Adaptive control tutorial by Petros Ioannou, Barýp Fidan

By Petros Ioannou, Barýp Fidan

Designed to satisfy the wishes of a large viewers with out sacrificing mathematical intensity and rigor, Adaptive regulate instructional offers the layout, research, and alertness of a wide selection of algorithms that may be used to control dynamical structures with unknown parameters. Its tutorial-style presentation of the elemental options and algorithms in adaptive keep an eye on make it compatible as a textbook.

Adaptive keep an eye on educational is designed to serve the desires of 3 distinctive teams of readers: engineers and scholars attracted to studying tips to layout, simulate, and enforce parameter estimators and adaptive keep watch over schemes with no need to totally comprehend the analytical and technical proofs; graduate scholars who, as well as reaching the aforementioned targets, additionally are looking to comprehend the research of straightforward schemes and get an idea of the stairs keen on extra complicated proofs; and complicated scholars and researchers who are looking to research and comprehend the main points of lengthy and technical proofs with a watch towards pursuing study in adaptive regulate or similar themes.

The authors in attaining those a number of goals by means of enriching the publication with examples demonstrating the layout tactics and simple research steps and via detailing their proofs in either an appendix and electronically on hand supplementary fabric; on-line examples also are on hand. an answer handbook for teachers could be bought by means of contacting SIAM or the authors.

This e-book may be important to masters- and Ph.D.-level scholars in addition to electric, mechanical, and aerospace engineers and utilized mathematicians.

Preface; Acknowledgements; record of Acronyms; bankruptcy 1: advent; bankruptcy 2: Parametric versions; bankruptcy three: Parameter id: non-stop Time; bankruptcy four: Parameter id: Discrete Time; bankruptcy five: Continuous-Time version Reference Adaptive keep watch over; bankruptcy 6: Continuous-Time Adaptive Pole Placement keep watch over; bankruptcy 7: Adaptive regulate for Discrete-Time platforms;

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If ^-, however, is PE, then 0 = 9*. Convergence of the estimated parameters to constant values is a unique property of the pure LS algorithm. One of the drawbacks of the pure LS algorithm is that the covariance matrix P may become arbitrarily small and slow down adaptation in some directions. This is due to the fact that which implies that P ' may grow without bound, which in turn implies that P may reduce towards zero. This is the so-called covariance wind-up problem. Another drawback of the pure LS algorithm is that parameter convergence cannot be guaranteed to be exponential.

Since ^-, — € £00, J(0) is a convex function of 0 over 7Z" at each time t. 38) is therefore obtained by solving for 9(t), which yields the nonrecursive LS algorithm where is the so-called covariance matrix. Because QQ = QQ > 0 and 0r is positive semidefinite, P(t) exists at each time t. t. 45) depend on the value of the forgetting factor ft, as discussed in the following sections. 2. When ft > 0, stability cannot be established unless ^- is PE. 3. 45) in the case where ^- is PE. 7. 1. 45) guarantees that P, P~' e £00 and that 0(0 -» 0* as t —>• oo.

1 independent of 0, parameter convergence of 0(t) to 9* requires ^- to be PE. The important question that arises in this example is how to choose the plant input u so that ^- is PE. Since the plant is nonlinear, the choice of u that makes ^- PE depends on the form of the nonlinear functions f ( x ) , g(x) and it is not easy, if possible at all, to establish conditions similar to those in the LTI case for a general class of nonlinearities. 40 Chapters. 6 Consider the dynamics of a hard-disk drive servo system [96] given by where y is the position error of the head relative to the center of the track, kp is a known constant, and is a disturbance that is due to higher-order harmonics that arise during rotation of the disk drive.

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