Read e-book online Adaptive approximation based control: unifying neural, fuzzy PDF

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By Jay A. Farrell, Marios M. Polycarpou

ISBN-10: 0471727881

ISBN-13: 9780471727880

A hugely available and unified method of the layout and research of clever keep an eye on platforms Adaptive Approximation established regulate is a device each keep watch over dressmaker must have in his or her keep an eye on toolbox. blending approximation conception, parameter estimation, and suggestions regulate, this e-book offers a unified method designed to allow readers to use adaptive approximation dependent keep an eye on to current structures, and, extra importantly, to achieve sufficient instinct and realizing to control and mix it with different regulate instruments for purposes that experience no longer been encountered ahead of. The authors supply readers with a thought-provoking framework for carefully contemplating such questions as: * What houses may still the functionality approximator have? * Are definite households of approximators improved to others? * Can the steadiness and the convergence of the approximator parameters be assured? * Can keep watch over structures be designed to be strong within the face of noise, disturbances, and unmodeled results? * Can this process deal with major alterations within the dynamics because of such disruptions as process failure? * What kinds of nonlinear dynamic platforms are amenable to this procedure? * What are the constraints of adaptive approximation established keep an eye on? Combining theoretical formula and layout strategies with wide use of simulation examples, this booklet is a stimulating textual content for researchers and graduate scholars and a invaluable source for working towards engineers.

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Additional info for Adaptive approximation based control: unifying neural, fuzzy and traditional adaptive approximation approaches

Example text

RN. For simplicity, we will assume that the dimension of La is m. RNIvTw = 0 . V s E La}. The set L& is also a linear subspace of % N . Let { d , } for i = 1 . , , N -m denote a basis for L&. , 0 = @A) such that @'B = Y . Every other solution v tov'@ = Y can be expressed as czl w =8+ N-m a,d, 2=1 for some atE R1. FUNCTION APPROXIMATION 33 Since 6' is orthogonal to C,"=;'" aidi by construction, llwll = ll6'll+ I/ C,";" aidill which is always greater than Il6'il. 7 of [29]. 3 Summary This section has discussed the offline problem of fitting a function to a fixed batch of data.

In discrete-time the corresponding adaptive gain O ( t ) (sometimes referred to as step size) needs to be sufficiently small in order to guarantee convergence; however, in continuous-time r(t ) simply needs to be positive definite (due to the infinitesimal change of the derivative 6 ( t ) ) . r)y(r)dTand P - l ( t ) = (b(7)4(T)'d.. 27) Note by the defini- = #(t)y(t) Since P ( t ) P - l ( t ) = I , differentiation and rearrangement shows that in general the time derivative of a matrix and its inverse must satisfy P = -P$ [P-'(t)]P; therefore, in least squares estimation P = -P(t)$(t)q(t)TP(t).

In' this text, we will use adaptation to refer to temporal changes. For example, adaptive control is applicable when the estimated parameters are slowly varying functions of time. We will use learning to refer to methods that retain information as a function of measured variables. Herein, learning is implemented via function approximation. Therefore, learning has a spatial connotation whereas adaptation refers to temporal effects. The process of learning requires adaptation, but the retention of information as a function of other variables in learning implies that learning is a higher level process than is adaptation.

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Adaptive approximation based control: unifying neural, fuzzy and traditional adaptive approximation approaches by Jay A. Farrell, Marios M. Polycarpou


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