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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank

Mathematical models. --- Nonlinear systems. --- Mechanics, Applied. --- Discrete-time systems. --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics

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This first volume is concerned with discrete systems - the study of which constitutes the cornerstone of all mechanical systems, linear or non-linear. It covers the formulation of equations of motion and the systematic study of free and forced vibrations. The book goes into detail about subjects such as generalized coordinates and kinematical conditions; Hamilton's principle and Lagrange equations; linear algebra in N-dimensional linear spaces and the orthogonal basis of natural modes of vibration of conservative systems. Also included are the Laplace transform and forced responses of linear d

Mechanics, Applied. --- Discrete-time systems. --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics

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The book begins by introducing signals and systems, and then discusses Time-Domain analysis and Frequency-Domain analysis for Continuous-Time systems. It also covers Z-transform, state-space analysis and system synthesis. The author provides abundant examples and exercises to facilitate learning, preparing students for subsequent courses on circuit analysis and communication theory.

Discrete-time systems. --- System analysis. --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems

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This book belongs to the subject of control and systems theory. The discrete-time adaptive iterative learning control (DAILC) is discussed as a cutting-edge of ILC and can address random initial states, iteration-varying targets, and other non-repetitive uncertainties in practical applications. This book begins with the design and analysis of model-based DAILC methods by referencing the tools used in the discrete-time adaptive control theory. To overcome the extreme difficulties in modeling a complex system, the data-driven DAILC methods are further discussed by building a linear parametric data mapping between two consecutive iterations. Other significant improvements and extensions of the model-based/data-driven DAILC are also studied to facilitate broader applications. The readers can learn the recent progress on DAILC with consideration of various applications. This book is intended for academic scholars, engineers and graduate students who are interested in learning control, adaptive control, nonlinear systems, and related fields.

Control theory. --- Discrete-time systems. --- Iterative methods (Mathematics). --- Iteration (Mathematics) --- Numerical analysis --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Dynamics --- Machine theory --- Engineering. --- Construction --- Industrial arts --- Technology

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Automatic control. --- Control theory. --- Discrete-time systems. --- DES (System analysis) --- Discrete event systems --- Sampled-data systems --- Digital control systems --- Discrete mathematics --- System analysis --- Linear time invariant systems --- Dynamics --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers