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

Consensusability of discrete-time multi-agent systems

The study of multi-agent systems (MAS) focuses on systems in which many intelligent agents interact within an environment. The agents are considered to be autonomous entities. MAS can be used to solve problems that are difficult or impossible for an individual agent to solve. The main feature which is achieved when developing MAS, if they work, is flexibility, since MAS can be added to, modified and reconstructed, without the need for detailed rewriting of the application. MAS can manifest self-organization as well as self-steering related complex behaviors even when the individual strategies of all their agents are simple. The goal of MAS research is to find methods that allow us to build complex systems composed of autonomous agents who, while operating on local knowledge and possessing only limited abilities, are nonetheless capable of enacting the desired global behaviors. We want to know how to take a description of what a system of agents should do and break it down into individual agent behaviors. This thesis investigates the problem when discrete-time MAS are consensusable under undirected graph. A discussion is provided to show how the problem differs from continuous time system. Then a consensusability condition is derived in terms of the Mahler measure of the agent system for single input single out systems (SISO) and result shows that there is an improved consensusability by a power of two. An algorithm is proposed for distributed consensus feedback control law when the consensusability holds. Also the case of output feedback is considered in which the consensusability problem becomes more complicated. To solve this we decompose the problem into two parts i.e. state feedback and state estimation. Simulation results demonstrate the effectiveness of the established results

Communication-constrained feedback stability and Multi-agent System consensusability in Networked Control Systems

With the advances in wireless communication, the topic of Networked Control Systems (NCSs) has become an interesting research subject. Moreover, the advantages they offer convinced companies to implement and use data networks for remote industrial control and process automation. Data networks prove to be very efficient for controlling distributed systems, which would otherwise require complex wiring connections on large or inaccessible areas. In addition, they are easier to maintain and more cost efficient. Unfortunately, stability and performance control is always going to be affected by network and communication issues, such as band-limited channels, quantization errors, sampling, delays, packet dropouts or system architecture. The first part of this research aims to study the effects of both input and output quantization on an NCS. Both input and output quantization errors are going to be modeled as sector bounded multiplicative uncertainties, the main goal being the minimization of the quantization density, while maintaining feedback stability. Modeling quantization errors as uncertainties allows for robust optimal control strategies to be applied in order to study the accepted uncertainty levels, which are directly related to the quantization levels. A new feedback law is proposed that will improve closed-loop system stability by increasing the upper bound of allowed uncertainty, and thus allowing the use of a coarser quantizer. Another aspect of NCS deals with coordination of the independent agents within a Multi-agent System (MAS). This research addresses the consensus problem for a set of discrete-time agents communicating through a network with directed information flow. It examines the combined effect of agent dynamics and network topology on agents\u27 consensusability. Given a particular consensus protocol, a sufficient condition is given for agents to be consensusable. This condition requires the eigenvalues of the digraph modeling the network topology to be outer bounded by a fan-shaped area determined by the Mahler measure of the agents\u27 dynamics matrix

Designing Fully Distributed Consensus Protocols for Linear Multi-agent Systems with Directed Graphs

This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this paper, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.Comment: 16 page, 3 figures. To appear in IEEE Transactions on Automatic Contro

Decentralized Event-Triggered Consensus of Linear Multi-agent Systems under Directed Graphs

An event-triggered control technique for consensus of multi-agent systems with general linear dynamics is presented. This paper extends previous work to consider agents that are connected using directed graphs. Additionally, the approach shown here provides asymptotic consensus with guaranteed positive inter-event time intervals. This event-triggered control method is also used in the case where communication delays are present. For the communication delay case we also show that the agents achieve consensus asymptotically and that, for every agent, the time intervals between consecutive transmissions is lower-bounded by a positive constant.Comment: 9 pages, 5 figures, A preliminary version of this manuscript has been submitted to the 2015 American Control Conferenc

Multiagent LQR-based Control Design and Gain tuning for Quadcopters Fleet

An LQR-based Control design and gain tuning strategies proposals for a multi-agent system are presented in this article, the agents are connected in an undirected graph. Controller gains tuning are adjusted by selecting the Q and R weighting matrices of the Linear Quadratic Regulator. Agreement (consensus) is one of the fundamental problems in multi-agent control, where a set of agents must agree on a joint state value. In the proposed design, first considering that the behavior of the agreement protocol is undirected and static, the main objective is to highlight the complexity of the relationship between the convergence properties of this protocol and the structure of adjacent interconnections. The effects on the formation due to static geometry are analyzed from the resulting data according to the proximity between the agents, where behavior and stability are analyzed based on the desired formation geometry through the construction of the Laplacian matrix