By Petros Ioannou, Barýp Fidan
Designed to satisfy the desires of a large viewers with out sacrificing mathematical intensity and rigor, Adaptive regulate educational provides the layout, research, and alertness of a large choice of algorithms that may be used to control dynamical platforms with unknown parameters. Its tutorial-style presentation of the elemental recommendations and algorithms in adaptive regulate make it compatible as a textbook.
Adaptive regulate instructional is designed to serve the wishes of 3 distinctive teams of readers: engineers and scholars attracted to studying easy methods to layout, simulate, and enforce parameter estimators and adaptive regulate schemes with no need to completely comprehend the analytical and technical proofs; graduate scholars who, as well as achieving the aforementioned goals, additionally are looking to comprehend the research of easy schemes and get an idea of the stairs keen on extra complicated proofs; and complex scholars and researchers who are looking to examine and comprehend the main points of lengthy and technical proofs with a watch towards pursuing study in adaptive keep an eye on or similar themes.
The authors in attaining those a number of ambitions via enriching the e-book with examples demonstrating the layout techniques and uncomplicated research steps and by way of detailing their proofs in either an appendix and electronically on hand 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 publication may be worthy 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: advent; bankruptcy 2: Parametric types; bankruptcy three: Parameter id: non-stop Time; bankruptcy four: Parameter id: Discrete Time; bankruptcy five: Continuous-Time version Reference Adaptive keep an eye on; bankruptcy 6: Continuous-Time Adaptive Pole Placement regulate; bankruptcy 7: Adaptive regulate for Discrete-Time structures;
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Extra resources for Adaptive Control Tutorial (Advances in Design and Control)
Gradient Algorithms Based on the Linear Model 37 where a is a scalar and P is a matrix selected by the designer. 30) are common to several algorithms that are generated in the following sections. 31). At each time t, J (9) is a convex function of 0 and therefore has a global minimum. The gradient algorithm takes the form where F = YT > 0 is a design matrix referred to as the adaptive gain. 29) constitute the gradient parameter identification algorithm based on the instantaneous cost function whose stability properties are given by the following theorem.
0, we write Chapter 2. Parametric Models 21 by adding and subtracting the term /U. We then rewrite it as Letting we obtain another DPM. 8 Consider the second-order plant where and are matrices with unknown elements. The SSPM is generated as where aw, > 0 is a design constant. 9 (parametric model for nth-SISO LTI system) cONSIDER THE siso lti system described by the I/O relation where and u and y are the plant scalar input and output, respectively. We can also express the above system as an nth-order differential equation given by Lumping all the parameters in the vector 22 Chapter 2.
In practice, however, the effect of noise on the measurements of 0(0, especially when 0(0 is close to zero, may lead to erroneous parameter estimates. Another approach is to update 9(t} in a direction that minimizes a certain cost of the estimation error £. With this approach, 0(0 is adjusted in a direction that makes |s| smaller and smaller until a minimum is reached at which |e| — 0 and updating is terminated. As an example, consider the cost criterion which we minimize with respect to 9 using the gradient method to obtain where y > 0 is a scaling constant or step size which we refer to as the adaptive gain and where VJ(0) is the gradient of J with respect to 9.