Download or read book Input to State Stability for PDEs written by Iasson Karafyllis and published by Springer. This book was released on 2018-06-07 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Input to State Stability written by Andrii Mironchenko and published by Springer Nature. This book was released on 2023-03-30 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Boundary Control of PDEs written by Miroslav Krstic and published by SIAM. This book was released on 2008-01-01 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Extremum Seeking Through Delays and PDEs written by Tiago Roux Oliveira and published by SIAM. This book was released on 2022-12-05 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Adaptive Control of Parabolic PDEs written by Andrey Smyshlyaev and published by Princeton University Press. This book was released on 2010-07-01 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Proceedings of 2023 Chinese Intelligent Systems Conference written by Yingmin Jia and published by Springer Nature. This book was released on 2023-11-08 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Hybrid Dynamical Systems written by Rafal Goebel and published by Princeton University Press. This book was released on 2012-03-18 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, this book presents a complete theory of robust asymptotic stability for hybrid dynamical systems that is applicable to the design of hybrid control algorithms--algorithms that feature logic, timers, or combinations of digital and analog components. With the tools of modern mathematical analysis, Hybrid Dynamical Systems unifies and generalizes earlier developments in continuous-time and discrete-time nonlinear systems. It presents hybrid system versions of the necessary and sufficient Lyapunov conditions for asymptotic stability, invariance principles, and approximation techniques, and examines the robustness of asymptotic stability, motivated by the goal of designing robust hybrid control algorithms. This self-contained and classroom-tested book requires standard background in mathematical analysis and differential equations or nonlinear systems. It will interest graduate students in engineering as well as students and researchers in control, computer science, and mathematics.

Download or read book Materials Phase Change PDE Control Estimation written by Shumon Koga and published by Springer Nature. This book was released on 2020-11-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Advances in Distributed Parameter Systems written by Jean Auriol and published by Springer Nature. This book was released on 2022-04-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Control Of Partial Differential Equations written by Jean-michel Coron and published by World Scientific. This book was released on 2023-04-11 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Traffic Congestion Control by PDE Backstepping written by Huan Yu and published by Springer Nature. This book was released on 2022-12-16 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Delay Compensation for Nonlinear Adaptive and PDE Systems written by Miroslav Krstic and published by Springer Science & Business Media. This book was released on 2010-01-23 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Robust Event Triggered Control of Nonlinear Systems written by Tengfei Liu and published by Springer Nature. This book was released on 2020-06-25 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book PDE Control of String Actuated Motion written by Ji Wang and published by Princeton University Press. This book was released on 2022-10-25 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Delay Adaptive Linear Control written by Yang Zhu and published by Princeton University Press. This book was released on 2020-04-28 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stability and Boundary Stabilization of 1 D Hyperbolic Systems written by Georges Bastin and published by Birkhäuser. This book was released on 2016-07-26 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations. It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them. With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching. They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis. Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones. They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs. The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering. The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.

Download or read book Nonlinear Control Under Nonconstant Delays written by Nikolaos Bekiaris-Liberis and published by SIAM. This book was released on 2013-09-25 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors have developed a methodology for control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. In addition to control synthesis, they introduce tools to quantify the performance and the robustness properties of the designs provided in the book. The book is based on the concept of predictor feedback and infinite-dimensional backstepping transformation for linear systems and the authors guide the reader from the basic ideas of the concept?with constant delays only on the input?all the way through to nonlinear systems with state-dependent delays on the input as well as on system states. Readers will find the book useful because the authors provide elegant and systematic treatments of long-standing problems in delay systems, such as systems with state-dependent delays that arise in many applications. In addition, the authors give all control designs by explicit formulae, making the book especially useful for engineers who have faced delay-related challenges and are concerned with actual implementations and they accompany all control designs with Lyapunov-based analysis for establishing stability and performance guarantees.