Markovian Switching Topologies Research Articles

Event-triggered leader-following consensus for multi-agent systems with semi-Markov switching topologies

This paper investigates the event-triggered leader-following consensus problem for a multi-agent system with semi-Markov switching topologies. A sampled-data-based event-triggered transmission scheme is introduced to reduce unnecessary communication. By modeling the switching of network topologies by a semi-Markov process and adopting an event-triggered transmission scheme, a new consensus protocol is proposed. Compared with the traditional Markovian switching topologies, the transition rates in the semi-Markov switching topologies are time-varying, which is more general and practicable. Through utilization of an appropriate Lyapunov–Krasovskii functional, some sufficient conditions are derived, which guarantee that the leader-following consensus can be achieved in mean-square sense. Moreover, the consensus gain matrices and parameter of the event-triggered scheme can be efficiently solved out. Finally, a numerical example illustrates the effectiveness of the proposed design technique.

Mean-square consensus of heterogeneous multi-agent systems with nonconvex constraints, Markovian switching topologies and delays

Abstract This paper addresses the velocity-constrained mean-square consensus problem of heterogeneous multi-agent systems with Markovian switching topologies and time-delay, which consist of first-order and second-order agents. A distributed control law with time-varying gains is proposed to make the position states of both first-order and second-order agents mean-square converge to a common point and the velocities of second-order agents mean-square converge to zero, while their velocities remain in the corresponding nonconvex constraint sets. Based on novel multiple model transformations, the consensus analysis is completed by studying the asymptotic dynamics of a time-varying matrix system. Finally, simulations are provided to demonstrate the effectiveness of the proposed algorithms.

Energy-to-peak consensus for multi-agent systems with stochastic disturbances and Markovian switching topologies

This paper is concerned with the problem of energy-to-peak consensus for a class of multi-agent systems with both stochastic disturbances and Markovian switching topologies. The objective is to design a control protocol in the form of dynamic output feedback, such that the multi-agent system reaches mean square consensus and has a prescribed energy-to-peak disturbance attenuation level. By using linear transformations, the problem is transformed into a standard energy-to-peak control problem. Then a new bounded real lemma is established. On the basis of this, an approach for the design of the control protocol is developed, by which the desired gain can be obtained via solving a number of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

Event-Based Time Varying Formation Control for Multiple Quadrotor UAVs with Markovian Switching Topologies

Time varying formation control problem for a group of quadrotor unmanned aerial vehicles (UAVs) under Markovian switching topologies is investigated through a modified dynamic event-triggered control protocol. The formation shape is specified by a time varying vector, which prescribes the relative positions and bearings among the whole agents. Instead of the general stochastic topology, the graph is governed by a set of Markov chains to the edges, which can recover the traditional Markovian switching topologies in line with the practical communication network. The stability proof for the state space origin of the overall closed-loop system is derived from the singular perturbation method and Lyapunov stability theory. An event-triggered formation control protocol in terms of a dynamically varying threshold parameter is delicately carried out, while acquiring satisfactory resource efficiency, and Zeno behavior of triggering time sequences is excluded. Finally, simulations on six quadrotor UAVs are given to verify the effectiveness of the theoretical results.

Master‐slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation

SummaryIn this paper, the master‐slave synchronization for coupled neural networks with Markovian jumping topology and stochastic perturbation is discussed. Based on a graph theory, the ergodic property of the Markovian chain, and the strong law of the large numbers for local martingales, several sufficient conditions are established to ensure the almost sure exponential synchronization or asymptotic synchronization in mean square for coupled neural networks with Markovian jumping topology. By the pinning control method, the chaotic synchronization between the master system and the slave systems with stochastic disturbance is achieved. The effectiveness of the results is finally illustrated by a numerical example.

Group tracking control of second-order multi-agent systems with fixed and Markovian switching topologies

Abstract This paper studies the group consensus tracking issues of discrete time second-order multi-agent systems (MASs) with directed fixed and Markovian switching topologies, respectively. For MASs with m leaders, we first introduce a method to divide the whole MASs into m subgroups. Based on the subgroup-divided method, the condensation directed graph G of the communication topology of the whole MASs becomes a directed acyclic graph (DAG). Then, for MASs with fixed/Markovian switching topology, some sufficient/necessary and sufficient group consensus tracking criteria are established. Finally, simulation examples are given to illustrate the effectiveness of our results.

Exponential consensus of non‐linear multi‐agent systems with semi‐Markov switching topologies

This study investigates the leader-following consensus problem for non-linear multi-agent systems with semi-Markov switching topologies. The dynamics of the leader agent and the follower agents is described by a general linear system. Since the transition rates of the semi-Markov switching topologies are time-varying, they are more general and practicable than the classic Markov switching topologies. A novel consensus protocol based on outdated states is proposed for multi-agent systems. By a system transformation, the consensus problem of multi-agent systems is converted into the stability problem of semi-Markov switching systems. The controller design condition is derived utilising the semi-Markov jump system theory and algebraic graph theory, which can guarantee that the multi-agent systems achieve a consensus with an exponential decay rate. A numerical example is given to illustrate the effectiveness of the proposed method.

Mean-square consensus of discrete-time multi-agent systems with Markovian switching topologies and persistent disturbances

This article deals with the leader-following mean-square consensus problem of discrete-time general linear multi-agent systems with Markovian switching topologies and persistent disturbances. Assume that the communication topology is not connected at any time but the union topology is connected. First, the estimators are designed to calculate the states of agents when external disturbance not exists. Based on the error information between the truth-values and estimated-values of states, the compensators are proposed to subject to the effect of persistent disturbances. And then, a new mean-square consensus control protocol is proposed for each agent. Second, by using the property of permutation matrix, the original closed-loop system is transferred into an equivalent system. Third, sufficient conditions for mean-square consensus are obtained in the form of matrix inequalities. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.

Event-based consensus for second-order multi-agent systems with actuator saturation under fixed and Markovian switching topologies

This paper studies the event-based consensus problem of second-order multi-agent systems with actuator saturation under fixed topology and Markovian switching topologies. By a model transformation, the consensus problem is first converted into the stability problem of the error system. Using discontinuous Lyapunov functional approach, two sufficient conditions on the consensus are derived for second-order multi-agent systems with fixed topology and Markovian switching topologies, respectively. The discontinuous Lyapunov functions take full account of the characteristics of the sawtooth delay, and thus lead to a less conservative consensus criterion. It is shown that the consensus condition depends on the parameters of sampling period, Laplacian matrix, and event-triggered parameter. In addition, this paper provides an effective method to co-design both the consensus controller and the event-triggered parameter. Finally, two numerical examples are provided to illustrate the effectiveness and feasibility of the proposed algorithm.

Consensus of multiple autonomous underwater vehicles with double independent Markovian switching topologies and timevarying delays**Project supported by the National Natural Science Foundation of China (Grant Nos. 51679057, 51309067, and 51609048), the Outstanding Youth Science Foundation of Heilongjiang Providence of China (Grant No. JC2016007), and the Natural Science Foundation of Heilongjiang Province, China (Grant No. E2016020).

A new method in which the consensus algorithm is used to solve the coordinate control problems of leaderless multiple autonomous underwater vehicles (multi-AUVs) with double independent Markovian switching communication topologies and time-varying delays among the underwater sensors is investigated. This is accomplished by first dividing the communication topology into two different switching parts, i.e., velocity and position, to reduce the data capacity per data package sent between the multi-AUVs in the ocean. Then, the state feedback linearization is used to simplify and rewrite the complex nonlinear and coupled mathematical model of the AUVs into a double-integrator dynamic model. Consequently, coordinate control of the multi-AUVs is regarded as an approximating consensus problem with various time-varying delays and velocity and position topologies. Considering these factors, sufficient conditions of consensus control are proposed and analyzed and the stability of the multi-AUVs is proven by Lyapunov–Krasovskii theorem. Finally, simulation results that validate the theoretical results are presented.

Distributed optimisation for multi-agent systems with the first-order integrals under Markovian switching topologies

ABSTRACTThis paper studies the distributed optimisation problem for multi-agent systems with the first-order dynamics over Markovian switching topologies. The interaction topology among agents’ switches following a Markov process and each topology is modelled as a state of the Markov process. The aim is to minimise the global cost functions and make the agents converge to the optimal point through the network communication between the agents, where each agent has a local convex cost function only known by itself. Utilising the knowledge of convex analysis and graph theory, we establish a distributed algorithm for the optimisation problem with randomly switching topologies. A sufficient condition for the existence of such algorithm is obtained by using the Lyapunov method. Besides, the result is also extended to the cases of a Markov process with partially unknown transition rates. Finally, numerical simulations are given to validate the proposed algorithm.

Mean-Square Consensus Seeking over Multi-Interconnection Dynamical Networks with Markovian Switching Topologies

This paper considers the mean-square consensus problem for a nonlinear complex dynamical network system with Markovian switching topologies, topology uncertainties and time-varying delays. For the system, each node is a Lure system whose nonlinearity satisfies a sector condition, and more than one interconnections are considered in view of the fact that the subsystems of networks may be multiple interconnected. By using the linear matrix inequality method and the partial stability theory, sufficient conditions of the exponentially mean-square consensus are obtained for the nonlinear complex dynamical network Lure system in the Markovian switching topologies. Moreover, a novel static output controller has been designed to make the system achieve exponentially mean-square consensus successfully. Finally, a numerical example is presented to illustrate the efficiency and applicability of the proposed methods.

Mean-square consensus of heterogeneous multi-agent systemsunder Markov switching topologies

This paper concerns the mean-square consensus of a heterogeneous multi-agent system, which consists of first- and second-order agents, under Markovian switching topologies. Firstly, based on information from neighboring agents, control protocols are designed for the first- and second-order agents, respectively. Secondly, by using the properties of a stochastic irreducible aperiodic matrix, the sufficient and necessary conditions for the heterogeneous multi-agent systems to realize mean-square consensus are obtained. Finally, numerical simulations are conducted to illustrate the effectiveness of the theoretical results.

Event‐triggered H ∞ Markovian switching pinning control for group consensus of large‐scale systems

This study investigates the pinning control issue for group consensus of large-scale systems (LSSs) with communication topology changes and network disturbances. A node selection principle is firstly designed to choose appropriate control nodes, and a centralised pinning control protocol is proposed to drive LSSs achieving group consensus. For reducing control command updates, an event-trigger is employed to determine whether control signal need be changed. Since the node receives compound exogenous disturbances from its communication neighbours, an improved point-to-area H ∞ index is advocated as a system robustness performance. Considering communication topology changes, an event-triggered H ∞ Markovian switching pinning control law is finally established and a sufficient controller and event-trigger co-design method is presented. Under this strategy, the group consensus of LSSs with a pre-scheduled H ∞ performance can be simultaneously achieved while the Markovian switching topologies are tolerated, moreover, only fewer nodes are controlled and seldom control commands are updated. Finally, illustrative examples are given to demonstrate the effectiveness of the proposed theoretical result.

Consensus stabilization in stochastic multi-agent systems with Markovian switching topology, noises and delay

This paper investigates the consensus stabilization problem of stochastic multi-agent systems with noises, Markovian switching topology, and communication delays. To solve the consensus problem of the group of interacting agents, it is supposed to use the stochastic approximation type algorithm with the step-size non-decreasing to zero. For stochastic approximation based consensus algorithms with switching topologies, the existing convergence analysis methods may be difficult to guarantee for switching digraphs because these techniques heavily relies on quadratic Lyapunov functions. To overcome the inherent limitations of the existing methods, we develop a new ergodicity approach for backward products of degenerating stochastic matrices via a discrete time dynamical system approach to analyze the consensus stabilization problem of stochastic multi-agent systems with noises, Markovian switching topology, and communication delays; and we attain necessary and sufficient condition of the consensus stabilization. Our approach does not require the double stochasticity condition typically assumed for the existence of a quadratic Lyapunov function, and provides an effective tool for analyzing consensus problems via the existing theory of stochastic matrices and ergodicity of backward products. Finally, numerical simulation is shown to demonstrate theoretical results.

Distributed sampled-data asynchronous H∞ filtering of Markovian jump linear systems over sensor networks

This paper is concerned with distributed sampled-data asynchronous H∞ filtering for a continuous-time Markovian jump linear system over a sensor network, where jumping instants of system modes and filter modes are asynchronous. A group of sensor nodes are deployed to measure the system׳s output and to collaboratively share the measurement with neighboring nodes in accordance with Markovian switching topologies. First, the measurement on each sensor node is sampled at separate discrete instants and transmitted to a remote filter through a communication network. Network-induced signal transmission delays are incorporated in data transmission channels. Second, distributed sampled-data asynchronous H∞ filters, governed by a finite piecewise homogeneous Markov process, are delicately constructed. The resultant filtering error system is transformed into a piecewise homogeneous Markovian jump linear system with delays. Third, sufficient conditions on the existence of desired distributed sampled-data asynchronous H∞ filters are derived such that the filtering error system is stochastically stable with the prescribed weighting average H∞ performance. Finally, three illustrative examples are given to show the effectiveness and advantage of the proposed theoretical results.

Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies

This paper concerns the synchronization problem of complex networks with the random switching topologies. By modeling the switching of network topologies as a Markov process, a novel event-triggered synchronization strategy is proposed. Unlike the existing strategies, the event detection of this strategy only works at the network topology switching time instant, which can significantly decrease the communication frequency between nodes and save the network resources. Under this strategy, the synchronization problem of complex network is equivalently converted to the stability of a class of Markovian jump systems with a time-varying delay. By using the Lyapunov–Krasovskii functional method and the weak infinitesimal operation, a sufficient condition for the mean square synchronization of the complex networks subject to Markovian switching topologies is established. Finally, a numerical simulation example is provided to demonstrate the theoretical results.

Couple-group consensus of continuous-time multi-agent systems under Markovian switching topologies

This paper studies the couple-group consensus problem of multi-agent systems with general linear time-invariant dynamics. The interaction among agents is governed by a continuous-time homogeneous Markov process, whose state space corresponds to all the possible communication topologies. A linear consensus protocol is introduced to realize the couple-group consensus, where the agents in one subnetwork reach a consistent state while those in the other subnetwork reach another consistent state. When the agent dynamics is stabilizable, it is found that the couple-group consensus can be achieved under some mild algebraic and topological conditions of the inter-communication and intra-communication of agents in the two subnetworks. Appropriate consensus gain is designed and the speed to consensus is derived. Finally, three numerical examples are included to illustrate the obtained results.

Guaranteed cost control of mobile sensor networks with Markov switching topologies

This paper investigates the consensus seeking problem of mobile sensor networks (MSNs) with random switching topologies. The network communication topologies are composed of a set of directed graphs (or digraph) with a spanning tree. The switching of topologies is governed by a Markov chain. The consensus seeking problem is addressed by introducing a global topology-aware linear quadratic (LQ) cost as the performance measure. By state transformation, the consensus problem is transformed to the stabilization of a Markovian jump system with guaranteed cost. A sufficient condition for global mean-square consensus is derived in the context of stochastic stability analysis of Markovian jump systems. A computational algorithm is given to synchronously calculate both the sub-optimal consensus controller gains and the sub-minimum upper bound of the cost. The effectiveness of the proposed design method is illustrated by three numerical examples.

Mean square containment control problems of multi-agent systems under Markov switching topologies

The paper investigates containment control for multi-agent systems under Markov switching topologies. By using graph theory and the tools of stochastic analysis, sufficient conditions of mean square containment control problems are derived for the second-order multi-agent systems. Then the obtained results are further extended to high-order multi-agent systems.