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Introduction

1.1 Motivation and Challenges

The current book investigates emerging applications of multiagent cooperative control. It is motivated by the ubiquity of networked systems and the need to control their behaviors for real-world applications. We first review collective behaviors and then introduce major technical challenges in cooperative control.

1.1.1 From Collective Behaviors to Cooperative Control

Collective behaviors are observed in natural systems. Groups of ants create colony architectures that no single ant intends. Populations of neurons create structured thought, permanent memories, and adaptive responses that no neuron can comprehend by itself. In the study of collective behaviors, usually some types of agent-based-models are expressed with mathematical and computational formalisms, and the descriptive model is capable of quantitative and objective predictions of the system under consideration. The descriptive equations of fish schools and other animal aggregations were proposed in Ref. [1] in the 1950s, and it is more than three decades later that renewed mainstream attention has been received in a range of fields-including computer graphics, physics, robotics, and controls. A distributed behavior model, which is based on the individual agent's motion, is built by Reynolds [2] and computer simulations are done therein for flock-like group motion. Individual-based models and simulation of collective behaviors are also addressed in Ref. [3] with discussions of collective effects of group characteristics. Simulated robots are used in Ref. [4] to simulate collective behaviors where different types of group motions are displayed. While the aforementioned work is mainly on descriptive models and simulated behaviors, controlling the movement of a group using simulated robots with dynamic motion is addressed in Ref. [5]. Collective behaviors such as seen in herds of animals and biological aggregations are also referred to as swarming in the literature. Models of swarming are discussed in Refs. [6, 7], where attraction-repulsion interactions are included in the system's dynamics. Stability analysis of swarms is given in Refs. [8, 9] based on certain artificial interaction forces. The research has progressed rapidly in recent years from modeling and simulation of specific examples toward a more fundamental explanation applicable to a wide range of systems with collective behaviors.

In physics, the phenomenon of collective synchronization, in which coupled oscillators lock to a common frequency, was studied in the early work [10, 11]. In the 1970s, Kuramoto proposed a tractable model (referred to as the Kuramoto model) for oscillator synchronization [12, 13]. A related problem, the collective motion and phase transition of particle systems, is considered from the perspective of analogies to biologically motivated interactions in Refs. [14, 15] where simulated behaviors are presented. The studied models are capable of explaining certain observed behaviors in biological systems, including collective motion (rotation and flocking) of bacteria, networks of pacemaker cells in the heart, circadian pacemaker cells in the nucleus of the brain, metabolic synchrony in yeast cell suspensions, and physical systems such as arrays of lasers and microwave oscillators. Despite 40 years having elapsed since Kuramoto proposed his important model, there remain important theoretical aspects of the collective motion that are not yet understood; see Ref. [16] for a review on the topic.

More recently, the phase transition behavior described by Vicsek and coauthors [15] was revisited and theoretically explained by Jadbabaie et al. [17]. Their work is significant since it provides a graph theory-based framework to analyze a group of networking systems. Since then, coordination of mobile agents has received considerable attention. The consensus problem, which considers the agreement upon certain quantities of interest, was posed and studied by Olfati-Saber and Murray [18]. Here, the network topology was explicitly configured and the relationship between this topology and the system convergence was addressed using graph theory-based methods. The problem is further studied in Refs. [19-22], and necessary and sufficient conditions are given for a networked system to achieve consensus with the switching topology (see a survey [19]). Subsequent studies extended the principles of cooperative control to applications related to vehicle systems, for example, in Refs. [23-29]. Since then, cooperative control has gone through periods of rapid development [30-33].

1.1.2 Challenges

Despite rapid development, the field of cooperative control is far from mature. Major technical challenges arise from system dynamics and network complexity, which include the following:

• Nonlinear agent dynamics: Most agent systems are nonlinear dynamic systems. For example, cooperating robot vehicles, such as ground, aerial, and underwater vehicles, are nonlinear dynamic systems: the states of the system vary in time in complicated ways. Most existing cooperative control based on graph theory methods assumes single integrator or simple linear dynamics, which is not adequate for real-world applications where the performance of the designed control system can deviate greatly from the performance suggested by these simplified system models. Design of cooperative control for nonlinear systems is not a trivial task. There is no general framework available for nonlinear cooperative control.
• Nonlinear agent interactions: In many natural systems, the adhesive and repulsive forces among agents are nonlinear. For example, the repulsive force between two agents may need to become very large (and approach infinity) when they are very close in order to avoid collisions. Similarly, when the distance between them is greater than a threshold, the repulsive force may either become very small or vanish. Most existing cooperative control framework addresses linear agent interactions, while many real-world multiagent systems, such as nanoscale particle systems, have complicated nonlinear interactions, for example, Morse-type interactions. New methodologies are called upon to solve cooperative control problems to support systems with more general (nonlinear) agent interactions.
• Robustness: Due to uncertainties in agent dynamics, communication links, and operating environments, robustness has to be considered for a successful system design. For example, uncertainties in the communication links of cognitive radio networks (CRNs) include time delay of information exchange and time-varying and/or switching of the network connectivity. Such uncertainties can lead to unexpected or perhaps unstable behaviors. Robustness consideration has been discussed for the basic consensus problem in existing work, but general robust cooperative control for complicated real-world systems has not been adequately addressed. The ultimate goal is that, under a well-designed control scheme, the closed-loop networked system will be tolerant of and robust to network and environment disturbances.
• Diversity of real-world problems and application domains: Networked systems are becoming increasingly ubiquitous. Depending on the domain of applications, the control objectives and constraints are inherently different. For example, control of nanoscale particle systems has strict confinement constraints, the system is not readily accessible, and not all particles can be targeted or controller individually. In addition feedback control is very difficult to implement since the characteristic time is usually shorter than that of the available control devices. Although cooperative control has provided analysis methods and synthesis tools that were successfully applied to real-world systems such as autonomous vehicle systems at the macro- and microscales, cooperative control in other application domains such as the nanoscale systems has not been fully explored yet. New real-world problems and application domains pose new challenges for nonlinear cooperative control design.

1.2 Background and Related Work

The book addresses real-world applications of cooperative control in three application domains: networked communication systems, cooperating multirobotic systems, and multiagent physics systems. In this section, we provide background and related work for each of the application domains.

1.2.1 Networked Communication Systems

Part I studies distributed consensus for networked communication systems. In particular, after presenting average consensus for quantized communication, two emerging applications of distributed consensus in CRNs will be discussed, which include distributed spectrum sensing and radio environment mapping (REM).

CRNs are an innovative approach to wireless engineering in which radios are designed with an unprecedented level of intelligence and agility. This advanced technology enables radio devices to use spectrum (i.e., radio frequencies) in entirely new and sophisticated ways. Cognitive radios have the ability to monitor, sense, and detect the conditions of their operating environment and also dynamically reconfigure their own characteristics to best match those conditions [34].

1.2.1.1 Cooperative Spectrum Sensing

Due to rapidly growing demands of emerging wireless services and new mobile applications for anytime and anywhere...