Fast Convergence in Consensus Control of Leader-Follower Multi-Agent Systems

In this thesis, different distributed consensus control strategies are introduced for a multi-agent network with a leader-follower structure. The proposed strategies are based on the nearest neighbor rule, and are shown to reach consensus faster than conventional methods. Matrix equations are given to obtain equilibrium state of the network based on which the average-based control input is defined accordingly. Two network control rules are subsequently developed, where in one of them the control input is only applied to the leader, and in the other one it is applied to the leader and its neighbors. The results are then extended to the case of a time-varying network with switching topology and a relatively large number of agents. The convergence performance under the proposed strategies in the case of a time-invariant network with fixed topology is evaluated based on the location of the dominant eigenvalue of the closed-loop system. For the case of a time-varying network with switching topology, on the other hand, the state transition matrix of the system is investigated to analyze the stability of the proposed strategies. Finally, the input saturation in agents' dynamics is considered and the stability of the network under the proposed methods in the presence of saturation is studied

HVAC-based cooperative algorithms for demand side management in a microgrid

The high penetration of renewable power generators and various loads have brought a great challenge for dispatching energy in a microgrid system. Heating ventilation air conditioning (HVAC) system, as a household appliance with high popularity, can be considered as an effective technology to alleviate energy dispatch issues. This paper presents novel distributed algorithms based on HVAC to solve the demand side management problem, where the microgrid system with HVAC units is considered as a multi-agent system (MAS). The approach provides a desirable operating frequency signal for each HVAC based on the power mismatch value occurring on each local bus. It utilizes demand response of the HVAC units to minimize the supply-demand mismatch, thus reducing the quantity and capacity of energy storage devices potentially to be required. Compared with existing approaches focusing on the distributed algorithms under a fixed communication network, this paper addresses a consensus problem under a switching topology by using the Lyapunov argument. It is verified that a jointly strong and connected topology is a sufficient condition in order to achieve an average consensus for a time-varying topology. A number of cases are studied to evaluate the effectiveness of the algorithms by taking into account its power constraints, dynamic behaviors, anti-damage characteristics and time-varying communication topology. Modelling these system interactions has demonstrated the feasibility of the proposed microgrid system

Consensuability Conditions of Multi Agent Systems with Varying Interconnection Topology and Different Kinds of Node Dynamics

Many systems in nature and of practical interest can be modeled as large collections of interacting subsystems. Such systems are referred as "Multi Agent Systems" (briefly MASs) and some examples include electrical power distribution networks (P. Kundur, 1994), communication (F. Paganini, 2001), and collections of vehicles traveling in formation (J.K. Hedrick et al., 1990). Several practical issues concern the design of decentralized controllers and the stability analysis ofMASs in the presence of uncertainties in the subsystem interconnection topology (i.e. due in practical applications to failures of transmission lines). The analysis and control of collections of interconnected systems have been widely studied in the literature. Early work on stability analysis and decentralized control of large-scale interconnected systems is found in (D. Limebeer & Y.S. Hung, 1983; A. Michel & R. Miller, 1977; P.J. Moylan & D.J. Hill, 1978; Siljak, 1978; J.C. Willems, 1976). Some of the more widely notable stability criteria are based on the passivity conditions (M. Vidyasagar, 1977) and on the well-known notion of connective stability introduced in (Siljak, 1978). More recently, MASs have appeared broadly in several applications including formation flight, sensor networks, swarms, collective behavior of flocks (Savkin, 2004; C.C. Cheaha et al., 2009; W. Ren, 2009) motivating the recent significative attention of the scientific community to distributed control and consensus problems (i.e. (R.O. Saber & R. Murray, 2004; Z. Lin et al., 2004; V. Blondel et al., 2005; J. N. Tsitsiklis et al., 1986)). One common feature of the consensus algorithm is to allow every agent automatically converge to a common consensus state using only local information received from its neighboring agents. "Consensusability" of MASs is a fundamental problem concerning with the existence conditions of the consensus state and it is of great importance in both theoretical and practical features of cooperative protocol (i.e. flocking, rendezvous problem, robot coordination). Results about consensuability of MASs are related to first and second order systems and are based on the assumption of jointly-connected interaction graphs (i.e. in (R.O. Saber & R. Murray, 2004; J. N. Tsitsiklis et al., 1986)). Extension to more general linear MASs whose agents are described by LTI (Linear Time Invariant) systems can be found in (Tuna, 2008) where the closed-loop MASs were shown to be asymptotic consensus stable if the topology had a spanning tree. In (L. Scardovi & R. Sepulchre, 2009) it is investigated the synchronization of a Consensuability Conditions of Multi Agent Systems with Varying Interconnection Topology and Different Kinds of Node Dynamics 18 network of identical linear state-space models under a possibly time-varying and directed interconnection structure. Many investigations are carried out when the dynamic structure is fixed and the communication topology is time varying (i.e. in (R.O. Saber & R. Murray, 2004; W. Ren & R. W. Beard, 2005; Ya Zhanga & Yu-Ping Tian, 2009)). One of main appealing field of research is the investigation of the MASs consensusability under both the dynamic agent structure and communication topology variations. In particular, it is worth analyzing the joint impact of the agent dynamic and the communication topology on the MASs consensusability. The aim of the chapter is to give consensusability conditions of LTI MASs as function of the agent dynamic structure, communication topology and coupling strength parameters. The theoretical results are derived by transferring the consensusability problem into the robust stability analysis of LTI-MASs. Differently from the existing works, here the consensuability conditions are given in terms of the adjacency matrix rather than Laplacian matrix.Moreover, it is shown that the interplay among consensusability, node dynamic and topology must be taken into account for MASs stabilization: specifically, consensuability of MASs is assessed for all topologies, dynamic and coupling strength satisfying a pre-specified bound. From the practical point of view the consensuability conditions can be used for both the analysis and planning of MASs protocols to guarantee robust stability for a wide range of possible interconnection topologies, coupling strength and node dynamics. Also, the number of subsystems affecting the overall system stability is taken into account as it is analyzed the robustness of multi agent systems if the number of subsystems changes. Finally, simulation examples are given to illustrate the theoretical analysis. 2

Distributed Consensus of Linear Multi-Agent Systems with Switching Directed Topologies

This paper addresses the distributed consensus problem for a linear multi-agent system with switching directed communication topologies. By appropriately introducing a linear transformation, the consensus problem is equivalently converted to a stabilization problem for a class of switched linear systems. Some sufficient consensus conditions are then derived by using tools from the matrix theory and stability analysis of switched systems. It is proved that consensus in such a multi-agent system can be ensured if each agent is stabilizable and each possible directed topology contains a directed spanning tree. Finally, a numerical simulation is given for illustration.Comment: The paper will be presented at the 2014 Australian Control Conference (AUCC 2014), Canberra, Australi