Discrete-Time Control Systems

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

Design and deploy advanced vibration protection systems based on elastic composites under post-buckling, with this essential reference. Methods for designing vibration protection systems with negative and quasi-zero stiffness are formulated, explained, and demonstrated in practice. All key steps of the system design are covered, including the type and number synthesis, modelling and studying of stress-strain state under post-buckling of elastic composite designs, chaotic dynamics and stability conditions, real-time dimensioning, and active motion control. In addition to coverage of underlying theory, the use in helicopters, buses, railroad vehicles, construction equipment and agricultural machinery are included. An excellent reference for researchers and practicing engineers, as well as a tutorial for university students and professors with an interest in study, development and application of alternative methods of vibration protection anywhere.

Combining clear explanations of elementary principles, advanced topics and applications with step-by-step mathematical derivations, this textbook provides a comprehensive yet accessible introduction to digital signal processing. All the key topics are covered, including discrete-time Fourier transform, z-transform, discrete Fourier transform and FFT, A/D conversion, and FIR and IIR filtering algorithms, as well as more advanced topics such as multirate systems, the discrete cosine transform and spectral signal processing. Over 600 full-color illustrations, 200 fully worked examples, hundreds of end-of-chapter homework problems and detailed computational examples of DSP algorithms implemented in MATLAB® and C aid understanding, and help put knowledge into practice. A wealth of supplementary material accompanies the book online, including interactive programs for instructors, a full set of solutions and MATLAB® laboratory exercises, making this the ideal text for senior undergraduate and

Rivers are important agents of change that shape the Earth's surface and evolve through time in response to fluctuations in climate and other environmental conditions. They are fundamental in landscape development, and essential for water supply, irrigation, and transportation. This book provides a comprehensive overview of the geomorphological processes that shape rivers and that produce change in the form of rivers. It explores how the dynamics of rivers are being affected by anthropogenic change, including climate change, dam construction, and modification of rivers for flood control and land drainage. It discusses how concern about environmental degradation of rivers has led to the emergence of management strategies to restore and naturalize these systems, and how river management techniques work best when coordinated with the natural dynamics of rivers. This textbook provides an excellent resource for students, researchers, and professionals in fluvial geomorphology, hydrology, ri

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Mathematical analysis is key to the modeling and management of natural resources. By presenting required mathematical methods, classic dynamic models for non-renewable and renewable resources, and by exploring several contemporary problems, this text provides a foundation for advanced research. Topics include seminal models in fishery, forestry and non-renewable resource management, as well as an extensive collection of contemporary applications that include the optimal transition from fossil fuels to clean energy, the optimal timing of interventions to save endangered species, pest control and the optimal management of antibiotic resistance. Deterministic and stochastic models in both discrete and continuous time are covered. The book encourages students to pursue a deeper understanding of the analytics of resource problems and to deploy numerical methods when analytical results prove intractable. The combination of analysis, theory and applications will launch the next generation of

Digital Signal Processing:A Primer with MATLAB (R) provides excellent coverage of discrete-time signals and systems. At the beginning of each chapter, an abstract states the chapter objectives. All pr

The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier–Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.

This book combines a comprehensive state-of-the-art analysis of bifurcations of discrete-time dynamical systems with concrete instruction on implementations (and example applications) in the free MATLAB® software MatContM developed by the authors. While self-contained and suitable for independent study, the book is also written with users in mind and is an invaluable reference for practitioners. Part I focuses on theory, providing a systematic presentation of bifurcations of fixed points and cycles of finite-dimensional maps, up to and including cases with two control parameters. Several complementary methods, including Lyapunov exponents, invariant manifolds and homoclinic structures, and parts of chaos theory, are presented. Part II introduces MatContM through step-by-step tutorials on how to use the general numerical methods described in Part I for simple dynamical models defined by one- and two-dimensional maps. Further examples in Part III show how MatContM can be used to analyze

This new edition explains how vibrations can be used in a broad spectrum of applications and how to meet the challenges faced by engineers and system designers. The text integrates linear and nonlinear systems, and covers the time domain and the frequency domain, responses to harmonic and transient excitations, and discrete and continuous system models. It focuses on modeling, analysis, prediction, and measurement to provide a complete understanding of the underlying physical vibratory phenomena and their relevance for engineering design. Knowledge is put into practice through numerous examples with real-world applications in a range of disciplines, detailed design guidelines applicable to various vibratory systems, and over forty online interactive graphics which provide a visual summary of system behaviors and enable students to carry out their own parametric studies. Some thirteen new tables act as a quick reference for self-study, detailing key characteristics of physical systems a

Intelligent Control of Connected Plug-in Hybrid Electric Vehicles presents the development of real-time intelligent control systems for plug-in hybrid electric vehicles, which involves control-oriente

Reporting a novel breakthrough in the identification and investigation of solvable and integrable nonlinearly coupled evolution ordinary differential equations (ODEs) or partial differential equations (PDEs), this text includes practical examples throughout to illustrate the theoretical concepts. Beginning with systems of ODEs, including second-order ODEs of Newtonian type, it then discusses systems of PDEs, and systems evolving in discrete time. It reports a novel, differential algorithm which can be used to evaluate all the zeros of a generic polynomial of arbitrary degree: a remarkable development of a fundamental mathematical problem with a long history. The book will be of interest to applied mathematicians and mathematical physicists working in the area of integrable and solvable non-linear evolution equations; it can also be used as supplementary reading material for general applied mathematics or mathematical physics courses.

Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustnessThe interest in finite-time control has continu

This book covers block pulse and related functions for the analysis and identification of continuous and discrete-time systems. It covers ‘functions related to block pulse functions’ and pulse-width m

Reliability Modelling and Analysis in Discrete Time provides an overview of the probabilistic and statistical aspects connected with discrete reliability systems. This engaging book discusses their di

The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reprodu

The proceedings of the summer school held at the Université Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations.

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorith

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorith

This volume is the first to present a unified perspective on the control of underactuated mechanical systems. Based on real-time implementation of parameter identification, this book provides a variet

This book assembles new methods showing the automotive engineer for the first time how hybrid vehicle configurations can be modeled as systems with discrete and continuous controls. These hybrid syste

This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing termina

This tutorial reference takes the reader from use cases to complete architectures for real-time embedded systems using SysML, UML, and MARTE and shows how to apply the COMET/RTE design method to real-world problems. The author covers key topics such as architectural patterns for distributed and hierarchical real-time control and other real-time software architectures, performance analysis of real-time designs using real-time scheduling, and timing analysis on single and multiple processor systems. Complete case studies illustrating design issues include a light rail control system, a microwave oven control system, and an automated highway toll system. Organized as an introduction followed by several self-contained chapters, the book is perfect for experienced software engineers wanting a quick reference at each stage of the analysis, design, and development of large-scale real-time embedded systems, as well as for advanced undergraduate or graduate courses in software engineering, comp

This book develops a coherent theoretical approach to algorithm design for iterative learning control based on the use of optimization concepts. Concentrating initially on linear, discrete-time system

Designed for a three-hour semester course on signals and systems, this textbook presents continuous-time and discrete-time signals and systems to electrical and computer engineering students in a mann

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for

Optimization of a dynamic system has immense importance in Management Science. Both discrete time and continuous time optimal control systems are very useful instruments in this regard. To simulate un

Variance-Constrained Multi-Objective Stochastic Control and Filtering establishes a unified framework for filtering and control problems for various discrete-time nonlinear stochastic systems with eng

This book covers the modeling, analysis, and design of linear discrete control systems, providing case studies of practical implementations. It describes z- and modified z-transforms, sampling and dat

This book focuses on filtering, control and model-reduction problems for two-dimensional (2-D) systems with imperfect information. The time-delayed 2-D systems covered have system parameters subject t

Real-time systems are used in a wide range of applications, including control, sensing, multimedia, etc. Scheduling is a central problem for these computing/communication systems since responsible of

Real-time systems are used in a wide range of applications,including control, sensing, multimedia, etc. Scheduling is acentral problem for these computing/communication systems since itis responsible

This monograph introduces a newly developed robust-control design technique for a wide class of continuous-time dynamical systems called the “attractive ellipsoid method.” Along with a coherent introd

Dependability metrics are omnipresent in every engineering field, from simple ones through to more complex measures combining performance and dependability aspects of systems. This book presents the mathematical basis of the analysis of these metrics in the most used framework, Markov models, describing both basic results and specialised techniques. The authors first present both discrete and continuous time Markov chains before focusing on dependability measures, which necessitate the study of Markov chains on a subset of states representing different user satisfaction levels for the modelled system. Topics covered include Markovian state lumping, analysis of sojourns on subset of states of Markov chains, analysis of most dependability metrics, fundamentals of performability analysis, and bounding and simulation techniques designed to evaluate dependability measures. The book is of interest to graduate students and researchers in all areas of engineering where the concepts of lifetime

This textbook offers a fresh approach to digital signal processing (DSP) that combines heuristic reasoning and physical appreciation with sound mathematical methods to illuminate DSP concepts and practices. It uses metaphors, analogies and creative explanations, along with examples and exercises to provide deep and intuitive insights into DSP concepts. Practical DSP requires hybrid systems including both discrete- and continuous-time components. This book follows a holistic approach and presents discrete-time processing as a seamless continuation of continuous-time signals and systems, beginning with a review of continuous-time signals and systems, frequency response, and filtering. The synergistic combination of continuous-time and discrete-time perspectives leads to a deeper appreciation and understanding of DSP concepts and practices. • For upper-level undergraduates • Illustrates concepts with 500 high-quality figures, more than 170 fully worked examples, and hundreds of end-of-ch

This book describes recent advances on hybrid intelligent systems using soft computing techniques for diverse areas of application, such as intelligent control and robotics, pattern recognition, time

This textbook is ideal for a course in engineering systems dynamics and controls. The work is a comprehensive treatment of the analysis of lumped parameter physical systems. Starting with a discussion of mathematical models in general, and ordinary differential equations, the book covers input/output and state space models, computer simulation and modeling methods and techniques in mechanical, electrical, thermal and fluid domains. Frequency domain methods, transfer functions and frequency response are covered in detail. The book concludes with a treatment of stability, feedback control (PID, lead-lag, root locus) and an introduction to discrete time systems. This new edition features many new and expanded sections on such topics as: solving stiff systems, operational amplifiers, electrohydraulic servovalves, using Matlab with transfer functions, using Matlab with frequency response, Matlab tutorial and an expanded Simulink tutorial. The work has 40% more end-of-chapter exercises and 3

This exciting reference text is concerned with fluid power control. It is an ideal reference for the practising engineer and a textbook for advanced courses in fluid power control. In applications in which large forces and/or torques are required, often with a fast response time, oil-hydraulic control systems are essential. They excel in environmentally difficult applications because the drive part can be designed with no electrical components and they almost always have a more competitive power/weight ratio compared to electrically actuated systems. Fluid power systems have the capability to control several parameters, such as pressure, speed, position, and so on, to a high degree of accuracy at high power levels. In practice there are many exciting challenges facing the fluid power engineer, who now must preferably have a broad skill set.