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Adaptive Control of Linear Hyperbolic PDEs provides a comprehensive treatment of adaptive control of linear hyperbolic systems, using the backstepping method. It develops adaptive control strategies for different combinations of measurements and actuators, as well as for a range of different combinations of parameter uncertainty. The book treats boundary control of systems of hyperbolic partial differential equations (PDEs) with uncertain parameters. The authors develop designs for single equations, as well as any number of coupled equations. The designs are accompanied by mathematical proofs, which allow the reader to gain insight into the technical challenges associated with adaptive control of hyperbolic PDEs, and to get an overview of problems that are still open for further research. Although stabilization of unstable systems by boundary control and boundary sensing are the particular focus, state-feedback designs are also presented. The book also includes simulation examples with implementational details and graphical displays, to give readers an insight into the performance of the proposed control algorithms, as well as the computational details involved. A library of MATLAB® code supplies ready-to-use implementations of the control and estimation algorithms developed in the book, allowing readers to tailor controllers for cases of their particular interest with little effort. These implementations can be used for many different applications, including pipe flows, traffic flow, electrical power lines, and more. Adaptive Control of Linear Hyperbolic PDEs is of value to researchers and practitioners in applied mathematics, engineering and physics; it contains a rich set of adaptive control designs, including mathematical proofs and simulation demonstrations. The book is also of interest to students looking to expand their knowledge of hyperbolic PDEs.
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.
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.
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.
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.
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.
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.
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.
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.
Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.