Input To State Stability For Pdes

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Input-to-State Stability for PDEs

Iasson Karafyllis,Miroslav Krstic
Input to State Stability for PDEs Book PDF

Author : Iasson Karafyllis,Miroslav Krstic
Publisher : Springer
Page : 287 pages
File Size : 55,9 Mb
Release : 2018-06-07
Category : Technology & Engineering
ISBN : 9783319910116

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Input-to-State Stability for PDEs by Iasson Karafyllis,Miroslav Krstic Pdf

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.

Input-to-State Stability

Andrii Mironchenko
Input to State Stability Book PDF

Author : Andrii Mironchenko
Publisher : Springer Nature
Page : 417 pages
File Size : 48,8 Mb
Release : 2023-03-30
Category : Science
ISBN : 9783031146749

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Input-to-State Stability by Andrii Mironchenko Pdf

Input-to-State Stability presents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, and stability of nonlinear interconnected control systems. The applications of input-to-state stability (ISS) are manifold and include mechatronics, aerospace engineering, and systems biology. Although the book concentrates on the ISS theory of finite-dimensional systems, it emphasizes the importance of a more general view of infinite-dimensional ISS theory. This permits the analysis of more general system classes and provides new perspectives on and a better understanding of the classical ISS theory for ordinary differential equations (ODEs). Features of the book include: • a comprehensive overview of the theoretical basis of ISS; • a description of the central applications of ISS in nonlinear control theory; • a detailed discussion of the role of small-gain methods in the stability of nonlinear networks; and • an in-depth comparison of ISS for finite- and infinite-dimensional systems. The book also provides a short overview of the ISS theory for other systems classes (partial differential equations, hybrid, impulsive, and time-delay systems) and surveys the available results for the important stability properties that are related to ISS. The reader should have a basic knowledge of analysis, Lebesgue integration theory, linear algebra, and the theory of ODEs but requires no prior knowledge of dynamical systems or stability theory. The author introduces all the necessary ideas within the book. Input-to-State Stability will interest researchers and graduate students studying nonlinear control from either a mathematical or engineering background. It is intended for active readers and contains numerous exercises of varying difficulty, which are integral to the text, complementing and widening the material developed in the monograph.

Extremum Seeking Through Delays and PDEs

Tiago Roux Oliveira,Miroslav Krstic
Extremum Seeking Through Delays and PDEs Book PDF

Author : Tiago Roux Oliveira,Miroslav Krstic
Publisher : SIAM
Page : 461 pages
File Size : 46,6 Mb
Release : 2022-12-05
Category : Mathematics
ISBN : 9781611977356

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Extremum Seeking Through Delays and PDEs by Tiago Roux Oliveira,Miroslav Krstic Pdf

Extremum Seeking through Delays and PDEs, the first book on the topic, expands the scope of applicability of the extremum seeking method, from static and finite-dimensional systems to infinite-dimensional systems. Readers will find numerous algorithms for model-free real-time optimization are developed and their convergence guaranteed, extensions from single-player optimization to noncooperative games, under delays and PDEs, are provided, the delays and PDEs are compensated in the control designs using the PDE backstepping approach, and stability is ensured using infinite-dimensional versions of averaging theory, and accessible and powerful tools for analysis. This book is intended for control engineers in all disciplines (electrical, mechanical, aerospace, chemical), mathematicians, physicists, biologists, and economists. It is appropriate for graduate students, researchers, and industrial users.

Boundary Control of PDEs

Miroslav Krstic,Andrey Smyshlyaev
Boundary Control of PDEs Book PDF

Author : Miroslav Krstic,Andrey Smyshlyaev
Publisher : SIAM
Page : 197 pages
File Size : 51,9 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780898718607

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Boundary Control of PDEs by Miroslav Krstic,Andrey Smyshlyaev Pdf

The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg-Landau, Schrodinger, Kuramoto-Sivashinsky, KdV, beam, and Navier-Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.

Proceedings of 2023 Chinese Intelligent Systems Conference

Yingmin Jia,Weicun Zhang,Yongling Fu,Jiqiang Wang
Proceedings of 2023 Chinese Intelligent Systems Conference Book PDF

Author : Yingmin Jia,Weicun Zhang,Yongling Fu,Jiqiang Wang
Publisher : Springer Nature
Page : 870 pages
File Size : 53,6 Mb
Release : 2023-11-08
Category : Technology & Engineering
ISBN : 9789819968473

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Proceedings of 2023 Chinese Intelligent Systems Conference by Yingmin Jia,Weicun Zhang,Yongling Fu,Jiqiang Wang Pdf

This book constitutes the proceedings of the 19th Chinese Intelligent Systems Conference, CISC 2023, which was held during October 14–15, 2023, in Ningbo, Zhejiang, China. The book focuses on new theoretical results and techniques in the field of intelligent systems and control. This is achieved by providing in-depth studies of a number of important topics such as multi-agent systems, complex networks, intelligent robots, complex systems theory and swarm behavior, event-driven and data-driven control, robust and adaptive control, big data and brain science, process control, intelligent sensors and detection technology, deep learning and learning control, navigation and control of aerial vehicles, and so on. The book is particularly suitable for readers interested in learning intelligent systems and control and artificial intelligence. The book can benefit researchers, engineers and graduate students.

Materials Phase Change PDE Control & Estimation

Shumon Koga,Miroslav Krstic
Materials Phase Change PDE Control Estimation Book PDF

Author : Shumon Koga,Miroslav Krstic
Publisher : Springer Nature
Page : 352 pages
File Size : 44,8 Mb
Release : 2020-11-01
Category : Science
ISBN : 9783030584900

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Materials Phase Change PDE Control & Estimation by Shumon Koga,Miroslav Krstic Pdf

This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem. The algorithms can be used to improve the performance of various processes with phase changes, such as additive manufacturing. Using the authors' innovative design solutions, readers will also be equipped to apply estimation algorithms for real-world phase change dynamics, from polar ice to lithium-ion batteries. A historical treatment of the Stefan problem opens the book, situating readers in the larger context of the area. Following this, the chapters are organized into two parts. The first presents the design method and analysis of the boundary control and estimation algorithms. Part two then explores a number of applications, such as 3D printing via screw extrusion and laser sintering, and also discusses the experimental verifications conducted. A number of open problems and provided as well, offering readers multiple paths to explore in future research. Materials Phase Change PDE Control & Estimation is ideal for researchers and graduate students working on control and dynamical systems, and particularly those studying partial differential equations and moving boundaries. It will also appeal to industrial engineers and graduate students in engineering who are interested in this area.

Advances in Distributed Parameter Systems

Jean Auriol,Joachim Deutscher,Guilherme Mazanti,Giorgio Valmorbida
Advances in Distributed Parameter Systems Book PDF

Author : Jean Auriol,Joachim Deutscher,Guilherme Mazanti,Giorgio Valmorbida
Publisher : Springer Nature
Page : 301 pages
File Size : 41,8 Mb
Release : 2022-04-24
Category : Technology & Engineering
ISBN : 9783030947668

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Advances in Distributed Parameter Systems by Jean Auriol,Joachim Deutscher,Guilherme Mazanti,Giorgio Valmorbida Pdf

The proposed book presents recent breakthroughs for the control of distributed parameter systems and follows on from a workshop devoted to this topic. It introduces new and unified visions of the challenging control problems raised by distributed parameter systems. The book collects contributions written by prominent international experts in the control community, addressing a wide variety of topics. It spans the full range from theoretical research to practical implementation and follows three traverse axes: emerging ideas in terms of control strategies (energy shaping, prediction-based control, numerical control, input saturation), theoretical concepts for interconnected systems (with potential non-linear actuation dynamics), advanced applications (cable-operated elevators, traffic networks), and numerical aspects. Cutting-edge experts in the field contributed in this volume, making it a valuable reference source for control practitioners, graduate students, and scientists researching practical and theoretical solutions to the challenging problems raised by distributed parameter systems.

Control Of Partial Differential Equations

Jean-michel Coron,Tatsien Li,Zhiqiang Wang
Control Of Partial Differential Equations Book PDF

Author : Jean-michel Coron,Tatsien Li,Zhiqiang Wang
Publisher : World Scientific
Page : 315 pages
File Size : 42,9 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9789811271649

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Control Of Partial Differential Equations by Jean-michel Coron,Tatsien Li,Zhiqiang Wang Pdf

This book is mainly a collection of lecture notes for the 2021 LIASFMA International Graduate School on Applied Mathematics. It provides the readers some important results on the theory, the methods, and the application in the field of 'Control of Partial Differential Equations'. It is useful for researchers and graduate students in mathematics or control theory, and for mathematicians or engineers with an interest in control systems governed by partial differential equations.

Traffic Congestion Control by PDE Backstepping

Huan Yu,Miroslav Krstic
Traffic Congestion Control by PDE Backstepping Book PDF

Author : Huan Yu,Miroslav Krstic
Publisher : Springer Nature
Page : 363 pages
File Size : 54,9 Mb
Release : 2022-12-16
Category : Science
ISBN : 9783031193460

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Traffic Congestion Control by PDE Backstepping by Huan Yu,Miroslav Krstic Pdf

This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods. The first part of the text is concerned with basic backstepping control of freeway traffic using the Aw-Rascle-Zhang (ARZ) second-order PDE model. It begins by illustrating a basic control problem – suppressing traffic with stop-and-go oscillations downstream of ramp metering – before turning to the more challenging case for traffic upstream of ramp metering. The authors demonstrate how to design state observers for the purpose of stabilization using output-feedback control. Experimental traffic data are then used to calibrate the ARZ model and validate the boundary observer design. Because large uncertainties may arise in traffic models, adaptive control and reinforcement learning methods are also explored in detail. Part II then extends the conventional ARZ model utilized until this point in order to address more complex traffic conditions: multi-lane traffic, multi-class traffic, networks of freeway segments, and driver use of routing apps. The final chapters demonstrate the use of the Lighthill-Whitham-Richards (LWR) first-order PDE model to regulate congestion in traffic flows and to optimize flow through a bottleneck. In order to make the text self-contained, an introduction to the PDE backstepping method for systems of coupled first-order hyperbolic PDEs is included. Traffic Congestion Control by PDE Backstepping is ideal for control theorists working on control of systems modeled by PDEs and for traffic engineers and applied scientists working on unsteady traffic flows. It will also be a valuable resource for researchers interested in boundary control of coupled systems of first-order hyperbolic PDEs.

Adaptive Control of Parabolic PDEs

Andrey Smyshlyaev,Miroslav Krstic
Adaptive Control of Parabolic PDEs Book PDF

Author : Andrey Smyshlyaev,Miroslav Krstic
Publisher : Princeton University Press
Page : 344 pages
File Size : 53,8 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835362

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Adaptive Control of Parabolic PDEs by Andrey Smyshlyaev,Miroslav Krstic Pdf

This book introduces a comprehensive methodology for adaptive control design of parabolic partial differential equations with unknown functional parameters, including reaction-convection-diffusion systems ubiquitous in chemical, thermal, biomedical, aerospace, and energy systems. Andrey Smyshlyaev and Miroslav Krstic develop explicit feedback laws that do not require real-time solution of Riccati or other algebraic operator-valued equations. The book emphasizes stabilization by boundary control and using boundary sensing for unstable PDE systems with an infinite relative degree. The book also presents a rich collection of methods for system identification of PDEs, methods that employ Lyapunov, passivity, observer-based, swapping-based, gradient, and least-squares tools and parameterizations, among others. Including a wealth of stimulating ideas and providing the mathematical and control-systems background needed to follow the designs and proofs, the book will be of great use to students and researchers in mathematics, engineering, and physics. It also makes a valuable supplemental text for graduate courses on distributed parameter systems and adaptive control.

Delay Compensation for Nonlinear, Adaptive, and PDE Systems

Miroslav Krstic
Delay Compensation for Nonlinear Adaptive and PDE Systems Book PDF

Author : Miroslav Krstic
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 45,7 Mb
Release : 2010-01-23
Category : Mathematics
ISBN : 9780817648770

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Delay Compensation for Nonlinear, Adaptive, and PDE Systems by Miroslav Krstic Pdf

Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems. It is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay. Replete with examples, Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference guide for graduate students, researchers, and professionals in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

Robust Event-Triggered Control of Nonlinear Systems

Tengfei Liu,Pengpeng Zhang,Zhong-Ping Jiang
Robust Event Triggered Control of Nonlinear Systems Book PDF

Author : Tengfei Liu,Pengpeng Zhang,Zhong-Ping Jiang
Publisher : Springer Nature
Page : 264 pages
File Size : 53,8 Mb
Release : 2020-06-25
Category : Technology & Engineering
ISBN : 9789811550133

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Robust Event-Triggered Control of Nonlinear Systems by Tengfei Liu,Pengpeng Zhang,Zhong-Ping Jiang Pdf

This book presents a study on the novel concept of "event-triggered control of nonlinear systems subject to disturbances", discussing the theory and practical applications. Richly illustrated, it is a valuable resource for researchers, engineers and graduate students in automation engineering who wish to learn the theories, technologies, and applications of event-triggered control of nonlinear systems.

PDE Control of String-Actuated Motion

Ji Wang,Miroslav Krstic
PDE Control of String Actuated Motion Book PDF

Author : Ji Wang,Miroslav Krstic
Publisher : Princeton University Press
Page : 512 pages
File Size : 50,7 Mb
Release : 2022-10-25
Category : Science
ISBN : 9780691233482

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PDE Control of String-Actuated Motion by Ji Wang,Miroslav Krstic Pdf

New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevators Control applications in undersea construction, cable elevators, and offshore drilling present major methodological challenges because they involve PDE systems (cables and drillstrings) of time-varying length, coupled with ODE systems (the attached loads or tools) that usually have unknown parameters and unmeasured states. In PDE Control of String-Actuated Motion, Ji Wang and Miroslav Krstic develop control algorithms for these complex PDE-ODE systems evolving on time-varying domains. Motivated by physical systems, the book’s algorithms are designed to operate, with rigorous mathematical guarantees, in the presence of real-world challenges, such as unknown parameters, unmeasured distributed states, environmental disturbances, delays, and event-triggered implementations. The book leverages the power of the PDE backstepping approach and expands its scope in many directions. Filled with theoretical innovations and comprehensive in its coverage, PDE Control of String-Actuated Motion provides new design tools and mathematical techniques with far-reaching potential in adaptive control, delay systems, and event-triggered control.

Delay-Adaptive Linear Control

Yang Zhu,Miroslav Krstic
Delay Adaptive Linear Control Book PDF

Author : Yang Zhu,Miroslav Krstic
Publisher : Princeton University Press
Page : 354 pages
File Size : 42,6 Mb
Release : 2020-04-28
Category : Mathematics
ISBN : 9780691202549

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Delay-Adaptive Linear Control by Yang Zhu,Miroslav Krstic Pdf

Basic predictor feedback for single-input systems -- Basic idea of adaptive control for single-input systems -- Single-input systems with full relative degree -- Single-input systems with arbitrary relative degree -- Exact predictor feedback for multi-input systems -- Full-state feedback of uncertain multi-input systems -- Output feedback of uncertain multi-input systems -- Output feedback of systems with uncertain delays, parameters and ODE state -- Predictor feedback for uncertainty-free systems -- Predictor feedback of uncertain single-input systems -- Predictor feedback of uncertain multi-input systems.

Generalized Homogeneity in Systems and Control

Andrey Polyakov
Generalized Homogeneity in Systems and Control Book PDF

Author : Andrey Polyakov
Publisher : Springer Nature
Page : 454 pages
File Size : 42,7 Mb
Release : 2020-02-05
Category : Technology & Engineering
ISBN : 9783030384494

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Generalized Homogeneity in Systems and Control by Andrey Polyakov Pdf

This monograph introduces the theory of generalized homogeneous systems governed by differential equations in both Euclidean (finite-dimensional) and Banach/Hilbert (infinite-dimensional) spaces. It develops methods of stability and robustness analysis, control design, state estimation and discretization of homogeneous control systems. Generalized Homogeneity in Systems and Control is structured in two parts. Part I discusses various models of control systems and related tools for their analysis, including Lyapunov functions. Part II deals with the analysis and design of homogeneous control systems. Some of the key features of the text include: mathematical models of dynamical systems in finite-dimensional and infinite-dimensional spaces; the theory of linear dilations in Banach spaces; homogeneous control and estimation; simple methods for an "upgrade" of existing linear control laws; numerical schemes for a consistent digital implementation of homogeneous algorithms; and experiments confirming an improvement of PID controllers. The advanced mathematical material will be of interest to researchers, mathematicians working in control theory and mathematically oriented control engineers.