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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. Specific features and topics include: * A construction of explicit Lyapunov functionals, which can be used in control design or stability analysis, leading to a resolution of several long-standing problems in predictor feedback. * A detailed treatment of individual classes of problems—nonlinear ODEs, parabolic PDEs, first-order hyperbolic PDEs, second-order hyperbolic PDEs, known time-varying delays, unknown constant delays—will help the reader master the techniques presented. * Numerous examples ease a student new to delay systems into the topic. * Minimal prerequisites: the basics of function spaces and Lyapunov theory for ODEs. * The basics of Poincaré and Agmon inequalities, Lyapunov and input-to-state stability, parameter projection for adaptive control, and Bessel functions are summarized in appendices for the reader’s convenience. Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference for graduate students, researchers, and practitioners 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.

Delay lines. --- Feedback control systems. --- Nonlinear systems. --- Systems engineering. --- Feedback control systems --- Nonlinear systems --- Delay lines --- Adaptive control systems --- Civil & Environmental Engineering --- Mechanical Engineering --- Operations Research --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Mathematical models --- Adaptive control systems. --- Mathematical models. --- Systems, Nonlinear --- Feedback mechanisms --- Feedback systems --- Self-adaptive control systems --- Mathematics. --- Differential equations. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- System theory. --- Mechanical engineering. --- Control engineering. --- Applications of Mathematics. --- Systems Theory, Control. --- Control. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Mechanical Engineering. --- System theory --- Automatic control --- Automation --- Discrete-time systems --- Feedforward control systems --- Artificial intelligence --- Self-organizing systems --- Systems theory. --- Differential equations, partial. --- Differential Equations. --- Control and Systems Theory. --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- 517.91 Differential equations --- Differential equations --- Partial differential equations --- Math --- Science --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Systems, Theory of --- Systems science --- Engineering analysis --- Mathematical analysis --- Philosophy --- Mathematics --- Feedback control systems - Mathematical models --- Adaptive control systems - Mathematical models

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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. The basis of the approach used in the work is the recently developed continuous backstepping method for parabolic partial differential equations, expanding the applicability of boundary controllers for flow systems from low Reynolds numbers to high Reynolds number conditions. Efforts in flow control over the last few years have led to a wide range of developments in many different directions, but most implementable developments thus far have been obtained using discretized versions of the plant models and finite-dimensional control techniques. In contrast, the design methods examined in this book are based on the “continuum” version of the backstepping approach, applied to the PDE model of the flow. The postponement of spatial discretization until the implementation stage offers a range of numerical and analytical advantages. Specific topics and features: * Introduction of control and state estimation designs for flows that include thermal convection and electric conductivity, namely, flows where instability may be driven by thermal gradients and external magnetic fields. * Application of a special "backstepping" approach where the boundary control design is combined with a particular Volterra transformation of the flow variables, which yields not only the stabilization of the flow, but also the explicit solvability of the closed-loop system. * Presentation of a result unprecedented in fluid dynamics and in the analysis of Navier–Stokes equations: closed-form expressions for the solutions of linearized Navier–Stokes equations under feedback. * Extension of the backstepping approach to eliminate one of the well-recognized root causes of transition to turbulence: the decoupling of the Orr–Sommerfeld and Squire systems. Control of Turbulent and Magnetohydrodynamic Channel Flows 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 the above areas. The book may also be used as a supplementary text for graduate courses on control of distributed-parameter systems and on flow control. .

Boundary layer. --- Magnetohydrodynamics. --- Turbulence. --- Flow, Turbulent --- Turbulent flow --- Fluid dynamics --- Magneto-hydrodynamics --- MHD (Physics) --- Plasma dynamics --- Aerodynamics --- Systems theory. --- Hydraulic engineering. --- Differential equations, partial. --- Mechanical engineering. --- Engineering. --- Classical and Continuum Physics. --- Systems Theory, Control. --- Engineering Fluid Dynamics. --- Partial Differential Equations. --- Mechanical Engineering. --- Engineering Thermodynamics, Heat and Mass Transfer. --- System theory. --- Construction --- Industrial arts --- Technology --- Engineering, Mechanical --- Engineering --- Machinery --- Steam engineering --- Partial differential equations --- Engineering, Hydraulic --- Fluid mechanics --- Hydraulics --- Shore protection --- Systems, Theory of --- Systems science --- Science --- Philosophy --- Continuum physics. --- Fluid mechanics. --- Partial differential equations. --- Thermodynamics. --- Heat engineering. --- Heat transfer. --- Mass transfer. --- Mass transport (Physics) --- Thermodynamics --- Transport theory --- Heat transfer --- Thermal transfer --- Transmission of heat --- Energy transfer --- Heat --- Mechanical engineering --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat-engines --- Quantum theory --- Hydromechanics --- Continuum mechanics --- Classical field theory --- Continuum physics

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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.

Mathematics. --- System theory. --- Control engineering. --- Systems Theory, Control. --- Control. --- Computational intelligence. --- Time delay systems. --- Time delay control --- Time delay control systems --- Time delay controllers --- Time-delayed systems --- Feedback control systems --- Process control --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Systems theory. --- Control and Systems Theory. --- Systems theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Systems, Theory of --- Systems science --- Science --- Philosophy

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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.

Differential equations, Partial. --- Differential equations, partial. --- Telecommunication. --- Systems theory. --- Control and Systems Theory. --- Partial Differential Equations. --- Communications Engineering, Networks. --- Systems Theory, Control. --- Electric communication --- Mass communication --- Telecom --- Telecommunication industry --- Telecommunications --- Communication --- Information theory --- Telecommuting --- Partial differential equations --- Control engineering. --- Partial differential equations. --- Electrical engineering. --- System theory. --- Systems, Theory of --- Systems science --- Science --- Electric engineering --- Engineering --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Philosophy

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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. This book develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters.

Adaptive control systems --- Time delay systems --- Linear control systems --- Linear time invariant systems --- Differential equations, Linear. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Linear differential equations --- Linear systems --- Systems, Linear time invariant --- Discrete-time systems --- Automatic control --- Time delay control --- Time delay control systems --- Time delay controllers --- Time-delayed systems --- Feedback control systems --- Process control --- Self-adaptive control systems --- Artificial intelligence --- Self-organizing systems --- Mathematical models. --- Mathematics --- 3D printing. --- Multi-input systems. --- ODE delay notation. --- adaptive control of uncertain systems. --- aerospace engineering. --- backstepping transformation. --- biomedical engineering. --- chemical engineers. --- civil engineering. --- combustion systems. --- computer engineers. --- control designs. --- control synthesis techniques. --- control theorists. --- delay-related challenges. --- delayed telecommunication systems. --- delays in traffic flow dynamics. --- distinct discrete input delays. --- distributed input delays. --- electrical engineers. --- feedback of linear systems. --- finite-dimensional systems. --- global stability of nonlinear infinite-dimensional systems. --- mechanical engineers, aerospace engineers. --- multivariable multidelay systems. --- neuromuscular electrical stimulation. --- nonlinear infinite-dimensional stability study. --- process dynamic researchers. --- robotic manipulators. --- structural engineering. --- supply chains. --- time-delay systems. --- uncertainty combinations. --- unmanned aerial vehicles. --- unmeasured states.