Miroslav Krstic - Böcker

Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced with the new recursive design methodology--adaptive backstepping. Describes basic tools for nonadaptive backstepping design with state and output feedbacks.

An up-close look at the theory behind and application of extremum seekingOriginally developed as a method of adaptive control for hard-to-model systems, extremum seeking solves some of the same problems as today's neural network techniques, but in a more rigorous and practical way. Following the resurgence in popularity of extremum-seeking control in aerospace and automotive engineering, Real-Time Optimization by Extremum-Seeking Control presents the theoretical foundations and selected applications of this method of real-time optimization.Written by authorities in the field and pioneers in adaptive nonlinear control systems, this book presents both significant theoretic value and important practical potential. Filled with in-depth insight and expert advice, Real-Time Optimization by Extremum-Seeking Control:* Develops optimization theory from the points of dynamic feedback and adaptation* Builds a solid bridge between the classical optimization theory and modern feedback and adaptation techniques* Provides a collection of useful tools for problems in this complex area* Presents numerous applications of this powerful methodology* Demonstrates the immense potential of this methodology for future theory development and applicationsReal-Time Optimization by Extremum-Seeking Control is an important resource for both students and professionals in all areas of engineering-electrical, mechanical, aerospace, chemical, biomedical-and is also a valuable reference for practicing control engineers.

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.

Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor feedback has been a key tool for compensating such delays, but conventional predictor feedback algorithms assume that the delays and other parameters of a given system are known. When incorrect parameter values are used in the predictor, the resulting controller may be as destabilizing as without the delay compensation.Delay-Adaptive Linear Control develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters. Such estimators are designed as nonlinear differential equations, which dynamically adjust the parameters of the predictor. The design and analysis of the adaptive predictors involves a Lyapunov stability study of systems whose dimension is infinite, because of the delays, and nonlinear, because of the parameter estimators. This comprehensive book solves adaptive delay compensation problems for systems with single and multiple inputs/outputs, unknown and distinct delays in different input channels, unknown delay kernels, unknown plant parameters, unmeasurable finite-dimensional plant states, and unmeasurable infinite-dimensional actuator states.Presenting breakthroughs in adaptive control and control of delay systems, Delay-Adaptive Linear Control offers powerful new tools for the control engineer and the mathematician.

New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevatorsControl 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.

New adaptive and event-triggered control designs with concrete applications in undersea construction, offshore drilling, and cable elevatorsControl 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 presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control, with potential applications to turbulence control, weather forecasting, and plasma control. One of the main features of the book is a unique "backstepping" approach to parabolic partial differential equations, which yields not only the stabilization of the flow, but also the explicit solvability of the closed-loop system. The work is an excellent reference for a broad, interdisciplinary engineering and mathematics audience: control theorists, fluid mechanicists, mechanical engineers, aerospace engineers, chemical engineers, electrical engineers, applied mathematicians, as well as research and graduate students in these fields.

Some of the most common dynamic phenomena that arise in engineering practice—actuator and sensor delays—fall outside the scope of standard finite-dimensional system theory. The first attempt at infinite-dimensional feedback design in the field of control systems—the Smith predictor—has remained limited to linear finite-dimensional plants over the last five decades. 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. The book 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. Numerous examples and a detailed  treatment of individual classes of problems will help the reader master the techniques.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 concise and highly-usable textbook presents an introduction to backstepping, an elegant new approach to boundary control of partial differential equations (PDEs). Backstepping provides mathematical tools for constructing coordinate transformations and boundary feedback laws for converting complex and unstable PDE systems into elementary, stable, and physically intuitive ""target PDE systems"" that are familiar to engineers and physicists. Readers will be introduced to constructive control synthesis and Lyapunov stability analysis for distributed parameter systems.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. Boundary Control of PDEs is appropriate for courses in control theory and includes homework exercises and a solutions manual that is available from the authors upon request. The results are explicit and the style is accessible; students are not expected to have a background beyond that of a typical engineering or physics graduate. Even an instructor who is not an expert on control of PDEs will find it possible to teach effectively from this book. At the same time, an expert researcher in PDEs looking for novel technical challenges will find many topics of interest, particularly in control synthesis for unstable PDEs, nonlinear PDEs, and PDEs with unknown coefficients.

Stochastic Averaging and Extremum Seeking treats methods inspired by attempts to understand the seemingly non-mathematical question of bacterial chemotaxis and their application in other environments. The text presents significant generalizations on existing stochastic averaging theory developed from scratch and necessitated by the need to avoid violation of previous theoretical assumptions by algorithms which are otherwise effective in treating these systems. Coverage is given to four main topics. Stochastic averaging theorems are developed for the analysis of continuous-time nonlinear systems with random forcing, removing prior restrictions on nonlinearity growth and on the finiteness of the time interval. The new stochastic averaging theorems are usable not only as approximation tools but also for providing stability guarantees. Stochastic extremum-seeking algorithms are introduced for optimization of systems without available models. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms for non-cooperative/adversarial games is described. The analysis of their convergence to Nash equilibria is provided. The algorithms are illustrated on models of economic competition and on problems of the deployment of teams of robotic vehicles. Bacterial locomotion, such as chemotaxis in E. coli, is explored with the aim of identifying two simple feedback laws for climbing nutrient gradients. Stochastic extremum seeking is shown to be a biologically-plausible interpretation for chemotaxis. For the same chemotaxis-inspired stochastic feedback laws, the book also provides a detailed analysis of convergence for models of nonholonomic robotic vehicles operating in GPS-denied environments. The book contains block diagrams and several simulation examples, including examples arising from bacterial locomotion, multi-agent robotic systems, and economic market models. Stochastic Averaging and Extremum Seeking will be informative for control engineers from backgrounds in electrical, mechanical, chemical and aerospace engineering and to applied mathematicians. Economics researchers, biologists, biophysicists and roboticists will find the applications examples instructive.

Stochastic Averaging and Extremum Seeking treats methods inspired by attempts to understand the seemingly non-mathematical question of bacterial chemotaxis and their application in other environments. The text presents significant generalizations on existing stochastic averaging theory developed from scratch and necessitated by the need to avoid violation of previous theoretical assumptions by algorithms which are otherwise effective in treating these systems. Coverage is given to four main topics. Stochastic averaging theorems are developed for the analysis of continuous-time nonlinear systems with random forcing, removing prior restrictions on nonlinearity growth and on the finiteness of the time interval. The new stochastic averaging theorems are usable not only as approximation tools but also for providing stability guarantees. Stochastic extremum-seeking algorithms are introduced for optimization of systems without available models. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms for non-cooperative/adversarial games is described. The analysis of their convergence to Nash equilibria is provided. The algorithms are illustrated on models of economic competition and on problems of the deployment of teams of robotic vehicles. Bacterial locomotion, such as chemotaxis in E. coli, is explored with the aim of identifying two simple feedback laws for climbing nutrient gradients. Stochastic extremum seeking is shown to be a biologically-plausible interpretation for chemotaxis. For the same chemotaxis-inspired stochastic feedback laws, the book also provides a detailed analysis of convergence for models of nonholonomic robotic vehicles operating in GPS-denied environments. The book contains block diagrams and several simulation examples, including examples arising from bacterial locomotion, multi-agent robotic systems, and economic market models. Stochastic Averaging and Extremum Seeking will be informative for control engineers from backgrounds in electrical, mechanical, chemical and aerospace engineering and to applied mathematicians. Economics researchers, biologists, biophysicists and roboticists will find the applications examples instructive.

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. 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.

The book presents a solution to a problem in adaptive control design that was open for 40 years: robustification of disturbances without compromising asymptotic performance. This original methodology builds on foundational ideas, such as the use of a deadzone in the update law and nonlinear damping in the controller, and advances the tools for and the theory behind designing robust adaptive controllers, thus guaranteeing robustness properties stronger than previously achieved. Numerous examples provide detailed analyses of the new methodology. The authors present all stability notions that are useful in adaptive control, provide examples of all robustness problems (e.g. parameter drift), and analyze all approaches to robustification of adaptive controllers that have appeared in the literature;develop the Deadzone-Adapted Disturbance Suppression (DADS) control, a novel adaptive control scheme, and construct a novel robust identifier that can work in parallel with every direct adaptive controller (not only DADS);present the wing rock instability problem, an application of the DADS control scheme, solved with the DADS controller; andprovide ideas for the extension of the control scheme to cases not studied in the book.

In the 70+ year history of control theory and engineering, few applications have stirred as much excitement as flow control. The same can probably be said for the general area of fluid mechanics with its much longer history of several centuries. This excitement is understandable and justified. Turbulence in fluid flows has been recognized as the last great unsolved problem of classical 1 physics and has driven the careers of many leading mathematicians of the 20th century.2 Likewise, control theorists have hardly ever come across a problem this challenging. The emergence of flow control as an attractive new field is owed to the break­ throughs in micro-electro-mechanical systems (MEMS) and other technologies for instrumenting fluid flows on extremely short length and time scales. The remaining missing ingredient for turning flow control into a practical tool is control algorithms with provable performance guarantees. This research mono­ graph is the first book dedicated to this problem-systematic feedback design for fluid flows.

Efforts in nonlinear control have led to the level of generality in ehich conceptual solutions exist for all systems affine in control and the disturbance, and constructive designs exist for a specific class of nonlinear systems - although broad in terms of physical relevance. This monograph presents the fundamentals of global stabilization and optimal control of nonlinear systems with uncertain models. It offers a unified view of deterministic disturbance attenuation, stochastic control and adaptive control for nonlinear systems. It addresses a large audience of researchers, students, engineers and mathematicians.

The emergence of flow control as an attractive new field is owed to breakthroughs in MEMS (micro-electromechanical systems) and related technologies. The instrumentation of fluid flows on extremely short length and short time scales requires the practical tool of control algorithms with provable performance guarantees. Dedicated to this problem, Flow Control by Feedback, brings together controller design and fluid mechanics expertise in an exposition of the latest research results. Featuring: Exhaustive treatment of flow control core areas including stabilization and mixing control techniques; self-contained introductory sections on Navier-Stokes equations, linear and nonlinear control and sensors and MEMS to facilitate accessibility to this cross-disciplinary subject; a comprehensive survey of feedback algorithms for flow control that are currently available. In response to the intense interest in flow control, this volume will be an essential addition to the library of researchers and graduate students in control theory, fluid mechanics, mathematics and physics.Content structure is ideal for instruction on flow control modules or as supplementary reading on fluid dynamics and infinite dimensional systems courses.

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); andfeedback 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.

This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem.

This monograph introduces breakthrough control algorithms for partial differential equation models with moving boundaries, the study of which is known as the Stefan problem.

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.

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.

This monograph bridges the gap between the nonlinear predictor as a concept and as a practical tool, presenting a complete theory of the application of predictor feedback to time-invariant, uncertain systems with constant input delays and/or measurement delays. It supplies several methods for generating the necessary real-time solutions to the systems’ nonlinear differential equations, which the authors refer to as approximate predictors.Predictor feedback for linear time-invariant (LTI) systems is presented in Part I to provide a solid foundation on the necessary concepts, as LTI systems pose fewer technical difficulties than nonlinear systems. Part II extends all of the concepts to nonlinear time-invariant systems. Finally, Part III explores extensions of predictor feedback to systems described by integral delay equations and to discrete-time systems.The book’s core is the design of control and observer algorithms with which global stabilization, guaranteed in the previous literature with idealized (but non-implementable) predictors, is preserved with approximate predictors developed in the book.An applications-driven engineer will find a large number of explicit formulae, which are given throughout the book to assist in the application of the theory to a variety of control problems. A mathematician will find sophisticated new proof techniques, which are developed for the purpose of providing global stability guarantees for the nonlinear infinite-dimensional delay system under feedback laws employing practically implementable approximate predictors.Researchers working on global stabilization problems for time-delay systems will find this monograph to be a helpful summary of the state of the art, while graduate students in the broad field of systems and control will advance their skills in nonlinear control design and the analysis of nonlinear delay systems.

Rather than use integrals of the systems vector field, we employ Lie-bracket-based (i.e., derivative-based) averaging. The brief contains numerous examples and applications, including examples with unknown control directions and experiments with charged particle accelerators.

This monograph bridges the gap between the nonlinear predictor as a concept and as a practical tool, presenting a complete theory of the application of predictor feedback to time-invariant, uncertain systems with constant input delays and/or measurement delays. It supplies several methods for generating the necessary real-time solutions to the systems’ nonlinear differential equations, which the authors refer to as approximate predictors.Predictor feedback for linear time-invariant (LTI) systems is presented in Part I to provide a solid foundation on the necessary concepts, as LTI systems pose fewer technical difficulties than nonlinear systems. Part II extends all of the concepts to nonlinear time-invariant systems. Finally, Part III explores extensions of predictor feedback to systems described by integral delay equations and to discrete-time systems.The book’s core is the design of control and observer algorithms with which global stabilization, guaranteed in the previous literature with idealized (but non-implementable) predictors, is preserved with approximate predictors developed in the book.An applications-driven engineer will find a large number of explicit formulae, which are given throughout the book to assist in the application of the theory to a variety of control problems. A mathematician will find sophisticated new proof techniques, which are developed for the purpose of providing global stability guarantees for the nonlinear infinite-dimensional delay system under feedback laws employing practically implementable approximate predictors.Researchers working on global stabilization problems for time-delay systems will find this monograph to be a helpful summary of the state of the art, while graduate students in the broad field of systems and control will advance their skills in nonlinear control design and the analysis of nonlinear delay systems.