Stability analysis of flocking for multi-agent dynamic systems

This paper is focused on the stability analysis of flocking for multi-agent dynamic systems under weakened assumptions on the connectivity of graphs. Sufficient conditions guaranteeing the emergence of collective behavior of a group of dynamic agents are established. We also consider the case when there is a leader among group of agents.     

A storage model for data communication systems

We consider a storage model where the input and demand are modulated by an underlying Markov chain. Such models arise in data communication systems. The input is a Markov-compound Poisson process and the demand is a Markov linear process. The demand is satisfied if physically possible. We study the properties of the demand and its inverse, which may be viewed as transformed time clocks. We show that the unsatisfied demand is related to the infimum of the net input and that, under suitable conditions, it is an additive functional of the input process. The study of the storage level is based on a detailed analysis of the busy period, using techniques based on infinitesimal generators. The transform of the busy period is the unique solution of a certain matrix-functional equation. Steady state results are also obtained; these are not obvious generalizations of the results for simple storage models. In particular, a generalization of the Pollaczek-Khinchin formula brings new insight.Research supported by Grant BD/645/90-RM from Junta Nacional de Investigação Cientifica e Tecnológica.     

Sampled-data distributed protocol for coordinated aggregation of multi-agent systems subject to communication delays

This paper studies the coordinated aggregation problem of a multi-agent system. Particularly, all the agents reach a consensus within a pre-specified target region. However, only a subset of agents have access to this target region, and each agent merely interacts with its neighbors by communication. Moreover, there exist unknown heterogeneous delays in communication channels. The underlying communication topology is characterized by a digraph. To accommodate the practical digital disposal, a sampled-data distributed protocol is proposed, where the sampling is asynchronous in the sense that the sampling periods of distinct agents are heterogeneous. The resulting closed-loop system from the proposed sampled-data distributed protocol is in a hybrid fashion that the continuous system is fed-back by using discrete states at sampling instants. The convergence performance of this hybrid closed-loop system is analyzed based on the contraction theory. More specifically, it is first shown that all the states are coordinated to aggregate within the target region, i.e., coordinated aggregation. With this result, it is next shown that all the states are coordinated towards a consensus, i.e., state agreement. These together guarantee the fulfillment of the concerned coordinated aggregation objective. Finally, a simulation example is given to validate the theoretical results.     

Mutual synchronization behavior for chaotic systems via limited capacity communication channels

Several important properties of chaos synchronization of bidirectional coupled systems remain still unexplored. This article investigates synchronization behavior for chaotic systems subject to states quantization. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed to strictly synchronize chaotic systems via limited capacity communication channels. Furthermore, it is important to point out that the mutual synchronization behavior for bidirectional coupled systems is determined by the amount of transmitting information and the initial states of coupled systems. © 2015 Wiley Periodicals, Inc. Complexity 21: 335–342, 2016     

Hybrid consensus for multi-agent systems with time-driven jumps

In this paper, the behavior of scalar multi-agent systems over networks subject to time-driven jumps. Assuming that all agents communicate through distinct communication digraphs at jump and flow times, the asymptotic multi-consensus behavior of the hybrid network is explicitly characterized. The hybrid multi-consensus is shown to be associated with a suitable partition that is almost equitable for both the jump and flow communication digraphs. In doing so, no assumption on the underlying digraphs is introduced. Finally, the coupling rules making the multi-consensus subspace attractive are established. Several simulation examples illustrate the theoretical results.     

Leader-following finite-time consensus for multi-agent systems with jointly-reachable leader

Finite-time consensus problems of the leader-following multi-agent systems with jointly-reachable leader and switching jointly-reachable leader are studied in this paper. Based on the graph theory, LaSalle’s invariance principle and Lyapunov stability theory, the finite-time consensus protocols are presented for the first-order and second-order leader-following systems. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

Queueing models for the analysis of communication systems

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.     

An optimal repair policy for systems with a limited number of repairs

Traditionally in reliability literature, the repair facilities are always available. This work considers a more general case in which the repair facilities are not always available, but are available only until a fixed number of repairs have been completed. Different assumptions are made to analytically determine an optimal repair policy maximizing the expected reward.     

Reliability analysis of complex communication systems

This paper deals with a first-come, first-served (FCFS) queueing model to analyze the asymptotic behavior of a heterogeneous finite-source communication system with a single processor. Each source and the processor are assumed to operate in independent random environments, allowing the arrival and service processes to be Markov-modulated ones. Each message is characterized by its own exponentially distributed source and processing time with parameter, depending on the state of the corresponding environment, that is, the arrival and service rates are subject to random fluctuations. Assuming that the arrival rates of the messages are many times greater than their service rates (“fast” arrival), it is shown that the time to the first system failure converges in distribution, under appropriate norming, to an exponentially distributed random variable. Some simple examples are considered to illustrate the effectiveness of the method proposed by comparing the approximate results to the exact ones. Supported by the Hungarian National Foundation for Scientific Research (grant No. OTKA T14974/95). Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.     

Consensus of heterogeneous multi-agent systems with linear and nonlinear dynamics

In this paper, we perform an in-depth study about the consensus problem of heterogeneous multi-agent systems with linear and nonlinear dynamics.Specifically, this system is composed of two classes of agents respectively described by linear and nonlinear dynamics. By the aid of the adaptive method and Lyapunov stability theory, the mean consensus problem is realized in the framework of first-order case and second-order case under undirected and connected networks.Still, an meaningful example is provided to verify the effectiveness of the gained theoretical results. Our study is expected to establish a more realistic model and provide a better understanding of consensus problem in the multi-agent system.     

Interleaving multi-agent systems and social networks for organized adaptation

Ad hoc networks can be formed from arbitrary collections of sensors, mobile routers, or business processes. These networks are open systems, in the sense that the network nodes share a common language but do not necessarily share a common goal or common knowledge, and there is no centralised controller or global data repository. Such systems have numerous advantages in terms of enabling autonomous, heterogeneous components to achieve individual goals without central direction and with only partial knowledge. However, operational problems stem from potential conflicts over resource allocation, miscommunication, and sub-ideal operation, and the general need of embedded systems to change behaviour according to changes in the environment. To address these problems, we propose to converge aspects of norm-governed specification from distributed multi-agent systems, opinion formation from social networks, and voting procedures from computational social choice. In particular, we develop a prototype system which interleaves gossiping, expressed preferences (voting) and norms, to configure rules and assign roles. This is another demonstration of the use of socially-inspired mechanisms for regulation of decentralised systems and a key step towards the realization of organized adaptation for open multi-agent systems.     

Robust fixed-time consensus protocols for multi-agent systems with nonlinear state measurements

This paper solves the robust fixed-time consensus problem for multi-agent systems with nonlinear state measurements. Sufficient conditions are established for the proposed protocol to reach fixed-time consensus under time-varying undirected and fixed directed topology with the aid of Lyapunov functions. It is proved that the finite settling time of the presented protocol for robust consensus is uniformly bounded for any initial condition, which makes it possible for people to design and estimate the convergence time off-line. Numerical simulations are preformed to show the effectiveness of our proposed protocol.     

On consensus speed of multi-agent systems with double-integrator dynamics

The performance of multi-agent systems is an important issue. In this paper, it is focused on consensus speed for multi-agent systems with double-integrator dynamics and fixed undirected graphes under a kind of consensus protocols. It is revealed that, under some conditions, the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the Laplacian matrix of the undirected connected graph. Based on the mentioned results, arbitrary desired consensus speed can be achieved by choosing suitable feedback gains. Numerical simulations are given to illustrate the main results.     

Consensus of second-order discrete-time multi-agent systems with fixed topology

This paper studies the consensus of second-order discrete-time multi-agent systems with fixed topology. First, we formulate the problem and give some preliminaries. Then, by algebraic graph theory and matrix theory, the convergence of system matrix is analyzed. Our main results indicate that the consensus of second-order system can be achieved if and only if the topology graph has a directed spanning tree and the values of the scaling parameters satisfy a range. The eigenvalues of the corresponding Laplacian matrix play a key role in reaching consensus. Finally, numerical simulations are given to illustrate the results.     

Impulsive consensus of multi-agent systems with stochastically switching topologies

In this paper, the impulsive consensus problem for multi-agent systems is investigated. The purpose of this paper is to provide a valid consensus protocol that overcomes the difficulty caused by stochastically switching structures via impulsive control. Some sufficient conditions of almost sure consensus are proposed when the switching structures are the independent process or the Markov process. It is shown that the sum-zero rows of matrix play a key role in achieving group consensus. Furthermore, simulation examples are provided to illustrate and visualize the effectiveness of these results.     

Multi-period forecasting and scenario generation with limited data

Data for optimization problems often comes from (deterministic) forecasts, but it is naïve to consider a forecast as the only future possibility. A more sophisticated approach uses data to generate alternative future scenarios, each with an attached probability. The basic idea is to estimate the distribution of forecast errors and use that to construct the scenarios. Although sampling from the distribution of errors comes immediately to mind, we propose instead to approximate rather than sample. Benchmark studies show that the method we propose works well.     

Consensus of second-order and high-order discrete-time multi-agent systems with random networks

This paper studies the convergence and convergence speed for the second-order and the high-order discrete-time multi-agent systems with random networks and arbitrary weights. Random networks mean that the existence of any edge is probabilistic and independent of any other edge. By introducing the agreement set, velocity control gain and high-order state control gain, some consensus protocols are provided for the discrete-time random networks. Moreover, the per-step and asymptotic convergence factors are proposed to measure the convergence and convergence speed. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.     

Formation control for second-order multi-agent systems with time-varying delays under directed topology

In this paper, we investigate a formation control problem for second-order multi-agent systems with directed graph interconnection topologies that contain time-varying coupling delays. By using a special multiple leaders’ framework, sufficient conditions are obtained for both time-invariant and time-varying formations as well as for time-varying formations for trajectory tracking, which guarantees the attainment of the formations is at exponentially converging speeds. Some numerical simulations are also conducted to validate the theoretical results.