By Petros Ioannou, Barýp Fidan

Designed to fulfill the desires of a large viewers with no sacrificing mathematical intensity and rigor, Adaptive keep watch over educational provides the layout, research, and alertness of a large choice of algorithms that may be used to regulate dynamical platforms with unknown parameters. Its tutorial-style presentation of the basic ideas and algorithms in adaptive keep watch over make it appropriate as a textbook.

Adaptive regulate educational is designed to serve the desires of 3 precise teams of readers: engineers and scholars drawn to studying find out how 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 ambitions, additionally are looking to comprehend the research of easy schemes and get an concept of the stairs fascinated about 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 learn in adaptive keep watch over or comparable themes.

The authors in attaining those a number of pursuits by means of enriching the publication with examples demonstrating the layout strategies and uncomplicated research steps and by means of detailing their proofs in either an appendix and electronically to be had supplementary fabric; on-line examples also are to be had. an answer guide for teachers should be acquired via contacting SIAM or the authors.

This ebook might be beneficial 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 types; bankruptcy three: Parameter id: non-stop Time; bankruptcy four: Parameter identity: Discrete Time; bankruptcy five: Continuous-Time version Reference Adaptive keep an eye on; bankruptcy 6: Continuous-Time Adaptive Pole Placement regulate; bankruptcy 7: Adaptive keep an eye on for Discrete-Time platforms;

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**Example text**

To satisfy V? Q > 0. The PE property of — is guaranteed by choosing the input u appropriately. Appropriate choices of u for this particular example include (i) u = c > 0, (ii) u — sin a>t for any u> ^ 0 and any bounded input u that is not vanishing with time. 16) is necessary and sufficient for exponential convergence of 0(f) -> 9* (see Problem 4). 1). The above analysis for the scalar example carries over to the vector case without any significant modifications, as demonstrated in the next section.

45) reduces to which is referred to as the pure LS algorithm. 2. , consists of at least n+™+l distinct frequencies, then

Proof. , where P — PJ > 0 i s a constant matrix. Let us now consider the identity where the last two equalities are obtained using lim,^oo 0(f) = PP^'^O), which implies that 46 Chapters. Parameter Identification: Continuous Time Because P(t} < P0 and 0(t) = P(t)PQlO(0) we have 0,0 e C^, which, together with -£- e £00, implies that sm s = — ^ and e, sms e £00- Let us now consider th. 46) we have Since P, •£-, £ms € £00, and ew^ € £2, we have # e £00 n £2, which completes the proof for (i) and (ii).