In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

/pdf/consensus-problems-in-networks-of-agents-with-switching-25c3hqvtd8.pdf

Consensus problems in networks of agents with switching topology and time-delays

In this paper, we intend to formulate a new meta-heuristic algorithm, called Cuckoo Search (CS), for solving optimization problems. This algorithm is based on the obligate brood parasitic behaviour of some cuckoo species in combination with the Levy flight behaviour of some birds and fruit flies. We validate the proposed algorithm against test functions and then compare its performance with those of genetic algorithms and particle swarm optimization. Finally, we discuss the implication of the results and suggestion for further research.

Cuckoo Search via Lévy flights

http://masou-keshtkar.persiangig.com/document/sdarticle.pdf

GSA: A Gravitational Search Algorithm

In this paper, we present a theoretical framework for design and analysis of distributed flocking algorithms. Two cases of flocking in free-space and presence of multiple obstacles are considered. We present three flocking algorithms: two for free-flocking and one for constrained flocking. A comprehensive analysis of the first two algorithms is provided. We demonstrate the first algorithm embodies all three rules of Reynolds. This is a formal approach to extraction of interaction rules that lead to the emergence of collective behavior. We show that the first algorithm generically leads to regular fragmentation, whereas the second and third algorithms both lead to flocking. A systematic method is provided for construction of cost functions (or collective potentials) for flocking. These collective potentials penalize deviation from a class of lattice-shape objects called /spl alpha/-lattices. We use a multi-species framework for construction of collective potentials that consist of flock-members, or /spl alpha/-agents, and virtual agents associated with /spl alpha/-agents called /spl beta/- and /spl gamma/-agents. We show that migration of flocks can be performed using a peer-to-peer network of agents, i.e., "flocks need no leaders." A "universal" definition of flocking for particle systems with similarities to Lyapunov stability is given. Several simulation results are provided that demonstrate performing 2-D and 3-D flocking, split/rejoin maneuver, and squeezing maneuver for hundreds of agents using the proposed algorithms.

/pdf/flocking-for-multi-agent-dynamic-systems-algorithms-and-5efqu9aidp.pdf

Flocking for multi-agent dynamic systems: algorithms and theory

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

In this study, we analyze formation control (formation of a geometrical shape) of an autonomous multi-robot system with the use of artificial potential functions and Newton's iteration. The method is independent of the low-level vehicle dynamics of the robots and therefore it can be applied to different type of robots. We also perform numerical simulations to examine the performance of the method.

Formation control with potential functions and Newton's iteration

In this article we consider a class of multi-agent dynamic systems with uncertainties and the problem of moving in a predefined formation along a reference trajectory. The reference trajectory is generated by switched exosystems each of which are neutrally stable and have unknown parameters. The problem is formulated as a nonlinear servomechanism problem and an adaptive internal model based controller is used to solve this problem. Various formation maneuvers such as expansion/contraction, rotation, and reconfiguration (change of shape) are also considered. The performance of the system is verified with simple numerical simulations.

Adaptive internal model based formation control of a class of multi-agent systems with switched exosystems

Using discrete-time adaptive control tools found in literature, we develop an adaptive particle swarm optimizer. We show, using Lyapunov's direct method, that our devised error system is ultimately uniformly bounded, ultimately goes to zero by Lasalle-Yoshizawa theorem, and our optimizer is stable.

Stable adaptive Particle Swarm Optimization

In this paper we consider the aggregation of swarms whose agents are moving in 2-dimensions with a non-holonomic agent dynamics. We approach this problem using artificial potentials and sliding mode control. The main contribution is the extension of the recent results in the literature based on a similar approach for simple integrator agent dynamics model to a significantly more realistic and more difficult setting with non-holonomic unicycle agent dynamics model. In particular, we design a continuous-time control scheme via a constructive analysis based on artificial potentials and sliding mode control techniques. The effectiveness of the proposed design for solving the swarm aggregation problem is demonstrated analytically as well as via a set of simulation results.

Aggregation in a swarm of non-holonomic agents using artificial potentials and sliding mode control

In this study, we compare three different orientation agreement strategies of multi-agent/particle systems under different conditions. We investigate the behavior of multi-agent systems utilizing these strategies with different combinations of the following properties: (i) the multi-agent systems may be synchronous or asynchronous, (ii) they may travel in bounded or unbounded regions and (iii) the mobile agents may have turning speed restrictions. The agents/particles are assumed to move with constant speed and update their orientation of motion based on three different strategies. Based on these strategies, simulations are performed and the effects on the clustering performance are investigated. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Comparison of three orientation agreement strategies in self-propelled particle systems with turn angle restrictions in synchronous and asynchronous settings†

Veysel Gazi

Papers

Formation control with potential functions and Newton's iteration

Adaptive internal model based formation control of a class of multi-agent systems with switched exosystems

Stable adaptive Particle Swarm Optimization

Aggregation in a swarm of non-holonomic agents using artificial potentials and sliding mode control

Comparison of three orientation agreement strategies in self-propelled particle systems with turn angle restrictions in synchronous and asynchronous settings†