Data-Driven, Nonparametric, Adaptive Control Theory
Description
Data-Driven, Nonparametric, Adaptive Control Theory introduces a novel approach to the control of deterministic, nonlinear ordinary differential equations affected by uncertainties. The methods proposed enforce satisfactory trajectory tracking despite functional uncertainties in the plant model. The book employs the properties of reproducing kernel Hilbert (native) spaces to characterize both the functional space of uncertainties and the controller's performance. Classical control systems are extended to broader classes of problems and more informative characterizations of the controllers' performances are attained.
Following an examination of how backstepping control and robust control Lyapunov functions can be ported to the native setting, numerous extensions of the model reference adaptive control framework are considered. The authors' approach breaks away from classical paradigms in which uncertain nonlinearities are parameterized using a regressor vector provided a priori or reconstructed online. The problem of distributing the kernel functions that characterize the native space is addressed at length by employing data-driven methods in deterministic and stochastic settings.
The first part of this book is a self-contained resource, systematically presenting elements of real analysis, functional analysis, and native space theory. The second part is an exposition of the theory of nonparametric control systems design. The text may be used as a self-study book for researchers and practitioners and as a reference for graduate courses in advanced control systems design. MATLAB® codes, available on the authors' website, and suggestions for homework assignments help readers appreciate the implementation of the theoretical results.
Reviews / Votes
"The book is written in the form of lecture notes for students that may have quite diverse backgrounds. Therefore, the authors start by building all of the ingredients from the bottom up. ... References to the literature are given after each chapter." (A. Bultheel, Mathematical Reviews, February, 2026)
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Persons
Professor Andrew J. Kurdila is an expert in reproducing kernel Hilbert spaces, Koopman theory, approximation theory, and control on native spaces. Among his numerous recognitions, we recall the W. Martin Johnson Professorship at Virginia Tech, the TEES faculty fellowship at Texas A&M University, and the AIAA associate fellowship to name a few. He is the author of 5 books on various topics in the general area of control theory and more than 300 peer-reviewed journal and conference papers.
Professor Andrea L'Afflitto is an expert in robust model reference adaptive control theory and its applications to autonomous aerospace systems. Dr. L'Afflitto is an AIAA Associate Fellow, one of the 2018 DARPA Young Faculty Awardees, and received numerous externally funded awards for his research in the area of adaptive control theory and autonomous uninhabited aerial vehicles. Presently, Dr. L'Afflitto is the Senior Editor for the Autonomous Systems track of the IEEE Transactions on Aerospace and Electronic Systems and is a member of the IEEE Editorial Board. He is the authors of a monograph on flight controls, 3 book chapters, and more than 40 peer-reviewed journal and conference papers. Finally, he served as the first editor for a contributed book on the guidance, navigation, and control of advanced aerospace systems.
Professor John A. Burns is the Hatcher Professor of Mathematics and Director of the Interdisciplinary Center for Applied Mathematics at Virginia Tech. He is an IEEE Lifetime Fellow, SIAM Fellow, and recipient of numerous awards in mathematics including the W.T. and Idalia Reid Prize. Dr. Burns is an expert in optimal control theory, control of partial differential equations, and estimation theory. He is the author of 1 book on calculus of variations and more than 200 peer-reviewed journal and conference papers. Furthermore, he served as co-editor of two contributed books and principal or co-principal investigator for more than40 externally funded competitive research projects. Finally, Professor Burns delivered more than 250 invited talks at universities, world-class research centers, and international conferences. Presently, Dr. Burns serves as the Series Editor for the Monograph and Research Notes in Mathematics and served as editor-in-chief, associate editor, and editor for numerous journals in mathematics and control theory.
Content
Chapter 1. Introduction.- Chapter 2. Elements of Real and Functional Analysis.- Chapter 3. Elements of Native Space Theory.- Chapter 4. Elements of Dynamical Systems Theory.- Chapter 5. Native Space Embedding Control Methods.- Chapter 6. Data-Driven Methods and Adaptive Control: Deterministic Analysis.- Chapter 7. Data-Driven Methods and Adaptive Control: Stochastic Analysis.- Chapter 8. Conclusion.- Appendix.