor spaces, factorize S as CIS C = y, A Y A AY where A~ = diag(~l""'~ ) and where P the estimated eigenvalues A1 > A2 > •.. 5) that under the assumption that plim(S) = L n PAL A. L -1 1=r+1 -+ 2 X (p-r) (p-r) if the first r population eigenvalues A1 > ••• > Ar are distinct (and 40 stay distinct as n £ ~ =) and the last (p-r) population eigenvalues are zero. =r+ 1~' can be used as a test statistic. Another procedure -l. is to select the dimension according to the number of eigenvalues greater than or equal to one.

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Dynamic Feature Space Modelling, Filtering and Self-Tuning Control of Stochastic Systems: A Systems Approach with Economic and Social Applications by Pieter W. Otter

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