By Iven Mareels
Loosely talking, adaptive platforms are designed to accommodate, to evolve to, chang ing environmental stipulations when protecting functionality pursuits. through the years, the idea of adaptive platforms advanced from rather basic and intuitive techniques to a posh multifaceted idea facing stochastic, nonlinear and endless dimensional structures. This booklet presents a primary advent to the idea of adaptive platforms. The publication grew out of a graduate path that the authors taught a number of instances in Australia, Belgium, and The Netherlands for college students with an engineering and/or mathemat ics heritage. once we taught the direction for the 1st time, we felt that there has been a necessity for a textbook that will introduce the reader to the most elements of edition with emphasis on readability of presentation and precision instead of on comprehensiveness. the current publication attempts to serve this desire. we think that the reader could have taken a easy path in linear algebra and mul tivariable calculus. except the elemental thoughts borrowed from those parts of arithmetic, the publication is meant to be self contained.
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Additional resources for Adaptive Systems: An Introduction
Notice that e == 0 does not imply that the plant parameter estimates equal the plant parameters. , the control objective is achieved whether or not the parameters are correctly estimated. This phenomenon is analyzed extensively in Chapters 4 and 5. Here we see again the dual nature of the adaptation error. It is indicative of the control objective, and it is the driving force in the adaptation mechanism. ", is nontrivial. It is one of the key (theoretical) difficulties in indirect adaptive control to be able to deal with these singular points.
65) The corresponding polynomials are: A(~, Cl ) = ~ - 2 - ~-I + 2~-2 B(~, ~-I) = 1 + ~-I - 2~-2. 66) Notice that deg A(~, ~-I) = 3 and deg B(~, ~-I) = 2. r(~,~-I). 69) 48 Chapter 2. 57). 2 we conclude that the system is not controllable. 65) is defined by the matrix triple: A~[! ~ ~2]b~[-2]c~[O 0 ']. 5. 65) itself is not controllable. 12 A word about the notation In this chapter we have tried to be rather precise about the underlying algebraic structure of the difference equations describing the behaviors.
The importance of universal controllers in the adaptive literature is that they focus attention on the minimal information that is required about a linear plant such that a single stabilizing controller for a whole class of systems can be constructed. , any one linear (unknown) system stabilizable by a controller of given complexity, see ~~~6. 5 Echo cancelling As a final example we consider a signal processing application. 6: Echo cancelling problem. 6. 4. Illustrating the concepts link to the substation and a four-wire connection between substations.