Housheng Su

Flocking of Multi-Agents With a Virtual Leader

All agents being informed and the virtual leader traveling at a constant velocity are the two critical assumptions seen in the recent literature on flocking in multi-agent systems. Under these assumptions, Olfati-Saber in a recent IEEE Transactions on Automatic Control paper proposed a flocking algorithm which by incorporating a navigational feedback enables a group of agents to track a virtual leader. This paper revisits the problem of multi-agent flocking in the absence of the above two assumptions. We first show that, even when only a fraction of agents are informed, the Olfati-Saber 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 Olfati-Saber 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.

Brief paper: Adaptive second-order consensus of networked mobile agents with nonlinear dynamics

We investigate second-order consensus of multiple nonlinear dynamical mobile agents with a virtual leader in a dynamic proximity network. We assume that only a small fraction of agents in the group have access to the information about the position and velocity of the virtual leader through, for example, certain pre-designed communication mechanism such as wireless broadcasting or sensing. To avoid fragmentation, we propose a connectivity-preserving second-order consensus algorithm. Under the assumption that the initial network is connected, we introduce local adaptation strategies for both the weights on the velocity navigational feedback and the velocity coupling strengths that enable all agents to synchronize with the virtual leader even when only one agent is informed, without requiring any knowledge of the agent dynamics. We finally provide some convincing simulation results to illustrate the theoretical results.

Semi-Global Leader-Following Consensus of Linear Multi-Agent Systems With Input Saturation via Low Gain Feedback

This paper investigates the problem of leader-following consensus of a linear multi-agent system on a switching network. The input of each agent is subject to saturation. Low gain feedback based distributed consensus protocols are developed. It is established that, under the assumptions that each agent is asymptotically null controllable with bounded controls and that the network is connected or jointly connected, semi-global leader-following consensus of the multi-agent system can be achieved. Numerical examples are presented to illustrate this result.

Rendezvous of multiple mobile agents with preserved network connectivity

Abstract In coordinative control of a network of multi-agent systems, to guarantee the stability of the coordinated motion, a basic assumption typically is that the underlying topology of the network can maintain its connectivity frequently enough during the motion evolution. However, for a given set of initial conditions, this assumption is very difficult to satisfy and verify. In particular, the connectivity of the initial network generally cannot guarantee the connectivity of the network throughout the evolution. In this paper, we propose a rendezvous protocol with double-integrator dynamics, which combines the functions of motion control and connectivity preservation. This protocol can enable the group of mobile agents to converge to the same position and move with the same velocity while preserving the connectivity of the whole network during the evolution if the initial network is connected. We find that there is a trade-off between the maximum overshoot and the settling time of the velocity convergence. Furthermore, we investigate the rendezvous protocol with a virtual leader and show that all agents can asymptotically attain a desired velocity even if only one agent in the team has information about the virtual leader. We finally show some numerical simulations to verify and illustrate the theoretical results.

Decentralized Adaptive Pinning Control for Cluster Synchronization of Complex Dynamical Networks

In this brief, we investigate pinning control for cluster synchronization of undirected complex dynamical networks using a decentralized adaptive strategy. Unlike most existing pinning-control algorithms with or without an adaptive strategy, which require global information of the underlying network such as the eigenvalues of the coupling matrix of the whole network or a centralized adaptive control scheme, we propose a novel decentralized adaptive pinning-control scheme for cluster synchronization of undirected networks using a local adaptive strategy on both coupling strengths and feedback gains. By introducing this local adaptive strategy on each node, we show that the network can synchronize using weak coupling strengths and small feedback gains. Finally, we present some simulations to verify and illustrate the theoretical results.

A connectivity-preserving flocking algorithm for multi-agent systems based only on position measurements

Most existing flocking algorithms rely on information about both relative position and relative velocity among neighbouring agents. In this article, we investigate the flocking problem with only position measurements. We propose a provably-stable flocking algorithm, in which an output vector is produced by distributed filters based on position information alone but not velocity information. Under the assumption that the initial interactive network is connected, the flocking algorithm not only can steer a group of agents to a stable flocking motion, but also can preserve the connectivity of the interactive network during the dynamical evolution. Moreover, we investigate the flocking algorithm with a virtual leader and show that all agents can asymptotically attain a desired velocity even if only one agent in the team has access to the information of the virtual leader. We finally show some numerical simulations to illustrate the theoretical results.

Semiglobal Observer-Based Leader-Following Consensus With Input Saturation

This paper studies the observer-based leader-following consensus of a linear multiagent system on switching networks, in which the input of each agent is subject to saturation. Based on a low-gain output feedback method, distributed consensus protocols are developed. Under the assumptions that the networks are connected or jointly connected and that each agent is asymptotically null controllable with bounded controls and detectable, semiglobal observer-based leader-following consensus of the multiagent system can be reached on switching networks. A numerical example is presented to illustrate the theoretical results.

Brief paper: Synchronization of coupled harmonic oscillators in a dynamic proximity network

In this paper, we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network. Unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity, we show that the coupled harmonic oscillators can always be synchronized, without imposing any network connectivity assumption. Moreover, we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader, again without any assumption on connectivity of the followers. Numerical simulation illustrates the theoretical results.

Stabilizing Solution and Parameter Dependence of Modified Algebraic Riccati Equation With Application to Discrete-Time Network Synchronization

This technical note deals with a modified algebraic Riccati equation (MARE) and its corresponding inequality and difference equation, which arise in modified optimal control and filtering problems and are introduced into the cooperative control problems recently. The stabilizing property of the solution to MARE is presented. Then, the uniqueness is proved for the almost stabilizing and positive semi-definite solution. Next, the parameter dependence of MARE is analyzed. An obtained parameter dependence result is finally applied to the study of semi-global synchronization of leader-following networks with discrete-time linear dynamics subject to actuator saturation.

A Note on Observers for Discrete-Time Lipschitz Nonlinear Systems

This brief considers observer design for a class of discrete-time nonlinear systems with Lipschitz nonlinearities. We first remark some statements and results in a recent brief by Zemouche and Boutayeb. In particular, we show that their results are more conservative than an existing one, rather than less conservative as claimed. Moreover, most of the existing results are only applicable to some particular classes of Lipschitz systems with a Lipschitz constant less than one. In order to obtain less conservative results, the concept of a one-sided Lipschitz condition, which is an extension of its well-known Lipschitz counterpart, is introduced. Sufficient conditions ensuring the existence of state observers for one-sided Lipschitz nonlinear systems are then presented. A numerical example is included to illustrate the advantages and effectiveness of the proposed design.