Impulsive consensus algorithms for second-order multi-agent networks with sampled information

Asynchronous impulsive control for consensus of second-order multi-agent networks

This technical note presents a second-order multi-agent network for distributed optimization with a sum of convex objective functions subject to bound constraints. In the multi-agent network, the agents connect each others locally as an undirected graph and know only their own objectives and constraints. The multi-agent network is proved to be able to reach consensus to the optimal solution under mild assumptions. Moreover, the consensus of the multi-agent network is converted to the convergence of a dynamical system, which is proved using the Lyapunov method. Compared with existing multi-agent networks for optimization, the second-order multi-agent network herein is capable of solving more general constrained distributed optimization problems. Simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi-agent network.

A multiconsensus problem of multiagent networks is solved in this paper, where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks. A distributed impulsive protocol is proposed to achieve multiconsensus of second-order multiagent networks in terms of three categories: 1) stationary multiconsensus; 2) the first dynamic multiconsensus; and 3) the second dynamic multiconsensus. This impulsive protocol utilizes only sampled position data and is implemented at sampling instants. For those three categories of multiconsensus, the control parameters in the impulsive protocol are designed, respectively. Moreover, necessary and sufficient conditions are derived, under which each multiconsensus can be reached asymptotically. Several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results.

This paper studies a class of modified Olfati-Saber flocking control algorithms in the 2nd-order particle multi-agents with single virtual leaders driven autonomously for translational performances and rotational manoeuvrability; curl/divergence aspects of the individual/average trajectories are scrutinised and related to time response features. More specifically, the modified algorithms are embedded with time-varying weighting matrices for achieving multi-agent formation flocking with translational performances (in terms of formation scaling, sub-dimensional confinement and trajectory expansive/conservative/dissipative-ness) and rotational maneuverabilities (in terms of trajectory rotation and curving swiftness). Flocking existence is validated analytically and individual/average trajectory formulas are derived. Simulations in 2D and 3D cases are sketched to show efficacy and significance of the study.

On fast queue consensus of discrete-time second-order multi-agent networks over directed topologies

Manoeuvrable (or time-varying) formation control of second-order integral multi-agent networks with single virtual leaders is contrived by incorporating time-varying weighting matrices into flocking algorithms. Existence and properties are examined, including control bounded-ness, average trajectory and formation manoeuvrability with respect to the weighting matrices and virtual leader reference input. More specifically, it is shown that under the time-varying flocking algorithms, the multi-agents ultimately run into lattice formations and their kinematical features in terms of orientation, scaling, subspace specification and homogeneous/heterogeneous consensus can be manoeuvred. Moreover, by gain-scheduling assignment for the leader-average dynamics via the variation-of-constant formula and iterative learning optimisation, trajectory-tracking manoeuvrable formation control can be achieved. Technical advantages include: flexible formations rather than rigid ones can be dealt with; formation and trajectory tracking can be designed separately and implemented simultaneously; diverse formations are achievable by selecting the weighting matrices; trajectory-tracking control is independent of trajectory modelling. Numerical examples are illustrated to show the main results.

Power systems are special multi-agent systems with nonlinear coupling function and symmetric structures. This paper extends these systems to a class of multi-agent systems with mismatched parameters, linear coupling function, and asymmetric structures and investigates their velocity synchronization via sampled position data. The dynamics of the agents is adopted as that of generators with mismatched parameters, while the system structures are supposed to be complex. Two distributed linear consensus protocols are designed, respectively, for multi-agent systems without or with communication delay. Necessary and sufficient conditions based on the sampling period, the mismatched parameters, the delay, and the nonzero eigenvalues of the Laplacian matrix are established. It is shown that velocity synchronization of multi-agent systems with mismatched parameters can be achieved if the sampled period is chosen appropriately. Simulations are given to illustrate the effectiveness of the theoretical results.

Estimates of agents in a distributed consensus control are aligned with a particular value through interacting on communication graphs, which are of particular interest for researchers in the field of multi-agent coordination. Following this pattern, a discrete-time constrained consensus issue with generalized time delays is first established in this article, which is manipulated into an optimization problem via a quadratic performance index introduced as a global objective function. Then, a novel consensus scheme is investigated and proposed for handling this problem, enabling the consensus to approach the desired state globally and rapidly with optimal system property ensured. Besides, to advance the convergence speed and stability in resisting constant bias or oscillation, an adjustment control method is explored to construct a modified consensus scheme; further, to enhance the scene adaptability, fix topologies are extended to switching ones, and the latter is involved to develop another scheme on this basis. Moreover, the convergence and robustness of these three proposed consensus schemes are substantiated by theoretical analysis and numerical simulations. To highlight the practical implementations, the proposed consensus schemes are incorporated with a winner-take-all operation to accomplish multi-agent competitive coordination in a distributed way, and the results embody their effectiveness and superior consensus control ability, along with strong plasticity. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper is dedicated to investigating and optimizing distributed consensus schemes with time delays and output saturation with application to the competitive coordination of multi-agent systems. On the one hand, the consensus problem with output saturation receives limited attention, and few consensus algorithms consider both saturation limitation and channel gain. On the other hand, most existing studies on consensus with saturation consider simply the dynamic behaviour of agents without employing optimization, thus limiting further improvement of system performance. In this paper, a consensus algorithm is built from an optimization perspective that guarantees the state consensus of a multi-agent system with output constraints and generalized time delays. In addition, a consensus scheme is designed in a discrete-time framework and further modified and perfected along with the idea of considering time delays and expanding diverse topologies. Finally, experiments are conducted by applying the consensus scheme to a winner-take-all operation, with contributions of this paper verified.

Hybrid coordination of multi-agent networks with hierarchical leaders

SummaryA new type of fast distributed Kalman consensus filtering algorithm based on local information feedback is presented to tackle filtering problems in wireless sensor networks. First, this fast filtering issues are transformed into a stochastic stability problem of the dynamic estimation errors, which can be solved by Lyapunov's second method and matrix theory. Then, two sufficient conditions about the proportional‐like feedback (double gains regulation) method and incremental Proportional‐Integral‐Derivative (PID) feedback method for the asymptotical stability of the systems are presented, respectively. Moreover, to achieve a faster convergence rate, a novel optimal method is given by combing a genetic algorithm and incremental PID. Finally, an illustrative example is presented to give a comparison of the convergence speed between the three filtering algorithms in the same condition, and verify the effectiveness and advantage of the proposed theoretical results in this article.

Modeling and analysis of a modified Leslie–Gower type three species food chain model with an impulsive control strategy

In this manuscript, the stability and consensus problem of the leader-following multi-agent system is studied. The state information of the leader is only available to the dynamics of all the followers, while the communication among the agents occurs at sampling instant. The innovative part of this paper is to reach the consensus and attain the stability for prescribed MASs with interval time varying delay using impulsive control in the presence of leader. The interaction between the agent is illustrated by an undirected graph. A class of distributed impulsive protocol relying on sampling information is suggested to reach the leader following consensus. The consensus is critically relying on the sampling period, control gains. By performing the similar procedures, the consensus problem of multi-agent system is converted to stability problem of the error system. By utilizing the stability theory of impulsive systems, algebraic graph theory, sufficient conditions are derived to guarantee the leader-following consensus of the multi-agent system. Terminally, a numerical example is given to show an efficacy of this presented approach and the sureness of theoretical analysis.

In this paper, the consensus problem of multiagent nonlinear directed networks (MNDNs) is discussed in the case that a MNDN does not have a spanning tree to reach the consensus of all nodes. By using the Lie algebra theory, a linear node-and-node pinning method is proposed to achieve a consensus of a MNDN for all nonlinear functions satisfying a given set of conditions. Based on some optimal algorithms, large-size networks are aggregated to small-size ones. Then, by applying the principle minor theory to the small-size networks, a sufficient condition is given to reduce the number of controlled nodes. Finally, simulation results are given to illustrate the effectiveness of the developed criteria.

Discrete-Time Analysis of Multi-Agent Networks with Multiple Consensus Equilibria**This work was sponsored by BAP Project 9141 and Scientific and Technical Research Council of Turkey (TUBITAK) under Grant 114E613.

The design of sensor networks capable of reaching a consensus on a globally optimal decision test, without the need for a fusion center, is a problem that has received considerable attention in the last years. Many consensus algorithms have been proposed, with convergence conditions depending on the graph describing the interaction among the nodes. In most works, the graph is undirected and there are no propagation delays. Only recently, the analysis has been extended to consensus algorithms incorporating propagation delays. In this correspondence, we propose a consensus algorithm able to converge to a globally optimal decision statistic, using a wideband wireless network, governed by a fairly simple MAC mechanism, where each link is a multipath, frequency-selective, channel. The main contribution of the correspondence is to derive necessary and sufficient conditions on the network topology and sufficient conditions on the channel transfer functions guaranteeing the exponential convergence of the consensus algorithm to a globally optimal decision value, for any bounded delay condition.