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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 for the first time examines periodic motions to chaos in time-delay systems, which exist extensively in engineering. For a long time, the stability of time-delay systems at equilibrium has been of great interest from the Lyapunov theory-based methods, where one cannot achieve the ideal results. Thus, time-delay discretization in time-delay systems was used for the stability of these systems. In this volume, Dr. Luo presents an accurate method based on the finite Fourier series to determine periodic motions in nonlinear time-delay systems. The stability and bifurcation of periodic motions are determined by the time-delayed system of coefficients in the Fourier series and the method for nonlinear time-delay systems is equivalent to the Laplace transformation method for linear time-delay systems. Facilitates discovery of analytical solutions of nonlinear time-delay systems; Illustrates bifurcation trees of periodic motions to chaos; Helps readers identify motion complexity and singularity; Explains procedures for determining stability, bifurcation and chaos.

Complexity, Computational. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Time delay control --- Time delay control systems --- Time delay controllers --- Time-delayed systems --- Engineering. --- Complexity. --- Complex Systems. --- Chaotic behavior in systems. --- Time delay systems. --- Feedback control systems --- Process control --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Construction --- Industrial arts --- Technology --- Computational complexity. --- System theory. --- Statistical physics. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Physics --- Mathematical statistics --- Systems, Theory of --- Systems science --- Science --- Statistical methods --- Philosophy