By Petros Ioannou, Barýp Fidan
Designed to satisfy the wishes of a large viewers with no sacrificing mathematical intensity and rigor, Adaptive keep an eye on instructional provides the layout, research, and alertness of a wide selection of algorithms that may be used to control dynamical platforms with unknown parameters. Its tutorial-style presentation of the basic suggestions and algorithms in adaptive keep an eye on make it appropriate as a textbook.
Adaptive regulate educational is designed to serve the wishes of 3 unique teams of readers: engineers and scholars drawn 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 concerned about extra advanced proofs; and complex scholars and researchers who are looking to learn and comprehend the main points of lengthy and technical proofs with an eye fixed towards pursuing learn in adaptive keep watch over or similar subject matters.
The authors in achieving those a number of pursuits by way of enriching the publication with examples demonstrating the layout systems and uncomplicated research steps and via 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 may be acquired by means of contacting SIAM or the authors.
This e-book may 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 versions; 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 watch over for Discrete-Time platforms;
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Additional resources for Adaptive Control Tutorial (Advances in Design and Control)
Let us assume that _y, y, u are available for measurement. We would like to generate online estimates for the parameters a, b. 17) in the SPM form where z = y, 0* = [b, a]T, 0 = [u, —y]T, and z, 0 are available for measurement. Step 2: Parameter Identification Algorithm Estimation Model where 0(0 is the estimate of 0* at time t. Estimation Error where ms is the normalizing signal such that •£- e £00. A straightforward choice for ms is mj — I + <*070 for any a > 0. Adaptive Law We use the gradient method to minimize the cost, where 0i = u, fa — —y, and set where r = FT > 0 is the adaptive gain, and 0 t , 02 are the elements of 0 — [6\, 62}*.
Another class of state-space models that appear in adaptive control is of the form where B is also unknown but is positive definite, is negative definite, or the sign of each of its elements is known. We refer to this class of parametric models as bilinear state-space parametric models (B-SSPM). The B-SSPM model can be easily expressed as a set of scalar B-SPM or B-DPM. The PI problem can now be stated as follows: For the SPM and DPM: Given the measurements z ( t ) , (f>(t), generate 6 ( t ) , the estimate of the unknown vector 0*, at each time t.
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. One important difference, however, is that in the case of a single parameter, convergence of the Lyapunov-like function V to a constant implies that the estimated parameter converges to a constant. Such a result cannot be established in the case of more than one parameter for the gradient algorithm.
Adaptive Control Tutorial (Advances in Design and Control) by Petros Ioannou, Barýp Fidan