Emergence of Hierarchy on a Network of Complementary Agents

Complementarity is one of the main features underlying the interactions in biological and biochemical systems. Inspired by those systems we propose a model for the dynamical evolution of a system composed by agents that interact due to their complementary attributes rather than their similarities. Each agent is represented by a bit-string and has an activity associated to it; the coupling among complementary peers depends on their activity. The connectivity of the system changes in time respecting the constraint of complementarity. We observe the formation of a network of active agents whose stability depends on the rate at which activity diffuses in the system. The model exhibits a non-equilibrium phase transition between the ordered phase, where a stable network is generated, and a disordered phase characterized by the absence of correlation among the agents. The ordered phase exhibits multi-modal distributions of connectivity and activity, indicating a hierarchy of interaction among different populations characterized by different degrees of activity. This model may be used to study the hierarchy observed in social organizations as well as in business and other networks.Comment: 13 pages, 4 figures, submitte

Information Theory and Cooperative Control in Networked Multi-Agent Systems with Applications to Smart Grid

This dissertation focuses on information theoretic aspects of and cooperative control techniques in networked multi-agent systems (NMAS) with communication constraints. In the first part of the dissertation, information theoretic limitations of tracking problems in networked control systems, especially leader-follower systems with communication constraints, are studied. Necessary conditions on the data rate of each communication link for tracking of the leader-follower systems are provided. By considering the forward and feedback channels as one cascade channel, we also provide a lower bound for the data rate of the cascade channel for the system to track a reference signal such that the tracking error has finite second moment. Finally, the aforementioned results are extended to the case in which the leader system and follower system have different system models. In the second part, we propose an easily scalable hierarchical decision-making and control architecture for smart grid with communication constraints in which distributed customers equipped with renewable distributed generation (RDG) interact and trade energy in the grid. We introduce the key components and their interactions in the proposed control architecture and discuss the design of distributed controllers which deal with short-term and long-term grid stability, power load balancing and energy routing. At microgrid level, under the assumption of user cooperation and inter-user communications, we propose a distributed networked control strategy to solve the demand-side management problem in microgrids. Moreover, by considering communication delays between users and microgrid central controller, we propose a distributed networked control strategy with prediction to solve the demand-side management problem with communication delays. In the third part, we consider the disturbance attenuation and stabilization problem in networked control systems. To be specific, we consider the string stability in a large group of interconnected systems over a communication network. Its potential applications could be found in formation tracking control in groups of robots, as well as uncertainty reduction and disturbance attenuation in smart grid. We propose a leader-following consensus protocol for such interconnected systems and derive the sufficient conditions, in terms of communication topology and control parameters, for string stability. Simulation results and performance in terms of disturbance propagation are also given. In the fourth part, we consider distributed tracking and consensus in networked multi-agent systems with noisy time-varying graphs and incomplete data. In particular, a distributed tracking with consensus algorithm is developed for the space-object tracking with a satellite surveillance network. We also intend to investigate the possible application of such methods in smart grid networks. Later, conditions for achieving distributed consensus are discussed and the rate of convergence is quantified for noisy time-varying graphs with incomplete data. We also provide detailed simulation results and performance comparison of the proposed distributed tracking with consensus algorithm in the case of space-object tracking problem and that of distributed local Kalman filtering with centralized fusion and centralized Kalman filter. The information theoretic limitations developed in the first part of this dissertation provide guildlines for design and analysis of tracking problems in networked control systems. The results reveal the mutual interaction and joint application of information theory and control theory in networked control systems. Second, the proposed architectures and approaches enable scalability in smart grid design and allow resource pooling among distributed energy resources (DER) so that the grid stability and optimality is maintained. The proposed distributed networked control strategy with prediction provides an approach for cooperative control at RDG-equipped customers within a self-contained microgrid with different feedback delays. Our string stability analysis in the third part of this dissertation allows a single networked control system to be extended to a large group of interconnected subsystems while system stability is still maintained. It also reveals the disturbance propagation through the network and the effect of disturbance in one subsystem on other subsystems. The proposed leader-following consensus protocol in the constrained communication among users reveals the effect of communication in stabilization of networked control systems and the interaction between communication and control over a network. Finally, the distributed tracking and consensus in networked multi-agent systems problem shows that information sharing among users improves the quality of local estimates and helps avoid conflicting and inefficient distributed decisions. It also reveals the effect of the graph topologies and incomplete node measurements on the speed of achieving distributed decision and final consensus accuracy

String Stability towards Leader thanks to Asymmetric Bidirectional Controller

This paper deals with the problem of string stability of interconnected systems with double-integrator open loop dynamics (e.g.~acceleration-controlled vehicles). We analyze an asymmetric bidirectional linear controller, where each vehicle is coupled solely to its immediate predecessor and to its immediate follower with different gains in these two directions. We show that in this setting, unlike with unidirectional or symmetric bidirectional controllers, string stability can be recovered when disturbances act only on a small ($N$-independent) set of leading vehicles. This improves existing results from the literature with this assumption. We also indicate that string stability with respect to arbitrarily distributed disturbances cannot be achieved with this controller.Comment: Version 2 corrects a typo in the proof, and adds the proof of stability before string stability. Slightly longer than published versio