Markovian Switching Topologies Research Articles

Optimal Model-Free Mean-Square Consensus for Multi-Agents with Markov Switching Topology

Due to the real applications, optimal consensus reinforcement learning with switching topology is still challenging due to the complexity of topological changes. This paper investigates the optimal consensus control problem for discrete multi-agent systems under Markov switching topologies. The goal is to design an appropriate algorithm to find the optimal control policies that minimize the performance index while achieving consensus among the agents. The concept of mean-square consensus is introduced, and the relationship between consensus error and tracking error to achieve mean-square consensus is studied. A performance function for each agent under switching topologies is established and a policy iteration algorithm using system data is proposed based on the Bellman optimality principle. The theoretical analysis shows that the consensus error realizes mean-square consensus and the performance function is optimized. The efficacy of the suggested approach is confirmed by numerical simulation using an actor–critic neural network. As a result, the value function is the optimum and the mean-square consensus can be reached using this technique.

Consensus for discrete-time second-order multi-agent systems in the presence of noises and semi-Markovian switching topologies

In this paper, we focus on the control problem of mean square consensus for second-order continuous-time multi-agent systems with multiplicative noises under Markovian switching topologies. A new Lyapunov function based on the Laplacian matrix of the corresponding union topology of all possible topologies is designed for the stochastic stability analysis of consensus. Applying matrix theory and stochastic stability for stochastic differential equations, we can analyze the consensus problem of the considered systems with the designed Lyapunov function. In addition, we present the sufficient conditions of the mean square consensus exponentially for the considered stochastic systems. Finally, we give an simulation example to numerically validate our theoretical results.

Stochastic distributed tracking of heterogeneous multi‐agent systems with Markovian switching topologies and infinite delays

Stochastic distributed tracking of heterogeneous multi‐agent systems with Markovian switching topologies and infinite delays

Finite-time formation trajectory tracking control for unmanned underwater vehicles with time delays and Markov-switch topology

ABSTRACT The formation trajectory tracking control strategy of unmanned underwater vehicles is proposed for communication time delay and communication topology random switching. The methods ensure that formation systems are finite-time bounded under discrete time. Firstly, based on the consistency theory and the exact feedback linearised dynamics model of unmanned underwater vehicle, a control strategy is proposed for discrete formation system with communication time delay. Secondly, a cooperative control method is designed for communication problems of Markovian switching topology and time delay. Then, definition of finite-time bounded and linear matrix inequality technique are applied to sufficient conditions of system stability for the above problem. Finally, the formation motion of discrete unmanned underwater vehicle system in three-dimensional space is simulated, fully demonstrating the feasibility of the method.

Novel Dynamic Event-Triggered Consensus Control of Multiagent Systems With Markovian Switching Topologies Under DoS Attacks.

This article focuses on the issue of novel dynamic event-triggered consensus control of multiagent systems (MASs) with denial-of-service (DoS) attacks. Different from the conventional Markovian switching topologies, the generally uncertain semi-Markovian (GUSM) switching topologies with partially unknown elements and time-dependent uncertainties are constructed for the leader-following MASs by considering the equipment performance and external uncertain environment influence. To save communication resources, the novel dynamic memory event-triggered strategy (DMETS) is presented to decrease the frequency of communication between agents. Some secure consensus control criteria are established for the MASs with GUSM switching topologies and DoS attacks due to the potential system communication disruption caused by attackers. Finally, two physical system examples are designed to prove the effectiveness of the presented method.

Partial component consensus in mean‐square for delayed nonlinear multi‐agent systems with uncertain nonhomogeneous Markov switching topologies and aperiodic denial‐of‐service cyber‐attacks

The partial component consensus in mean‐square for delayed nonlinear multi‐agent systems (NMASs) with uncertain nonhomogeneous Markov switching (UNMS) topologies subjected to aperiodic denial‐of‐service (DoS) cyber‐attacks is investigated. Firstly, the partial component ( ‐dimensional) consensus of the system ( ‐dimensional, ) is considered in this paper. When , the partial component consensus degrades into identical consensus. Secondly, the communication topologies governed by uncertain nonhomogeneous Markov chains are random. Thirdly, the communication topologies suffer from aperiodic DoS cyber‐attacks. Then, in view of stochastic analysis technology, distributed control theory and Lyapunov stability theory, the partial component consensus conditions are obtained using permutation matrix and inequality scaling skills. Eventually, the correctness of the results is verified through an example.

Practical finite‐time and fixed‐time multigroup consensus for second‐order nonlinear multi‐agent systems with Markov switching topology

AbstractPractical finite‐time and fixed‐time multigroup consensus questions for second‐order nonlinear multi‐agent systems (MASs) with Markov switching topologies are investigated in this article. Based on the topology of switching, each agent will appear to switch between different groups, and by setting up group switching signal variables embedded in error variables for each agent, finite‐time and fixed‐time control protocols are proposed, respectively, such that the conditions that must be satisfied for all agents to achieve practical finite‐time multigroup consensus and practical fixed‐time multigroup consensus can be obtained, respectively. For unknown nonlinear functions in the dynamical system, a radial basis function neural network (RBFNN) fit is used for approximation. Correspondingly, two examples are provided to verify the control effects of the control protocols.

Finite-time synchronization for coupled neural networks with time-delay jumping coupling

The finite-time synchronization problem is studied for coupled neural networks (CNNs) with time-delay jumping coupling. Markovian switching topologies, imprecise delay models, uncertain parameters and the unavailable of topology modes are considered in this work. A mode-dependent delay with pre-known conditional probability is built to handle the imprecise delay model problem. A hidden Markov model with uncertain parameters is introduced to describe the mode mismatch problem, and an asynchronous controller is designed. Besides, a set of Bernoulli processes models the random packet dropouts during data communication. Based on Markovian switching topologies, mode-dependent delays, uncertain probabilities and packet dropout, a sufficient condition that guarantees the CNNs reach finite-time synchronization (FTS) is derived. Finally, a numerical example is derived to demonstrate the efficiency of the proposed synchronous technique.

Almost sure finite-time synchronization of Markov jump complex dynamical networks with asynchronous switching

The almost sure finite-time synchronization for Markovian jump complex dynamical networks (CDNs) with time-varying delay is studied. The designed controller is supposed to be asynchronous with the CDNs states. The existing almost sure synchronization result of networks is explored within a finite time interval. The sampled-data control approach is employed to improve the control precision. Some sufficient criteria are obtained under the definition of almost sure finite-time synchronization for the CDNs with Markovian switching topology. To determine the asynchronous controller gain, the linear matrix inequality-based conditions are proposed. Then, two examples are given to illustrate the effectiveness.

$ H_\infty $ deployment of nonlinear multi-agent systems with Markov switching topologies over a finite-time interval based on T–S fuzzy PDE control

<abstract><p>The deployment of multi-agent systems (MASs) is widely used in the fields of unmanned agricultural machineries, unmanned aerial vehicles, intelligent transportation, etc. To make up for the defect that the existing PDE-based results are overly idealistic in terms of system models and control strategies, we study the PDE-based deployment of clustered nonlinear first-order and second-order MASs over a finite-time interval (FTI). By designing special communication protocols, the collective dynamics of numerous agents are modeled by simple fist-order and second-order PDEs. Two practical factors, external disturbance and Markov switching topology, are considered in this paper to better match actual situations. Besides, T–S fuzzy technology is used to approximate the unknown nonlinearity of MASs. Then, by using boundary control scheme with collocated measurements, two theorems are obtained to ensure the finite-time $ H_\infty $ deployment of first-order and second-order agents, respectively. Finally, numerical examples are provided to illustrate the effectiveness of the proposed approaches.</p></abstract>

A Novel Event-Triggered Bipartite Consensus for PDE-Based Multiagent Systems With Switching Topologies and Antagonistic Interactions.

Unlike the traditional studies on multiagent systems (MASs), this article investigates a class of MASs with spatial properties, whose agents are modeled by partial differential equations (PDE), in addition, to make the model more comprehensive, the Markovian switching topology with partially unknown probability is taken into account. The purpose of this article is to achieve the bipartite consensus for the above PDE-based MASs. In fact, the consideration of spatial factors in MASs will exacerbate the network transmission pressure, to overcome this problem, a novel spatiotemporal event-triggered mechanism is developed. Compared with the existing event-triggered mechanism, the proposed one is not only time-dependent but also covers the influence of spatial variables on the trigger conditions, which helps to further reduce the triggering frequency. Finally, three examples are given to verify the validity of the conclusion we proposed.

A leader-following consensus of multi-agent systems with actuator saturation and semi-Markov switching topologies.

The leader-following consensus (LFC) issue is investigated in this paper for multi-agent systems (MASs) subject to actuator saturation with semi-Markov switching topologies (SMST). A new consensus protocol is proposed by using a semi-Markov process to model the switching of network topologies. Compared to the traditional Markov switching topologies, the SMST is more general and practical because the transition rates are time-varying. By using the local sector conditions and a suitable Lyapunov-Krasovskii functional, some sufficient conditions are proposed such that the leaderfollowing mean-square consensus is locally achieved. Based on the derived sufficient conditions, an optimization problem is analyzed to determine the consensus feedback gains and to find a maximal estimate of the domain of consensus attraction (DOCA) of a closed-loop model. At the end, a numerical case is presented to verify the performance of the design method.

Adaptive Neural Consensus of Unknown Non-Linear Multi-Agent Systems with Communication Noises under Markov Switching Topologies

In this paper, the adaptive consensus problem of unknown non-linear multi-agent systems (MAs) with communication noises under Markov switching topologies is studied. Based on the adaptive control theory, a novel distributed control protocol for non-linear multi-agent systems is designed. It consists of the local interfered relative information and the estimation of the unknown dynamic. The Radial Basis Function networks (RBFNNs) approximate the nonlinear dynamic, and the estimated weight matrix is updated by utilizing the measurable state information. Then, using the stochastic Lyapunov analysis method, conditions for attaining consensus are derived on the consensus gain and the weight of RBFNNs. The main findings of this paper are as follows: the consensus control of multi-agent systems under more complicated and practical circumstances, including unknown nonlinear dynamic, Markov switching topologies and communication noises, is discussed; the nonlinear dynamic is approximated based on the RBFNNs and the local interfered relative information; the consensus gain k must to be small to guarantee the consensus performance; and the proposed algorithm is validated by the numerical simulations finally.

Practical finite-time and fixed-time containment for second-order nonlinear multi-agent systems with IDAs and Markov switching topology

In this article, the finite-time containment problem and the fixed-time containment problem accompanied by injection and deception attacks (IDAs) and Markov switching topology for second-order nonlinear multi-agent systems (MASs) are investigated, respectively. By introducing a radial basis function neural network (RBFNN), the approximation property of radial basis neural networks is used to solve the unmeasurable difficulties of nonlinear functions and injection attacks. Finite-time and fixed-time distributed control protocols are proposed for switching topologies and attack-induced state deception and control injection, and finite-time and fixed-time containment as well as obtaining their corresponding sufficient conditions are achieved, respectively. Correspondingly, two examples are shown to demonstrate the feasibility of the control protocols.

Distributed optimal consensus of multiagent systems with Markovian switching topologies: synchronous and asynchronous communications

Distributed optimal consensus of multiagent systems with Markovian switching topologies: synchronous and asynchronous communications

Fault detection and time-varying formation control for nonlinear multi-agent systems with Markov switching topology

Fault detection and time-varying formation control for nonlinear multi-agent systems with Markov switching topology

Consensus of nonlinear multiagent systems with mode‐dependent delay via stochastic sampled data under Markovian switching topologies

AbstractIn this article, we investigate the mean‐square consensus problem of multiagent systems with one leader and multiple followers. In consideration of the uncertain disturbance from external environment or internal change of system, the interaction topology and time‐varying delay switch randomly which are regulated by a time‐homogeneous Markovian chain. The distributed control protocol is designed based on the stochastic sampling information from its neighbors and the leader. Using stochastic Lyapunov theory and linear matrix inequality (LMI) approach, the sufficient condition is concluded to guarantee the mean‐square consensus. For the undirected topology case, a low‐dimensional LMI‐based consensus criterion is further derived based on the matrix diagonalization method. Finally, a numerical simulation is provided to demonstrate the reasonability of the theoretical results.

The cooperatability of the first-order multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies

We investigate the cooperatability of the first-order leader-following multi-agent systems consisting of a leader and a follower with multiplicative noises under Markov switching topologies. Each agent exhibits first-order linear dynamics, and there are multiplicative noises along with information exchange among the agents. What is more, the communication topologies are Markov switching topologies. By utilizing the stability theory of the stochastic differential equations with Markovian switching and the Markov chain theory, we establish the necessary and sufficient conditions for the cooperatability of the leader-following multi-agent systems. The conditions are outlined below: (ⅰ) The product of the system parameter and the square of multiplicative noise intensities should be less than 1/2; (ⅱ) The transition rate from the unconnected graph to the connected graph should be twice the system parameter; (ⅲ) The transition rate from the connected graph to the unconnected graph should be less than a constant that is related to the system parameter, the intensities of multiplicative noises, and the transition rate from the unconnected graph to the connected graph. Finally, the effectiveness of our control strategy is demonstrated by the population growth systems.

Secure Consensus Control for PDE-Based Multiagent Systems Resist Hybrid Attacks

This article investigates the secure consensus control for a class of multiagent systems (MASs). Considering the spatial dynamic behaviors of each agent, the model based on parabolic partial differential equations (PDE) is developed, which means the evolution of MASs' state with space and time is taken into account. In contrast to traditional consensus studies, this article considers the leader-following consensus control for MASs with Markovian switching topology and spatial distribution characteristic under replay and denial-of-service (DoS) attacks. The system is guaranteed to achieve asymptotical stability by the method of segmented Lyapunov functions with the requirement that all topologies have a directed spanning tree with the leader as the root. Additionally, to save communication resources in PDE-based MASs, an improved dynamic event-triggered mechanism is employed, and it can improve the dynamic performance of the system compared to the traditional ones. Finally, a numerical example and comparative analysis are provided to verify the work in this article.

Exponential stabilization of stochastic complex networks with Markovian switching topologies via intermittent discrete-time state observation control

This paper is concerned with the exponential stability of the stochastic complex networks with Markovian switching topologies. It is worth emphasizing that the topological structure of the stochastic complex networks is Markovian switching. Not all switching subnetworks must contain a spanning tree or be strongly connected. Moreover, a new type of aperiodically intermittent discrete-time state observation control is proposed, which is a significant extension of discrete-time state observation control and intermittent control. Based on the M-matrix, the Lyapunov method, and the graph theory, some sufficient conditions for exponential convergence. Moreover, we obtain that the average control rate in this paper is greater than the control rate proposed in the existing literature, which is less conservative. In addition, the theoretical results are used to discuss the exponential stability of stochastic coupled oscillators and a communication network model, respectively. Finally, two numerical examples are given to verify the effectiveness of the results.