Event-Triggered Algorithms for Leader-Follower Consensus of Networked Euler-Lagrange Agents

This paper proposes three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We firstly propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. By model-independent, we mean that each agent can execute its algorithm with no knowledge of the agent self-dynamics. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work concerning event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics which include the vector of gravitational potential forces, an adaptive algorithm is proposed which requires more information about the agent dynamics but can estimate uncertain agent parameters. For each algorithm, a trigger function is proposed to govern the event update times. At each event, the controller is updated, which ensures that the control input is piecewise constant and saves energy resources. We analyse each controllers and trigger function and exclude Zeno behaviour. Extensive simulations show 1) the advantages of our proposed trigger function as compared to those in existing literature, and 2) the effectiveness of our proposed controllers.Comment: Extended manuscript of journal submission, containing omitted proofs and simulation

Event-Triggered Consensus and Formation Control in Multi-Agent Coordination

The focus of this thesis is to study distributed event-triggered control for multi-agent systems (MASs) facing constraints in practical applications. We consider several problems in the field, ranging from event-triggered consensus with information quantization, event-triggered edge agreement under synchronized/unsynchronized clocks, event-triggered leader-follower consensus with Euler-Lagrange agent dynamics and cooperative event-triggered rigid formation control. The first topic is named as event-triggered consensus with quantized relative state measurements. In this topic, we develop two event-triggered controllers with quantized relative state measurements to achieve consensus for an undirected network where each agent is modelled by single integrator dynamics. Both uniform and logarithmic quantizers are considered, which, together with two different controllers, yield four cases of study in this topic. The quantized information is used to update the control input as well as to determine the next trigger event. We show that approximate consensus can be achieved by the proposed algorithms and Zeno behaviour can be completely excluded if constant offsets with some computable lower bounds are added to the trigger conditions. The second topic considers event-triggered edge agreement problems. Two cases, namely the synchronized clock case and the unsynchronized clock case, are studied. In the synchronized clock case, all agents are activated simultaneously to measure the relative state information over edge links under a global clock. Edge events are defined and their occurrences trigger the update of control inputs for the two agents sharing the link. We show that average consensus can be achieved with our proposed algorithm. In the unsynchronized clock case, each agent executes control algorithms under its own clock which is not synchronized with other agents' clocks. An edge event only triggers control input update for an individual agent. It is shown that all agents will reach consensus in a totally asynchronous manner. In the third topic, we propose three different distributed event-triggered control algorithms to achieve leader-follower consensus for a network of Euler-Lagrange agents. We firstly propose two model-independent algorithms for a subclass of Euler-Lagrange agents without the vector of gravitational potential forces. A variable-gain algorithm is employed when the sensing graph is undirected; algorithm parameters are selected in a fully distributed manner with much greater flexibility compared to all previous work concerning event-triggered consensus problems. When the sensing graph is directed, a constant-gain algorithm is employed. The control gains must be centrally designed to exceed several lower bounding inequalities which require limited knowledge of bounds on the matrices describing the agent dynamics, bounds on network topology information and bounds on the initial conditions. When the Euler-Lagrange agents have dynamics which include the vector of gravitational potential forces, an adaptive algorithm is proposed. This requires more information about the agent dynamics but allows for the estimation of uncertain agent parameters. The last topic discusses cooperative stabilization control of rigid formations via an event-triggered approach. We first design a centralized event-triggered formation control system, in which a central event controller determines the next triggering time and broadcasts the event signal to all the agents for control input update. We then build on this approach to propose a distributed event control strategy, in which each agent can use its local event trigger and local information to update the control input at its own event time. For both cases, the trigger condition, event function and trigger behaviour are discussed in detail, and the exponential convergence of the formation system is guaranteed

Attitude Synchronization of Spacecraft Formation with Optimization and Adaptation of Consensus Penalty Terms

The contribution of this thesis is on the temporal adjustment of the consensus weights, as applied to spacecraft formation control. Such an objective is attained by dynamically enforcing attitude synchronization via coupling terms included in each spacecraft controller. It is assumed that each spacecraft has identical dynamics but with unknown inertia parameters and external disturbances. By augmenting a standard adaptive controller that accounts for the unknown parameters, made feasible via an assumption on parameterization, with adaptation of the consensus weights, one opts to improve spacecraft synchronization. The coupling terms, responsible for enforcing synchronization amongst spacecraft, are weighted dynamically in proportion to the disagreement between the states of the spacecraft. The time adjustment of edge-dependent gains as well as the special cases of node-dependent and agent-independent constant gains are derived using Lyapunov redesign methods. The proposed adaptive control architectures which allow for adaptation of both parameter uncertainties and consensus penalty terms are demonstrated via extensive numerical studies of spacecraft networks with limited connectivity. By considering the sum of deviation-from-the-mean and rotational kinetic energy as appropriate metrics for synchronization and controller performance, the numerical studies also provide insights on the choice of optimal consensus gains

Distributed strategy-updating rules for aggregative games of multi-integrator systems with coupled constraints

In this paper, we explore aggregative games over networks of multi-integrator agents with coupled constraints. To reach the general Nash equilibrium of an aggregative game, a distributed strategy-updating rule is proposed by a combination of the coordination of Lagrange multipliers and the estimation of the aggregator. Each player has only access to partial-decision information and communicates with his neighbors in a weight-balanced digraph which characterizes players' preferences as to the values of information received from neighbors. We first consider networks of double-integrator agents and then focus on multi-integrator agents. The effectiveness of the proposed strategy-updating rules is demonstrated by analyzing the convergence of corresponding dynamical systems via the Lyapunov stability theory, singular perturbation theory and passive theory. Numerical examples are given to illustrate our results.Comment: 9 pages, 4 figure

Statistical Mechanics for Network Structure and Evolution

In this thesis, we address problems in complex networks using the methods of statistical mechanics and information theory. We particularly focus on the thermodynamic characterisation of networks and entropic analysis on statistics and dynamics of network evolution. After a brief introduction of background and motivation behind the thesis in Chapter 1, we provide a review of relevant literature in Chapter 2, and elaborate the main methods from Chapter 3 to Chapter 6. In Chapter 3, we explore the normalised Laplacian matrix as the Hamiltonian operator of the network which governs the particle occupations corresponding to Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. The relevant partition functions derive the thermodynamic quantities in revealing network structural characterisations. Chapter 4 further decomposes the global network entropy in three statistics on edge-connection components. This decompensation reflects the detailed distribution of entropy across the edges of a network, and is particularly useful if the analysis of non-homogeneous networks with a strong community and hub structure is being attempted. Furthermore, Chapter 5 and Chapter 6 provide the theoretical approaches to analyse the dynamic network evolution and the application of the real-world networks. In Chapter 5, we investigate both undirected and directed network evolution using the Euler-Lagrange equation. This variational principle is based on the von Neumann entropy for time-varying network structure. The presented model not only provides an accurate simulation of the degree statistics in network evolution, but also captures the topological variations taking place when the structure of a network changes violently. Chapter 6 studies the fMRI regional brain interaction networks using directed graphs. We further develop a novel method for characterising networks using Bose-Einstein entropy and the Jensen-Shannon divergence. It offers a high discrimination among patients with suspected Alzheimer's disease. Finally, Chapter 7 concludes the thesis and discusses the limitations of our methodologies, which also supplies the potential research in the future

Alignment and integration of complex networks by hypergraph-based spectral clustering

Complex networks possess a rich, multi-scale structure reflecting the dynamical and functional organization of the systems they model. Often there is a need to analyze multiple networks simultaneously, to model a system by more than one type of interaction or to go beyond simple pairwise interactions, but currently there is a lack of theoretical and computational methods to address these problems. Here we introduce a framework for clustering and community detection in such systems using hypergraph representations. Our main result is a generalization of the Perron-Frobenius theorem from which we derive spectral clustering algorithms for directed and undirected hypergraphs. We illustrate our approach with applications for local and global alignment of protein-protein interaction networks between multiple species, for tripartite community detection in folksonomies, and for detecting clusters of overlapping regulatory pathways in directed networks.Comment: 16 pages, 5 figures; revised version with minor corrections and figures printed in two-column format for better readability; algorithm implementation and supplementary information available at Google code at http://schype.googlecode.co

Analysis and synthesis of collective motion: from geometry to dynamics

The subject of this dissertation is collective motion, the coordinated motion of two or more individuals, in three-dimensional space. Inspired by the problems of understanding collective motion in nature and designing artificial collectives that can produce complex behaviors, we introduce mathematical methods for the analysis of collective motion data, and biologically-inspired algorithms for generating collective motion in engineered systems. We explore two complementary approaches to the analysis and synthesis of collective motion. The first "top-down" approach consists in exploiting the geometry of n-body systems to identify certain elementary components of collective motion. A main contribution of this thesis is to reveal a new geometrical structure (fiber bundle) of the translation-reduced configuration space and a corresponding classification of collective motions alternative to the classical one based on reduction to shape space. We derive a mathematical framework for decomposing arbitrary collective motions into elementary components, which can help identify the main modes of an observed collective phenomenon. We synthesize vector fields that implement some of the most interesting elementary collective motions, and suggest, whenever feasible, decentralized implementations. The second "bottom-up" approach consists in starting from known biologically-plausible individual control laws and exploring how they can be used to generate collective behaviors. This approach is illustrated using the motion camouflage proportional guidance law as a building block. We show that rich and coordinated motion patterns can be obtained when two individuals are engaged in mutual pursuit with this control law. An extension of these dynamics yields coordinated motion for a collective of n individuals