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

By Jay A. Farrell, Marios M. Polycarpou

ISBN-10: 0471727881

ISBN-13: 9780471727880

A hugely obtainable and unified method of the layout and research of clever regulate platforms Adaptive Approximation established keep watch over is a device each keep watch over fashion designer must have in his or her keep watch over toolbox. blending approximation concept, parameter estimation, and suggestions keep an eye on, this e-book offers a unified method designed to permit readers to use adaptive approximation established keep watch over to latest platforms, and, extra importantly, to realize adequate instinct and knowing to control and mix it with different keep an eye on instruments for purposes that experience now not been encountered sooner than. The authors supply readers with a thought-provoking framework for conscientiously contemplating such questions as: * What houses should still the functionality approximator have? * Are convinced households of approximators better 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 technique deal with major alterations within the dynamics because of such disruptions as procedure failure? * What sorts of nonlinear dynamic structures are amenable to this strategy? * What are the restrictions of adaptive approximation established regulate? Combining theoretical formula and layout recommendations with broad use of simulation examples, this e-book is a stimulating textual content for researchers and graduate scholars and a necessary source for training engineers.

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

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Due to the technical nature of and the broad background that would be required for the proofs, in most cases the proofs are not presented. Literature sources for the proofs are cited. 1 Parameter (Non)Linearity An initial decision that the designer must make is the form of the function approximator. 3 1) f^(z: 8,). RN, and the dimension of u depends on the approximator of interest. The approximator has a linear dependence on 8, but a nonlinear dependence on u. 6 The (N-I)-th order polynomial approximation f^(z: 8, N)= CE-' 8,zi for z E $3' has the form of eqn.

Preferred methods of solution are by QR, UD, or singular value decompositions [991. For a unique solution to exist, the number of free parameters (Lee,the dimension of 0) must be exactly equal to the number m of sample points 2 % Therefore, . the dimension of the approximator parameter vector must increase linearly with the number of training points. Under these conditions, the number of computations involved in solving eqn. 9 in [99]). In addition to this large computational burden, the condition number of often becomes small as m gets large.

21) with the dynamic system of eqn. 1). Dotted lines represent initial conditions. Dashed lines represent the actual functions. Solid lines represent the approximation after 3000 s of operation. be stated about convergence of the approximation outside this portion of D. If the same plots are analyzed after the first 100 s of training, the approximation error is very small near y = 20 and y = 60, but not significantly improved elsewhere. , best available apriori model) and the actual dynamics. The four methods are closely related and all depend on cancelling the dynamics of the assumed model.

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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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