Hybrid and Networked Dynamical Systems treats a class of systems that is ubiquitous in everyday life. From energy grids to fleets of robots or vehicles to social networks to biological networks, the same scenario arises: dynamical units interact locally through a connection graph to achieve a global task. The book shows how analysis and design tools can be adapted for control applications that combine the effects of network-induced interactions and hybrid dynamics with complex results.
Following a scene-setting introduction, the remaining 12 chapters of the book are divided into three parts and provide a unique opportunity to describe the big picture that is the culmination of years of recent research activity. The contributing authors expand on their ideas at greater length than is possible in an archival research paper and use in-depth examples to illustrate their theoretical work.
The widespread importance of hybrid and networked systems means that the book is of significant interest to academic researchers working in applied mathematics, control, and electrical, mechanical and chemical engineering and to their industrial counterparts.
Romain Postoyan is a researcher in the Centre de Recherche en Automatique de Nancy at the Université de Lorraine, France
Paolo Frasca is a researcher at GIPSA-lab, Grenoble, France
Elena Panteley is a Senior Researcher at the Laboratoire of Signaux et Systemes, France
Luca Zaccarian is professor in the Department of Industrial Engineering at the University of Trento
From Introduction (pag.1-2)
Networked dynamical systems are ubiquitous in our everyday life. From energy grids and fleets of robots or vehicles to social networks, the same scenario arises in each case: dynamical units interact locally to achieve a global task. When considering a networked system as a whole, very often continuous-time dynamics are affected by instantaneous changes, called jumps, leading to the so-called hybrid dynamical systems. These jumps may come from (i) the intrinsic dynamics of the nodes, like in multimedia delivery with fixed rate encoding, (ii) the intrinsic degrees of freedom of the control actions, like in power converters within energy grids, or valve-based controllers that switch between several modes of operation, (iii) the creation/loss of links or the addition/removal of nodes, like in social networks where opinion dynamics take place. These control applications call upon the development of powerful analysis and design tools capable of handling the multi-agent interaction patterns combined with the abovementioned hybrid nature of the dynamics.
Both hybrid systems and networked systems have been extensively studied during the last two decades. On the one hand, methods to deal with hybrid dynamics have witnessed a fast growth due to the emergence of powerful modeling and analytical tools . However, when dealing with such hybrid dynamics, the existing results typically require that a single global model be specified, which may be an obstacle when dealing with networked systems. More work needs to be done to develop tailored tools when investigating networked systems exhibiting hybrid dynamics. On the other hand, research in networked systems has a long history in many fields of science and engineering: in the years 2000, the interest of control researchers in networked systems, also called multi-agents systems, exploded thanks to the pioneering works of [11, 14, 22, 30], which unraveled the fundamental links between algebraic graph theory and stability in this context. Existing works mostly concentrate on simple node dynamics, often single or double integrators, with the exception of the passivity-based approach put forward in [1] or the recent works in, which allow dealing with more general nonlinear heterogeneous models. Despite these two bodies of work about hybrid systems and networked systems, works addressing hybrid networked dynamical systems are scarcer: we could cite among others for sampled-data systems, for networked control systems, for networks with hybrid nodes. Yet, hybrid phenomena in multi-agent systems remain largely unexplored despite their fundamental importance.
In this context, the aim of this book is to bring together recent, exciting contributions in the field of hybrid, networked dynamical systems with an opening to related emergent topics. Although each chapter is self-contained, the book has been organized in such a way that theme-related chapters are grouped together. The book is thus organized into three parts, which all address key aspects of the topic.
The chapters in Part I deal with networked systems and focus on two main challenges of the field: distributed control and estimation. Chapters 2 and 3 present distributed control design tools to enforce synchronization or consensus properties within a network of nonlinear dynamical agents using distributed, local rules. Chapter 4 in Part I is devoted to recovering the communication graph given only output information from the nodes.
Part II presents a range of novel hybrid techniques for analysis, control, and estimation purposes. Chapter 5 presents recent advances in the study of multiconsensus for classes of hybrid multi-agent systems. Chapter 6 surveys recent results on the observer design for hybrid dynamical systems with known jump times. Chapter 7 introduces tools to analyze stability properties of discrete-time switched linear systems driven by switching signals generated by an important class of automata, namely, deterministic Büchi automata, where the alphabet coincides with the modes of the switched system. Chapters 8 and 9 of Part II present hybrid control design techniques dedicated to uncertain systems and systems subject to input saturation.
Finally, Part III is devoted to emerging tools for analysis and design. In particular, Chapter 10 provides a survey of recent trends in the analysis of open multiagent systems, which are characterized by their time-varying number of agents, and discusses three applications of major importance: consensus, optimization and epidemics. Chapter 11 provides insights on how event-triggering control techniques can be used to reduce the computational effort required by neural network controllers, which are currently attracting a lot of attention within the control community. Chapter 12 explains how to (locally) stabilize nonlinear dynamical systems by only relying on available input-state data, and how to estimate the corresponding region of attraction. Finally, Chapt. 13 surveys recent results on harmonic control, which shed new light on the rigorous, frequency control of general dynamical systems.
We believe that the variety of topics covered in this book and the overall tutorial writing style that many of the authors have used will render this book a pleasant reading both for experts in the field and for young researchers who seek for an intuitive understanding of the main recent highlights in these research areas.
Courtesy by Springer.