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2025 | Buch

Kapitel lesen Erstes Kapitel lesen

Data-Driven, Nonparametric, Adaptive Control Theory

verfasst von: Andrew J. Kurdila, Andrea L'Afflitto, John A. Burns

Verlag: Springer Nature Switzerland

Buchreihe : Lecture Notes in Control and Information Sciences

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Inhaltsverzeichnis
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SUCHEN

Über dieses Buch

Data-Driven, Nonparametric, Adaptive Control Theory führt einen neuen Ansatz zur Kontrolle deterministischer, nichtlinearer gewöhnlicher Differentialgleichungen ein, die von Unsicherheiten beeinflusst werden. Die vorgeschlagenen Methoden erzwingen trotz funktionaler Unsicherheiten im Anlagenmodell eine zufriedenstellende Flugbahnverfolgung. Das Buch nutzt die Eigenschaften der Reproduktion von Hilbert-Kernräumen, um sowohl den Funktionsraum der Ungewissheiten als auch die Leistung des Controllers zu charakterisieren. Die klassischen Kontrollsysteme werden auf breitere Klassen von Problemen ausgeweitet und aussagekräftigere Charakterisierungen der Leistungen der Steuerungen erreicht. Nach einer Untersuchung, wie Rückschrittskontrolle und robuste Steuerung Lyapunov-Funktionen in die nativen Gegebenheiten portiert werden können, werden zahlreiche Erweiterungen des modellgestützten adaptiven Regelungsrahmens in Betracht gezogen. Der Ansatz der Autoren bricht mit klassischen Paradigmen, in denen unsichere Nichtlinearitäten mittels eines Regressorvektors parametriert werden, der a priori bereitgestellt oder online rekonstruiert wurde. Das Problem der Verteilung der Kernfunktionen, die den nativen Raum charakterisieren, wird ausführlich durch den Einsatz datengestützter Methoden in deterministischen und stochastischen Umgebungen angegangen. Der erste Teil dieses Buches ist eine in sich geschlossene Ressource, die systematisch Elemente realer Analyse, funktionaler Analyse und nativer Weltraumtheorie präsentiert. Der zweite Teil ist eine Darstellung der Theorie des Designs nichtparametrischer Kontrollsysteme. Der Text kann als Selbststudienbuch für Forscher und Praktiker und als Referenz für Graduiertenkurse in fortgeschrittener Steuerungssystementwicklung verwendet werden. MATLAB-Codes, die auf der Website der Autoren abrufbar sind, und Vorschläge für Hausaufgaben helfen den Lesern, die Umsetzung der theoretischen Ergebnisse zu schätzen.
Mit KI übersetzt

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
This chapter introduced the general problem addressed in this book, that is, the design of robust and adaptive control strategies for nonlinear, deterministic systems of ordinary differential equations affected by uncertainties, which are assumed to lie in some native space. The proposed framework is unique not only for its ability to forecast the performance of the controller as an explicit function of key properties of the native space elected to capture the functional uncertainties. The proposed framework is unique for having merged in a unique manner dynamical systems theory, machine learning theory, and approximation theory, and having extracted essential tools from each of these three macro research areas. This chapter is closed by a brief description of the content of this book to allow readers to choose their strategy for addressing the proposed topics.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Chapter 2. Elements of Real and Functional Analysis
Abstract
This chapter presents some key elements of real and functional analysis employed throughout this book. The scope of this chapter is not to provide a comprehensive discussion on this topic, which is widely covered by a plethora of well-referenced books. The purpose of this chapter is to present all foundational elements of this book succinctly, coherently, and rigorously. This chapter can be studied as a first step toward the main goal of this book, namely the design of control systems and machine learning methods based on reproducing kernel Hilbert spaces (native spaces), or can be consulted by the reader as a compendium of resources for a deeper understanding of the material presented in later chapters. Numerous references are provided throughout this chapter to guide the reader to a deeper understanding of the topics discussed herein.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Chapter 3. Elements of Native Space Theory
Abstract
After an overview of key elements of functional analysis, this chapter is devoted to a specific topic in the theory of Hilbert spaces, namely reproducing kernel Hilbert spaces (RKHSs), also known as native spaces. This chapter provides the reader with all the tools needed to comprehend the key topics of this book, namely the design of control systems and machine learning methods based on native space theory. Initially, scalar-valued RKHSs are examined and their properties are discussed in detail and a tutorial manner. Successively, scalar-valued RKHSs are examined and special emphasis is given to highlighting connections with results for scalar-valued RKHSs. Two sets of results in RKHS theory are analyzed, namely how to correlate different RKHSs and how to bound projection errors in RKHSs.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Chapter 4. Elements of Dynamical Systems Theory
Abstract
This chapter introduces key elements of dynamical systems theory with special emphasis on those concepts leveraged in the next chapters for the design of control systems and machine learning methods based on reproducing kernel Hilbert spaces. Special emphasis is given to the notions of stability, boundedness, attractivity, and control of Lyapunov functions. A dedicated section discusses distributed parameter systems.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Chapter 5. Native Space Embedding Control Methods
Abstract
Leveraging the material presented in the previous chapters, this chapter presents robust and adaptive control techniques for nonlinear plants affected by multiple forms of uncertainties. These results are obtained by extending classical and advanced nonlinear control techniques to account for uncertainties modeled as unknown elements of some operator-valued native space. We begin by designing robust control Lyapunov functions for nonlinear dynamical systems, and, successively, we design backstepping control systems under the assumption that functional uncertainties lie in some RKHS. A large portion of this chapter is dedicated to the design of model reference adaptive control systems (MRAC) that are robust to parametric, matched, unmatched, and functional uncertainties. To this goal, we generalize the dead-zone modification of MRAC, the \(\sigma \)-modification of MRAC, and the use of convex projection operators. Finally, we extend variable structure methods, such as the error bounding control architecture and the adaptive error bounding architecture, to the native embedding setting. The same numerical example is worked out multiple times and the underlying codes are presented in an Appendix to this book.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Chapter 6. Data-Driven Methods and Adaptive Control: Deterministic Analysis
Abstract
This chapter discusses how deterministic data-driven approaches can be applied to the design of adaptive control systems for nonlinear plants affected by parametric, matched, unmatched, and functional uncertainties. After a brief outlook on the learning problem in general, this chapter presents three specific approaches, namely learn-then-control (LTC), sequential learn-and-control (SLC), and concurrent learn-and-control (CLC). Whereas numerical examples are provided for each of these three techniques, special emphasis is given to the theoretical aspects of LTC and CLC. Consistently with the rest of the book and to better emphasize the role of the results in Chap. 5, this chapter exploits the properties of native spaces to create suitable approximations of the hypothesis space, and hence, of the functional uncertainties affecting the plant dynamics.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Chapter 7. Data-Driven Methods and Adaptive Control: Stochastic Analysis
Abstract
This chapter describes in detail how stochastic data-driven approaches can be employed to define the centers underlying a native space-based approach to the design of adaptive control systems for deterministic, continuous-time ordinary differential equations. Leveraging some key properties of native spaces, this chapter characterizes the ultimate bounds on the closed-loop trajectory tracking error. These bounds are explicit functions of the dimension of the approximating hypothesis space and the number of samples employed to estimate the matched functional uncertainty. Numerical examples demonstrate the applicability of these approaches in a learn-then-control and a switched learn-and-control framework.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Chapter 8. Conclusion
Abstract
This chapter summarizes the key achievements of this book and discusses how it extends in a nontrivial manner classical results on robust and adaptive control systems. It is discussed how the material in this book marks the starting point for a new branch in control theory, that is, nonparametric control. This chapter also summarizes some of the limitations of the proposed results and proactively recommends future areas of research and possible approaches. This book is finally closed recommending wholeheartedly that the interested readers contact the authors to explore additional topics from those addressed in this work.
Andrew J. Kurdila, Andrea L’Afflitto, John A. Burns
Backmatter
Metadaten
Titel
Data-Driven, Nonparametric, Adaptive Control Theory
verfasst von
Andrew J. Kurdila
Andrea L'Afflitto
John A. Burns
Copyright-Jahr
2025
Electronic ISBN
978-3-031-78003-5
Print ISBN
978-3-031-78002-8
DOI
https://doi.org/10.1007/978-3-031-78003-5