INTRODUCTION TO THE SPECIAL SECTION CHAOUKI T . ABDALLAH

W e live and operate in a networked world. We drive to work on a network of roads and fly across a web of cities connected by commercial airlines. We communicate using an increasingly elaborate set of devices from phones, to computers, to PDAs, all of which are connected through the Internet. We shop at stores and dine at restaurants connected through food and goods delivery networks, and when we reach for a light switch, we trigger a reaction across the power-delivery network. Our governments are networked as are our financial and societal infrastructures. Networks provide a powerful metaphor for describing system behavior from disciplines as diverse as biology, computer science, physics, social science, and engineering. In these fields, complex networks are being studied for the purpose of gaining insight into how properties such as community structure, small-world effects, phase transition, and giant components emerge [1]–[4]. In modern cars and airplanes, as well as in networked homes and office buildings, modern control systems are increasingly incorporating communication networks in feedback loops [5]. Control engineers are thus forced to expand their application domain by incorporating the communication infrastructure into their designs, and by considering the impact of link capacity, latency, and packet loss on the performance of feedback control systems [5], [6]. Significant attention is focused on devising local interaction mechanisms to reproduce the coordinated group behavior observed in biological systems [5], [6], motivated by studies in ecology and theoretical biology that describe the aggregation of animal groups into cohesive groups without centralized coordination. For such control designs to be efficient, we need to better understand how to control physical systems across networks, and to predict whether the network’s structure might give rise to specific behaviors [7], [8]. The need for new paradigms for control design is particularly evident in large-scale interconnected multi-agent systems. For such systems, signals need to flow quickly and efficiently, but interconnected components may not be able to store and manipulate the complete state of the system. Although complexity barriers render the design of controllers for high-dimensional systems impractical, the ability to reason about global network properties based on locally available information enables the design of decentralized control laws. Despite the similarities between the application domains of network theory and control engineering, the necessary links for the transfer of ideas and tools between the two fields have yet to be fully established. This situation is largely due to fundamental differences between the methodologies and goals of the two communities. While control engineers build feedback systems to satisfy closedloop design specifications, network theorists seek models to explain the observed behavior of existing networks [1]–[3]. As shown in Figure 1, the starting points and objectives of a complex-network theoretician and a control engineer are reversed, even though they face the same problems in trying to understand their target systems. Despite the use of different analysis tools, network properties such as connectivity, efficiency, and robustness are critical to both control design and complex-network modeling. Network theory provides tools that characterize the growth and topology of distributed networks [1]-[4], [8] in relation to their navigability, congestion, clustering, and robustness to failure [7]. For example, in systems such as social networks and the World Wide Web, not only do short paths exist between every pair of nodes, but such paths can be found under certain conditions using only local information [6], [7], [9]. The presence of such paths implies that distributed sensing and control might be possible over some networks. INTRODUCTION TO THE SPECIAL SECTION