By Petros Ioannou, Barýp Fidan
Designed to satisfy the desires of a large viewers with no sacrificing mathematical intensity and rigor, Adaptive keep watch over instructional offers the layout, research, and alertness of a large choice of algorithms that may be used to regulate dynamical structures with unknown parameters. Its tutorial-style presentation of the basic concepts and algorithms in adaptive keep an eye on make it appropriate as a textbook.
Adaptive keep watch over educational is designed to serve the desires of 3 exact teams of readers: engineers and scholars attracted to studying tips on how to layout, simulate, and enforce parameter estimators and adaptive keep watch over schemes with no need to completely comprehend the analytical and technical proofs; graduate scholars who, as well as achieving the aforementioned targets, additionally are looking to comprehend the research of easy schemes and get an concept of the stairs interested by extra advanced proofs; and complex scholars and researchers who are looking to research and comprehend the main points of lengthy and technical proofs with a watch towards pursuing learn in adaptive regulate or comparable issues.
The authors in attaining those a number of pursuits via enriching the e-book with examples demonstrating the layout methods and easy research steps and through 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 should be got by means of contacting SIAM or the authors.
This publication might be necessary to masters- and Ph.D.-level scholars in addition to electric, mechanical, and aerospace engineers and utilized mathematicians.
Preface; Acknowledgements; checklist of Acronyms; bankruptcy 1: creation; bankruptcy 2: Parametric versions; bankruptcy three: Parameter id: non-stop Time; bankruptcy four: Parameter id: Discrete Time; bankruptcy five: Continuous-Time version Reference Adaptive regulate; bankruptcy 6: Continuous-Time Adaptive Pole Placement keep watch over; bankruptcy 7: Adaptive keep an eye on for Discrete-Time platforms;
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Extra resources for Adaptive control tutorial
Simulations demonstrate that the gradient algorithm based on the integral cost gives better convergence properties than the gradient algorithm based on the instantaneous cost. The gradient algorithm based on the integral cost has similarities with the least-squares (LS) algorithms to be developed in the next section. 7 Least-Squares Algorithms The LS method dates back to the eighteenth century, when Gauss used it to determine the orbits of planets. The basic idea behind LS is fitting a mathematical model to a sequence of observed data by minimizing the sum of the squares of the difference between the observed and computed data.
The LS method has been widely used in parameter estimation both in recursive and nonrecursive forms mainly for discrete-time systems [46, 47, 77, 97, 98]. 7. Least-Squares Algorithms 43 In practice, dn may be due to sensor noise or external sources, etc. We examine the following estimation problem: Given the measurements of z(r), 0(t) for 0 < T < t, find a "good" estimate 0(0 of 9* at time t. One possible solution is to calculate 0(0 as by using the measurements of z(r), 0(r) at some T < t for which 0(r) ^ 0.
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. 3 In order to get some understanding of the properties of the pure LS algorithm, let us consider the scalar SPM where z, 0*, 0 € 7£. Let us assume that
Adaptive control tutorial by Petros Ioannou, Barýp Fidan