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We study solution concepts and their properties for hybrid systems that can flow and jump, affected by continuous-time inputs. While the solution concepts, the existence of solutions and (forward) completeness properties are extensively discussed in the absence of (external) inputs, there are surprisingly few results when inputs are present, certainly in the case where the flow and jump sets depend on the inputs. Given the relevance of this class of hybrid systems for many applications such as hybrid or networked control for plants subject to disturbances or measurement noise, we discuss in this paper notions of solutions in the presence of inputs and show through various examples the subtleties that can occur. Moreover, we provide tools to guarantee the existence of solutions and results to establish completeness properties.

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Stable operation of axial and centrifugal compressors is limited towards low mass flows due to the onset of surge. The stable operating region can be enlarged by active control. In this study, we use a control valve which is nominally closed and only opens to stabilize the system around the desired operating point. Hence, only non-negative control values are allowed which complicates the controller design considerably. A novel positive feedback controller is proposed with clear design parameters to obtain a desirable closedloop behavior. The technique has successfully been applied to a compression system model. For arbitrarily large control valve capacities, the system can be stabilized in the entire operating region. Simulations show that the surge point mass flow can be reduced up to 15% for the relatively small control valve to be implemented on the actual installation. Using this efficient control strategy, the stabilized operating point is reached with zero control valve mass flow.

ForewordThis book finds its origin in the WIDE PhD School on Networked Control Systems, which we organized in July 2009 in Siena, Italy. Having gathered experts on all the aspects of networked control systems, it was a small step to go from the summer school to the book, certainly given the enthusiasm of the lecturers at the school. We felt that a book collecting overviews on the important developments and open problems in the field of networked control systems could stimulate and support future research in this appealing area. Given the tremendous current interests in distributed control exploiting wired and wireless communication networks, the time seemed to be right for the book that lies now in front of you.The goal of the book is to set out the core techniques and tools that are available for the modeling, analysis and design of networked control systems. Roughly speaking, the book consists of three parts. The first part presents architectures for distributed control systems and models of wired and wireless communication networks. In particular, in the first chapter important technological and architectural aspects on distributed control systems are discussed. The second chapter provides insight in the behavior of communication channels in terms of delays, packet loss and information constraints leading to suitable modeling paradigms for communication networks.The second part focuses on decentralized and distributed control, estimation and optimization. The network aspect is here that not all information is available in one central controller, estimator or optimizer, but local agents have only limited information of the overall control, estimation or optimization problem and still aim at solving the central problem in an appropriate manner. Although the information might be limited for each individual agent, it is assumed that communication is ideal and imperfections such as communication delays, possible loss of information and quantization effects are ignored. Chapter 3 discusses distributed estimation and consensus problems and the fourth chapter surveys distributed optimization techniques. Chapter 5 and 6 provide overviews on decentralized and distributed control. The emphasis in chapter 5 is on decentralized and distributed model predictive control techniques. VI ForewordWhile communication imperfections induced by the presence of a non-ideal and uncertain network channel are ignored in the second part of the book, they form the main topic of the third part. Methods for stability analysis and controller synthesis of control loops closed over communication channels are treated in chapter 7. Using appropriate models of networked control systems it is investigated how networkinduced phenomena such as varying delays, varying sampling intervals, data loss and communication constraints influence the stability and performance of control loops. Chapter 8 studies the effects of the limited capacity of channels, e.g. limited bandwidth, on feedback control. Fundamental limitations in control using quantized infor...