Investigation on Robust Codesign Methods for Networked Control Systems

Investigation on Robust Codesign Methods for Networked Control Systems

Author: Sanad Al-Areqi

Publisher: Logos Verlag Berlin GmbH

Published: 2015-12-31

Total Pages: 180

ISBN-13: 3832541705

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The problem of jointly designing a robust controller and an intelligent scheduler for networked control systems (NCSs) is addressed in this thesis. NCSs composing of multiple plants that share a single channel communication network with uncertain time-varying transmission times are modeled as switched polytopic systems with additive norm-bounded uncertainty. Switching is deployed to represent scheduling, the polytopic uncertainty to overapproximatively describe the uncertain time-varying transmission times. Based on the resulting NCS model and a state feedback control law, the control and scheduling codesign problem is then introduced and formulated as a robust (minimax) optimization problem with the objective of minimizing the worst-case value of an associated infinite time-horizon quadratic cost function. Five robust codesign strategies are investigated for tackling the introduced optimization problem, namely: Periodic control and scheduling (PCS), Receding-horizon control and scheduling (RHCS), Implementation-aware control and scheduling (IACS), Event-based control and scheduling (EBCS), Prediction-based control and scheduling (PBCS). All these codesign strategies are determined from LMI optimization problems based on the Lyapunov theory. The properties of each are evaluated and compared in terms of computational complexity and control performance based on simulation and experimental study, showing their effectiveness in improving the performance while utilizing the limited communication resources very efficiently.


Book Synopsis Investigation on Robust Codesign Methods for Networked Control Systems by : Sanad Al-Areqi

Download or read book Investigation on Robust Codesign Methods for Networked Control Systems written by Sanad Al-Areqi and published by Logos Verlag Berlin GmbH. This book was released on 2015-12-31 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of jointly designing a robust controller and an intelligent scheduler for networked control systems (NCSs) is addressed in this thesis. NCSs composing of multiple plants that share a single channel communication network with uncertain time-varying transmission times are modeled as switched polytopic systems with additive norm-bounded uncertainty. Switching is deployed to represent scheduling, the polytopic uncertainty to overapproximatively describe the uncertain time-varying transmission times. Based on the resulting NCS model and a state feedback control law, the control and scheduling codesign problem is then introduced and formulated as a robust (minimax) optimization problem with the objective of minimizing the worst-case value of an associated infinite time-horizon quadratic cost function. Five robust codesign strategies are investigated for tackling the introduced optimization problem, namely: Periodic control and scheduling (PCS), Receding-horizon control and scheduling (RHCS), Implementation-aware control and scheduling (IACS), Event-based control and scheduling (EBCS), Prediction-based control and scheduling (PBCS). All these codesign strategies are determined from LMI optimization problems based on the Lyapunov theory. The properties of each are evaluated and compared in terms of computational complexity and control performance based on simulation and experimental study, showing their effectiveness in improving the performance while utilizing the limited communication resources very efficiently.

Packet-Based Control for Networked Control Systems

Packet-Based Control for Networked Control Systems

Author: Yun-Bo Zhao

Publisher: Springer

Published: 2017-09-14

Total Pages: 184

ISBN-13: 9811062501

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This book introduces a unique, packet-based co-design control framework for networked control systems. It begins by providing a comprehensive survey of state-of-the-art research on networked control systems, giving readers a general overview of the field. It then verifies the proposed control framework both theoretically and experimentally – the former using multiple control methodologies, and the latter using a unique online test rig for networked control systems. The framework investigates in detail the most common, communication constraints, including network-induced delays, data packet dropout, data packet disorders, and network access constraints, as well as multiple controller design and system analysis tools such as model predictive control, linear matrix inequalities and optimal control. This unique and complete co-design framework greatly benefits researchers, graduate students and engineers in the fields of control theory and engineering.


Book Synopsis Packet-Based Control for Networked Control Systems by : Yun-Bo Zhao

Download or read book Packet-Based Control for Networked Control Systems written by Yun-Bo Zhao and published by Springer. This book was released on 2017-09-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a unique, packet-based co-design control framework for networked control systems. It begins by providing a comprehensive survey of state-of-the-art research on networked control systems, giving readers a general overview of the field. It then verifies the proposed control framework both theoretically and experimentally – the former using multiple control methodologies, and the latter using a unique online test rig for networked control systems. The framework investigates in detail the most common, communication constraints, including network-induced delays, data packet dropout, data packet disorders, and network access constraints, as well as multiple controller design and system analysis tools such as model predictive control, linear matrix inequalities and optimal control. This unique and complete co-design framework greatly benefits researchers, graduate students and engineers in the fields of control theory and engineering.

Optimal and Robust Scheduling for Networked Control Systems

Optimal and Robust Scheduling for Networked Control Systems

Author: Stefano Longo

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 277

ISBN-13: 1466569557

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Optimal and Robust Scheduling for Networked Control Systems tackles the problem of integrating system components—controllers, sensors, and actuators—in a networked control system. It is common practice in industry to solve such problems heuristically, because the few theoretical results available are not comprehensive and cannot be readily applied by practitioners. This book offers a solution to the deterministic scheduling problem that is based on rigorous control theoretical tools but also addresses practical implementation issues. Helping to bridge the gap between control theory and computer science, it suggests that the consideration of communication constraints at the design stage will significantly improve the performance of the control system. Technical Results, Design Techniques, and Practical Applications The book brings together well-known measures for robust performance as well as fast stochastic algorithms to assist designers in selecting the best network configuration and guaranteeing the speed of offline optimization. The authors propose a unifying framework for modelling NCSs with time-triggered communication and present technical results. They also introduce design techniques, including for the codesign of a controller and communication sequence and for the robust design of a communication sequence for a given controller. Case studies explore the use of the FlexRay TDMA and time-triggered control area network (CAN) protocols in an automotive control system. Practical Solutions to Your Time-Triggered Communication Problems This unique book develops ready-to-use engineering tools for large-scale control system integration with a focus on robustness and performance. It emphasizes techniques that are directly applicable to time-triggered communication problems in the automotive industry and in avionics, robotics, and automated manufacturing.


Book Synopsis Optimal and Robust Scheduling for Networked Control Systems by : Stefano Longo

Download or read book Optimal and Robust Scheduling for Networked Control Systems written by Stefano Longo and published by CRC Press. This book was released on 2018-09-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal and Robust Scheduling for Networked Control Systems tackles the problem of integrating system components—controllers, sensors, and actuators—in a networked control system. It is common practice in industry to solve such problems heuristically, because the few theoretical results available are not comprehensive and cannot be readily applied by practitioners. This book offers a solution to the deterministic scheduling problem that is based on rigorous control theoretical tools but also addresses practical implementation issues. Helping to bridge the gap between control theory and computer science, it suggests that the consideration of communication constraints at the design stage will significantly improve the performance of the control system. Technical Results, Design Techniques, and Practical Applications The book brings together well-known measures for robust performance as well as fast stochastic algorithms to assist designers in selecting the best network configuration and guaranteeing the speed of offline optimization. The authors propose a unifying framework for modelling NCSs with time-triggered communication and present technical results. They also introduce design techniques, including for the codesign of a controller and communication sequence and for the robust design of a communication sequence for a given controller. Case studies explore the use of the FlexRay TDMA and time-triggered control area network (CAN) protocols in an automotive control system. Practical Solutions to Your Time-Triggered Communication Problems This unique book develops ready-to-use engineering tools for large-scale control system integration with a focus on robustness and performance. It emphasizes techniques that are directly applicable to time-triggered communication problems in the automotive industry and in avionics, robotics, and automated manufacturing.

Modelling and Control of an Autonomous Two-Wheeled Vehicle

Modelling and Control of an Autonomous Two-Wheeled Vehicle

Author: Alen Turnwald

Publisher: Logos Verlag Berlin GmbH

Published: 2020-11-13

Total Pages: 175

ISBN-13: 3832552057

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With respect to the future urban mobility, modern electrical bicycles, advanced motorcycles and innovative two-wheeled vehicles are arresting enormous amount of attention. Especially, model-based control and optimal trajectory planning for such vehicles are important to the research and development of the future. Therefore, a reliable and yet usable vehicle model as well as a systematic approach to motion control for two-wheeled vehicles are essential, to which this work makes a contribution. Currently available two-wheeled vehicle models are mostly either too complex to be used for a systematic control synthesis, or too simple such that the physical behaviour of the vehicle is no more represented. In this thesis, a unifying approach to modelling and control for autonomous two-wheeled vehicles is presented. The resulting model is generally valid and physically detailed enough to represent the characteristic dynamical behaviour such as the self-stability. At the same time, it is suited to a systematic control synthesis. Furthermore, the systematic extenddability, for instance by a rider, is demonstrated. The model is validated by simulations and by comparison to well-known models from the literature. The proposed vehicle model is derived in the Lagrangian and Hamiltonian framework and used for model-based optimal trajectory planning. Furthermore, a passivity-based trajectory tracking controller is designed based on the resulting port-Hamiltonian system using the so-called generalised canonical transformations. Such a controller is physically interpretable and robust against parameter uncertainties. To this end, existing approaches of passivity-based controller design are extended and adjusted for two-wheeled vehicles. Finally, a prototype two-wheeled vehicle is introduced which is used for experimental validation of the model and to demonstrate motion control algorithms for autonomous two-wheeled vehicles.


Book Synopsis Modelling and Control of an Autonomous Two-Wheeled Vehicle by : Alen Turnwald

Download or read book Modelling and Control of an Autonomous Two-Wheeled Vehicle written by Alen Turnwald and published by Logos Verlag Berlin GmbH. This book was released on 2020-11-13 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: With respect to the future urban mobility, modern electrical bicycles, advanced motorcycles and innovative two-wheeled vehicles are arresting enormous amount of attention. Especially, model-based control and optimal trajectory planning for such vehicles are important to the research and development of the future. Therefore, a reliable and yet usable vehicle model as well as a systematic approach to motion control for two-wheeled vehicles are essential, to which this work makes a contribution. Currently available two-wheeled vehicle models are mostly either too complex to be used for a systematic control synthesis, or too simple such that the physical behaviour of the vehicle is no more represented. In this thesis, a unifying approach to modelling and control for autonomous two-wheeled vehicles is presented. The resulting model is generally valid and physically detailed enough to represent the characteristic dynamical behaviour such as the self-stability. At the same time, it is suited to a systematic control synthesis. Furthermore, the systematic extenddability, for instance by a rider, is demonstrated. The model is validated by simulations and by comparison to well-known models from the literature. The proposed vehicle model is derived in the Lagrangian and Hamiltonian framework and used for model-based optimal trajectory planning. Furthermore, a passivity-based trajectory tracking controller is designed based on the resulting port-Hamiltonian system using the so-called generalised canonical transformations. Such a controller is physically interpretable and robust against parameter uncertainties. To this end, existing approaches of passivity-based controller design are extended and adjusted for two-wheeled vehicles. Finally, a prototype two-wheeled vehicle is introduced which is used for experimental validation of the model and to demonstrate motion control algorithms for autonomous two-wheeled vehicles.

A Hybrid Physical and Data-drivApproach to Motion Prediction and Control in Human-Robot Collaboration

A Hybrid Physical and Data-drivApproach to Motion Prediction and Control in Human-Robot Collaboration

Author: Min Wu

Publisher: Logos Verlag Berlin GmbH

Published: 2022-06-14

Total Pages: 212

ISBN-13: 383255484X

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In recent years, researchers have achieved great success in guaranteeing safety in human-robot interaction, yielding a new generation of robots that can work with humans in close proximity, known as collaborative robots (cobots). However, due to the lack of ability to understand and coordinate with their human partners, the ``co'' in most cobots still refers to ``coexistence'' rather than ``collaboration''. This thesis aims to develop an adaptive learning and control framework with a novel physical and data-driven approach towards a real collaborative robot. The first part focuses on online human motion prediction. A comprehensive study on various motion prediction techniques is presented, including their scope of application, accuracy in different time scales, and implementation complexity. Based on this study, a hybrid approach that combines physically well-understood models with data-driven learning techniques is proposed and validated through a motion data set. The second part addresses interaction control in human-robot collaboration. An adaptive impedance control scheme with human reference estimation is presented. Reinforcement learning is used to find optimal control parameters to minimize a task-orient cost function without fully knowing the system dynamic. The proposed framework is experimentally validated through two benchmark applications for human-robot collaboration: object handover and cooperative object handling. Results show that the robot can provide reliable online human motion prediction, react early to human motion variation, make proactive contributions to physical collaborations, and behave compliantly in response to human forces.


Book Synopsis A Hybrid Physical and Data-drivApproach to Motion Prediction and Control in Human-Robot Collaboration by : Min Wu

Download or read book A Hybrid Physical and Data-drivApproach to Motion Prediction and Control in Human-Robot Collaboration written by Min Wu and published by Logos Verlag Berlin GmbH. This book was released on 2022-06-14 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, researchers have achieved great success in guaranteeing safety in human-robot interaction, yielding a new generation of robots that can work with humans in close proximity, known as collaborative robots (cobots). However, due to the lack of ability to understand and coordinate with their human partners, the ``co'' in most cobots still refers to ``coexistence'' rather than ``collaboration''. This thesis aims to develop an adaptive learning and control framework with a novel physical and data-driven approach towards a real collaborative robot. The first part focuses on online human motion prediction. A comprehensive study on various motion prediction techniques is presented, including their scope of application, accuracy in different time scales, and implementation complexity. Based on this study, a hybrid approach that combines physically well-understood models with data-driven learning techniques is proposed and validated through a motion data set. The second part addresses interaction control in human-robot collaboration. An adaptive impedance control scheme with human reference estimation is presented. Reinforcement learning is used to find optimal control parameters to minimize a task-orient cost function without fully knowing the system dynamic. The proposed framework is experimentally validated through two benchmark applications for human-robot collaboration: object handover and cooperative object handling. Results show that the robot can provide reliable online human motion prediction, react early to human motion variation, make proactive contributions to physical collaborations, and behave compliantly in response to human forces.

Control Strategies and Co-Design of Networked Control Systems

Control Strategies and Co-Design of Networked Control Systems

Author: Héctor Benítez-Pérez

Publisher: Springer

Published: 2018-07-31

Total Pages: 178

ISBN-13: 3319970445

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This book presents Networked Control System (NCS) as a particular kind of a real-time distributed system (RTDS), composed of a set of nodes, interconnected by a network, and able to develop a complete control process. It describes important parts of the control process such as sensor and actuator activities, which rely on a real-time operating system, and a real-time communication network. As the use of common bus network architecture introduces different forms of uncertainties between sensors, actuators, and controllers, several approaches such as reconfigurable systems have been developed to tackle this problem. Moreover, modeling NCS is a challenging procedure, since there are several non-linear situations, like local saturations, uncertain time delays, dead-zones, or local situations, it is necessary to deal with. The book describes a novel strategy for modelling and control based on a fuzzy control approach and codesign strategies.


Book Synopsis Control Strategies and Co-Design of Networked Control Systems by : Héctor Benítez-Pérez

Download or read book Control Strategies and Co-Design of Networked Control Systems written by Héctor Benítez-Pérez and published by Springer. This book was released on 2018-07-31 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents Networked Control System (NCS) as a particular kind of a real-time distributed system (RTDS), composed of a set of nodes, interconnected by a network, and able to develop a complete control process. It describes important parts of the control process such as sensor and actuator activities, which rely on a real-time operating system, and a real-time communication network. As the use of common bus network architecture introduces different forms of uncertainties between sensors, actuators, and controllers, several approaches such as reconfigurable systems have been developed to tackle this problem. Moreover, modeling NCS is a challenging procedure, since there are several non-linear situations, like local saturations, uncertain time delays, dead-zones, or local situations, it is necessary to deal with. The book describes a novel strategy for modelling and control based on a fuzzy control approach and codesign strategies.

Optimal and Robust Scheduling for Networked Control Systems

Optimal and Robust Scheduling for Networked Control Systems

Author: Stefano Longo

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 280

ISBN-13: 1351831879

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Optimal and Robust Scheduling for Networked Control Systems tackles the problem of integrating system components—controllers, sensors, and actuators—in a networked control system. It is common practice in industry to solve such problems heuristically, because the few theoretical results available are not comprehensive and cannot be readily applied by practitioners. This book offers a solution to the deterministic scheduling problem that is based on rigorous control theoretical tools but also addresses practical implementation issues. Helping to bridge the gap between control theory and computer science, it suggests that the consideration of communication constraints at the design stage will significantly improve the performance of the control system. Technical Results, Design Techniques, and Practical Applications The book brings together well-known measures for robust performance as well as fast stochastic algorithms to assist designers in selecting the best network configuration and guaranteeing the speed of offline optimization. The authors propose a unifying framework for modelling NCSs with time-triggered communication and present technical results. They also introduce design techniques, including for the codesign of a controller and communication sequence and for the robust design of a communication sequence for a given controller. Case studies explore the use of the FlexRay TDMA and time-triggered control area network (CAN) protocols in an automotive control system. Practical Solutions to Your Time-Triggered Communication Problems This unique book develops ready-to-use engineering tools for large-scale control system integration with a focus on robustness and performance. It emphasizes techniques that are directly applicable to time-triggered communication problems in the automotive industry and in avionics, robotics, and automated manufacturing.


Book Synopsis Optimal and Robust Scheduling for Networked Control Systems by : Stefano Longo

Download or read book Optimal and Robust Scheduling for Networked Control Systems written by Stefano Longo and published by CRC Press. This book was released on 2018-09-03 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal and Robust Scheduling for Networked Control Systems tackles the problem of integrating system components—controllers, sensors, and actuators—in a networked control system. It is common practice in industry to solve such problems heuristically, because the few theoretical results available are not comprehensive and cannot be readily applied by practitioners. This book offers a solution to the deterministic scheduling problem that is based on rigorous control theoretical tools but also addresses practical implementation issues. Helping to bridge the gap between control theory and computer science, it suggests that the consideration of communication constraints at the design stage will significantly improve the performance of the control system. Technical Results, Design Techniques, and Practical Applications The book brings together well-known measures for robust performance as well as fast stochastic algorithms to assist designers in selecting the best network configuration and guaranteeing the speed of offline optimization. The authors propose a unifying framework for modelling NCSs with time-triggered communication and present technical results. They also introduce design techniques, including for the codesign of a controller and communication sequence and for the robust design of a communication sequence for a given controller. Case studies explore the use of the FlexRay TDMA and time-triggered control area network (CAN) protocols in an automotive control system. Practical Solutions to Your Time-Triggered Communication Problems This unique book develops ready-to-use engineering tools for large-scale control system integration with a focus on robustness and performance. It emphasizes techniques that are directly applicable to time-triggered communication problems in the automotive industry and in avionics, robotics, and automated manufacturing.

Co-design Approaches to Dependable Networked Control Systems

Co-design Approaches to Dependable Networked Control Systems

Author: Daniel Simon

Publisher: John Wiley & Sons

Published: 2013-03-04

Total Pages: 261

ISBN-13: 1118620666

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Networked Control Systems (NCS) is a growing field of application and calls for the development of integrated approaches requiring multidisciplinary skills in control, real-time computing and communication protocols. This book describes co-design approaches, and establishes the links between the QoC (Quality of Control) and QoS (Quality of Service) of the network and computing resources. The methods and tools described in this book take into account, at design level, various parameters and properties that must be satisfied by systems controlled through a network. Among the important network properties examined are the QoC, the dependability of the system, and the feasibility of the real-time scheduling of tasks and messages. Correct exploitation of these approaches allows for efficient design, diagnosis, and implementation of the NCS. This book will be of great interest to researchers and advanced students in automatic control, real-time computing, and networking domains, and to engineers tasked with development of NCS, as well as those working in related network design and engineering fields.


Book Synopsis Co-design Approaches to Dependable Networked Control Systems by : Daniel Simon

Download or read book Co-design Approaches to Dependable Networked Control Systems written by Daniel Simon and published by John Wiley & Sons. This book was released on 2013-03-04 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: Networked Control Systems (NCS) is a growing field of application and calls for the development of integrated approaches requiring multidisciplinary skills in control, real-time computing and communication protocols. This book describes co-design approaches, and establishes the links between the QoC (Quality of Control) and QoS (Quality of Service) of the network and computing resources. The methods and tools described in this book take into account, at design level, various parameters and properties that must be satisfied by systems controlled through a network. Among the important network properties examined are the QoC, the dependability of the system, and the feasibility of the real-time scheduling of tasks and messages. Correct exploitation of these approaches allows for efficient design, diagnosis, and implementation of the NCS. This book will be of great interest to researchers and advanced students in automatic control, real-time computing, and networking domains, and to engineers tasked with development of NCS, as well as those working in related network design and engineering fields.

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition

Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition

Author:

Publisher: ScholarlyEditions

Published: 2013-05-01

Total Pages: 1187

ISBN-13: 1490110119

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Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Random Structures and Algorithms. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Random Structures and Algorithms in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.


Book Synopsis Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition by :

Download or read book Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Random Structures and Algorithms. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Random Structures and Algorithms in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Control and Scheduling Codesign

Control and Scheduling Codesign

Author: Feng Xia

Publisher: Springer Science & Business Media

Published: 2008-10-11

Total Pages: 256

ISBN-13: 3540782559

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With emphasis on flexible resource management in networked and embedded real-time control systems operating in dynamic environments with uncertainty, this book is devoted to the integration of control with computing and communication. It covers the authors' recent and original research results within a unified framework of feedback scheduling. This useful reference also includes rich example problems, case studies, and extensive references to the literature.


Book Synopsis Control and Scheduling Codesign by : Feng Xia

Download or read book Control and Scheduling Codesign written by Feng Xia and published by Springer Science & Business Media. This book was released on 2008-10-11 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: With emphasis on flexible resource management in networked and embedded real-time control systems operating in dynamic environments with uncertainty, this book is devoted to the integration of control with computing and communication. It covers the authors' recent and original research results within a unified framework of feedback scheduling. This useful reference also includes rich example problems, case studies, and extensive references to the literature.