Book Abstract: Max-plus linear systems theory was inspired by and originated from classical linear systems theory more than three decades ago, with the purpose of dealing with nonlinear synchronization and delay phenomena in timed discrete event systems in a linear manner. Timed discrete event systems describe many problems in diverse areas such as manufacturing, communication, or transportation networks. This monograph provides a thorough survey of current research work in max-plus linear systems. It summarizes the main mathematical concepts required for a theory of max-plus linear systems, including idempotent semirings, residuation theory, fixed point equations in the max-plus algebra, formal power series, and timed-event graphs. The authors also review some recent major achievements in control and state estimation of max-plus linear systems. These include max-plus observer design, max-plus model matching by output or state feedback and observer-based control synthesis. Control and State Estimation for Max-Plus Linear Systems offers students, practitioners, and researchers an accessible and comprehensive overview of the most important recent work in max-plus Linear Systems.

Distributed Averaging and Balancing in Network Systems: with Applications to Coordination and Control

The problem addressed in this document concerns the coordinated allocation of a finite set of reusable resources to a set of concurrently running processes. These processes execute in a staged manner, and each stage requires a different subset of the system resources for its support. Furthermore, processes will hold upon the resources currently allocated to them until they will secure the necessary resources for their next processing stage. Such resource allocation dynamics currently arise in the context of many flexibly automated operations: from the workflow that takes place in various production shop floors and certain internet-supported platforms that seek to automate various service operations; to the traffic coordination in guidepath-based transport systems like industrial monorail and urban railway systems; to the resource allocation that takes place in the context of the contemporary multi-core computer architectures. From a theoretical standpoint, the resource allocation problems that are abstracted from the aforementioned applications, correspond to the problem of scheduling a stochastic network with blocking and deadlocking effects. This is an area of the modern scheduling theory with very limited results. To a large extent, this lack of results is due to the intricacies that arise from the blocking, and especially the deadlocking effects that take place in these networks, and prevents a tractable analysis of these problems through the classical modeling frameworks. Hence, the departing thesis of the work that is presented in this document, is the decomposition of the aforementioned scheduling problems to (i) a supervisory control problem that will seek to prevent the deadlock formation in the underlying resource allocation dynamics, and (ii) a scheduling problem that will be formulated on the admissible subspace to be defined by the adopted supervisory control policy. Each of these two subproblems can be further structured and addressed using some formal modeling frameworks borrowed, respectively, from the qualitative and the quantitative theory of Discrete Event Systems. At the same time, the above two subproblems possess considerable special structure that can be leveraged towards their effective and efficient solution. The presented material provides a comprehensive tutorial exposition of the current achievements of the corresponding research community with respect to the first of the two subproblems mentioned above. As it will be revealed by this exposition, the corresponding results are pretty rich in their theoretical developments and practically potent. At the same time, it is expected and hoped that the resulting awareness regarding the aforementioned results will also set the stage for undertaking a more orchestrated effort on the second of the two subproblems mentioned above.

Mathematical models are at the core of modern science and technology. An accurate description of behaviors, systems and processes often requires the use of complex models which are difficult to analyze and control. To facilitate analysis of and design for complex systems, model reduction theory and tools allow determining “simpler” models which preserve some of the features of the underlying complex description. A large variety of techniques, which can be distinguished depending on the features which are preserved in the reduction process, has been proposed to achieve this goal. One such a method is the moment matching approach. This monograph focuses on the problem of model reduction by moment matching for nonlinear systems. The central idea of the method is the preservation, for a prescribed class of inputs and under some technical assumptions, of the steady-state output response of the system to be reduced. We present the moment matching approach from this vantage point, covering the problems of model reduction for nonlinear systems, nonlinear time-delay systems, data-driven model reduction for nonlinear systems and model reduction for “discontinuous” input signals. Throughout the monograph linear systems, with their simple structure and strong properties, are used as a paradigm to facilitate understanding of the theory and provide foundation of the terminology and notation. The text is enriched by several numerical examples, physically motivated examples and with connections to well-established notions and tools, such as the phasor transform.

This tutorial investigates the problem of the occurrence of multiple faults in the sensors used to monitor and control a network of cyberphysical systems. The goal is to formulate a general methodology, which will be used for designing sensor fault diagnosis schemes with emphasis on the isolation of multiple sensor faults, and for analyzing the performance of these schemes with respect to the design parameters and system characteristics. The backbone of the proposed methodology is the design of several monitoring and aggregation cyber agents (modules) with specific properties and tasks. The monitoring agents check the healthy operation of sets of sensors and infer the occurrence of faults in these sensor sets based on structured robustness and sensitivity properties. These properties are obtained by deriving analytical redundancy relations of observer-based residuals sensitive to specific subsets of sensor faults, and adaptive thresholds that bound the residuals under healthy conditions, assuming bounded modeling uncertainty and measurement noise. The aggregation agents are employed to collect and process the decisions of the agents, while they apply diagnostic reasoning to isolate combinations of sensor faults that have possibly occurred. The design and performance analysis methodology is presented in the context of three different architectures: for cyber-physical systems that consist of a set of interconnected systems, a distributed architecture and a decentralized architecture, and for cyber-physical systems that are treated as monolithic, a centralized architecture. For all three architectures, the decomposition of the sensor set into subsets of sensors plays a key role in their ability to isolate multiple sensor faults. A discussion of the challenges and benefits of the three architectures is provided, based on the system scale, the type of system nonlinearities, the number of sensors and the communication needs. Lastly, this tutorial concludes with a discussion of open problems in fault diagnosis.

In this monograph we consider the class of continuous-time positive switched systems. We discuss several problems, including stability, performance analysis, stabilization via switching control, and optimization. The monograph starts with a chapter where several application examples are provided, to motivate the interest in this class of systems. The rest of the monograph is dedicated to the theory of stability, stabilization and performance optimization of positive switched systems. The main existing results are recalled, but also new challenging problems are proposed and solved. Special attention has been devoted to point out those results that specifically pertain to positive (linear) switched systems and do not find a counterpart for the wider class of (nonpositive) linear switched systems.

Recent advances in wired and wireless technology lead to the emergence of large-scale networks such as Internet, wireless mobile ad-hoc networks, swarm robotics, smart-grid, and smart-sensor networks. The advances gave rise to new applications in networks including decentralized resource allocation in multi-agent systems, decentralized control of multi-agent systems, collaborative decision making, decentralized learning and estimation, and decentralized in-network signal processing. The advances also gave birth to new large cyber-physical systems such as sensor and social networks. These network systems are typically spatially distributed over a large area and may consists of hundreds of agents in smart-sensor networks to millions of agents in social networks. As such, they do not possess a central coordinator or a central point for access to the complete system information. This lack of central entity makes the traditional (centralized) optimization and control techniques inapplicable, thus necessitating the development of new distributed computational models and algorithms to support efficient operations over such networks. This tutorial provides an overview of the convergence rate of distributed algorithms for coordination and its relevance to optimization in a system of autonomous agents embedded in a communication network, where each agent is aware of (and can communicate with) its local neighbors only. The focus is on distributed averaging dynamics for consensus problems and its role in consensusbased gradient methods for convex optimization problems, where the network objective function is separable across the constituent agents.

Positive Markov Jump Linear Systems are piecewise positive linear systems affected by a stochastic signal generated by a Markov chain. Positive systems naturally arise in the description of biological systems, compartmental models, population dynamics, traffic modeling, chemical reactions, queue processes, and so on. A rich literature on positive linear systems is now available. Positive Markov Jump Linear Systems is the first work to provide an overview of these developments. It outlines the typical applications of such systems, giving a detailed description of the mathematical theory underpinning the subject. Positive Markov Jump Linear Systems provides a comprehensive and timely introduction to the study of such systems. Readers who are new to the topic will find everything required to understand such systems in a concise and accessible form.

An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel developments and relationships with other formalisms. Port-Hamiltonian systems theory yields a systematic framework for network modeling of multi-physics systems. Examples from different areas show the range of applicability. While the emphasis is on modeling and analysis, the last part provides a brief introduction to control of port-Hamiltonian systems.

Hybrid dynamical systems are a class of complex systems that involve interacting discrete-event and continuous-variable dynamics. They are important in applications in embedded systems, cyber-physical systems, robotics, manufacturing systems, traffic management, bio-molecular networks, and have recently been at the center of intense research activity in the control theory, computer-aided verification, and artificial intelligence communities. This paper provides a tutorial introduction to this multidisciplinary research area. A number of fundamental topics, such as modeling, abstraction, verification, supervisory control, stability analysis, stabilization, and optimal control of hybrid systems are introduced and discussed. Additionally, more advanced topics are briefly discussed at the end of each chapter with references given for further reading.