A control theoretic perspective on social networks

This thesis discusses the application of control theory to the study of complex networks, drawing inspiration from the behavior of social networks. There are three topic areas covered by the thesis. The first area considers the ability to control a dynamical system which evolves over a network. Specifically, this thesis introduces a network controllability notion known as herdability. Herdability quantifies the ability to encourage general behavioral change in a system via a set-based reachability condition, which describes a class of desirable behaviors for the application of control in a social network setting. The notion is closely related to the classical notion of controllability, however ensuring complete controllability of large complex networks is often unnecessary for certain beneficial behaviors to be achieved. The basic theory of herdability is developed in this thesis. The second area of study, which builds directly on the first, is the application of herdability to the study of complex networks. Specifically, this thesis explores how to make a network herdable, an extension of the input selection problem which is often discussed in the context of controllability. The input selection problem in this case considers which nodes to select to ensure the maximal number of nodes in the system are herdable. When there are multiple single node sets which can be used to make a system completely herdable, a herdability centrality measure is introduced to differentiate between them. The herdability centrality measure, a measure of importance with respect to the ability to herd the network with minimum energy, is compared to existing centrality measures. The third area explores modeling the spread of the adoption of a beneficial behavior or an idea, in which the spread is encouraged by the action of a social network. A novel model of awareness-coupled epidemic spread is introduced, where agents in a network are aware of a virus (here representing something which should be spread) moving through the network. If the agents have a high opinion of the virus, they are more likely to adopt it. The behavior of this viral model is considered both analytically and in simulation.Ph.D

Distance-Based Formation Control of Multi-Agent Systems

This Ph.D. dissertation studies the distance-based formation control of multi-agent systems. A new approach to the distance-based formation control problem is proposed in this thesis. We formulated distance-based formation in a nonlinear optimal control framework and used the state-dependent Riccati equation (SDRE) technique as the primary tool for solving the optimal control problem. In general, a distance-based formation can be undirected, where distance constraints between pairs of agents are actively controlled by both adjacent agents, or directed, where just one of the neighboring agents is responsible for maintaining the desired distance. This thesis presents both, undirected and directed formations, and provides extensive simulations to verify the theoretical results. For undirected topologies, we studied the formation control problem where we showed that the proposed control law results in the global asymptotic stability of the closed-loop system under certain conditions. The formation tracking problem was studied, and the uniform ultimate boundedness of the solutions is rigorously proven. The proposed method guarantees collision avoidance among neighboring agents and prevents depletion of the agents' energy. In the directed distance-based formation control case, we developed a distributed, hierarchical control scheme for a particular class of directed graphs, namely directed triangulated and trilateral Laman graphs. The proposed controller ensures the global asymptotic stability of the desired formation. Rigorous stability analyses are carried out in all cases. Moreover, we addressed the flip-ambiguity issue by using the signed area and signed volume constraints. Additionally, we introduced a performance index for a formation mission that can indicate the controller's overall performance. We also studied the distance-based formation control of nonlinear agents. We proposed a method that can guarantee asymptotic stability of the distance-based formation for a broad category of nonlinear systems. Furthermore, we studied a distance-based formation control of uncertain nonlinear agents. Based on the combination of integral sliding mode control (ISMC) theory with the SDRE method, we developed a robust optimal formation control scheme that guarantees asymptotic stability of the desired distance-based formation in the presence of bounded uncertainties. We have shown that the proposed controller can compensate for the effect of uncertainties in individual agents on the overall formation

Vision-based control of multi-agent systems

Scope and Methodology of Study: Creating systems with multiple autonomous vehicles places severe demands on the design of decision-making supervisors, cooperative control schemes, and communication strategies. In last years, several approaches have been developed in the literature. Most of them solve the vehicle coordination problem assuming some kind of communications between team members. However, communications make the group sensitive to failure and restrict the applicability of the controllers to teams of friendly robots. This dissertation deals with the problem of designing decentralized controllers that use just local sensor information to achieve some group goals.Findings and Conclusions: This dissertation presents a decentralized architecture for vision-based stabilization of unmanned vehicles moving in formation. The architecture consists of two main components: (i) a vision system, and (ii) vision-based control algorithms. The vision system is capable of recognizing and localizing robots. It is a model-based scheme composed of three main components: image acquisition and processing, robot identification, and pose estimation.Using vision information, we address the problem of stabilizing groups of mobile robots in leader- or two leader-follower formations. The strategies use relative pose between a robot and its designated leader or leaders to achieve formation objectives. Several leader-follower formation control algorithms, which ensure asymptotic coordinated motion, are described and compared. Lyapunov's stability theory-based analysis and numerical simulations in a realistic tridimensional environment show the stability properties of the control approaches