Flocking Problem In Multi-agent Systems

Recently, coordinated control in multi-agent systems attracts more and more attentions from various fields of science and engineering. In this dissertation, we investigate the flocking problem in multi-agent systems. Flocking is the phenomenon in which a large number of agents, using only limited environmental information and simple rules, organize into a coordinated motion. Recently, there has been a surge of interest among control theorists in flocking problems, partly due to the wide applications of flocking in many control areas including cooperative control of mobile robots and design of mobile sensor networks. This dissertation surveys the recent advances in the flocking algorithms, and emphasizes on the design and stability analysis of flocking algorithms. The main work can be summarized as follows:1. Investigation on the flocking algorithm with a virtual leader. We first show that, even when only a fraction of agents are informed, the flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be influenced by the informed agents from time to time during the evolution. Numerical simulation demonstrates that a very small group of the informed agents can cause most of the agents to move with the desired velocity and the larger the informed group is the bigger portion of agents will move with the desired velocity. In the situation where the virtual leader travels with a varying velocity, we propose modification to the flocking algorithm and show that the resulting algorithm enables the asymptotic tracking of the virtual leader. That is, the position and velocity of the center of mass of all agents will converge exponentially to those of the virtual leader. The convergent rate is also given.2. Investigation on the flocking algorithm with multiple virtual leaders. We investigate the problem of controlling a group of mobile autonomous agents to track multiple virtual leaders with varying velocities in the sense that agents with the same virtual leader attain the same velocity and track the corresponding leader. We propose a provably-stable flocking algorithm. Moreover, we show that the position and velocity of the center of the mass of all agents will exponentially converge to weighted average position and velocity of the virtual leaders.3. Investigation on the flocking algorithm with connectivity preserving. We propose a flocking algorithm with connectivity preserving. This protocol can enable the group to converge at the same position and move with the same velocity while preserving connectivity of the network during the evolution only if the initial network is connected. Moreover, we find that there is a trade-off between maximum overshoot and settling time of velocity convergence and analyze its reasons. Furthermore, we investigate the flocking algorithm with a virtual leader and show that all agents can asymptotically attain the desired velocity even if only one agent in the team has access to the virtual leader.4. Investigation on the flocking algorithm based only on position measurements. We propose a provably-stable flocking algorithm, in which an output vector is produced by distributed filters based on position information to replace velocity information. Under the assumption that the initial interactive network is connected, the flocking algorithm can not only steer a group of agents to a stable flocking motion, but also preserve connectivity of the interactive network during the evolution. Moreover, we investigate the flocking algorithm with a virtual leader.5. Investigation on the flocking algorithm with coupling delay. Stability analysis is performed based on Lyapunov-Krasovskii functional method. Delay-dependent asymptotical stability condition in terms of linear matrix inequalities (LMIs) is derived for the second-order consensus algorithm of delayed dynamical networks. Both delay-independent and delay-dependent asymptotical stability conditions in terms of LMIs are derived for the second-order consensus algorithm with information feedback.