Markovian Switching Topologies Research Articles

Formula omitted] delayed tracking protocol design of nonlinear singular multi-agent systems under Markovian switching topology

The consensus tracking of singular multi-agent systems (MASs) with Lipschitz-type nonlinearities and exogenous disturbances is researched in this paper. Governed by a Markov chain, the network interaction randomly switches in a directed graph set, where the directed spanning tree is not contained in each graph while exists in the union rooting at the leader node. By utilizing a collection of in-neighbors’ information that involves communication delay, the intention is to design a protocol such that the resultant consensus error system is stochastic admissible with an H∞ disturbance attenuation level. Based on algebraic graph theory, stochastic admissibility analysis and linear matrix inequality (LMI) technique, tracking consistency is first regulated in the concerned MAS by considering the case of completely known transition probabilities. Then, thanks to a group of free-connection weighting matrices, the obtained result is extended to the case that transition probabilities are partially known. Finally, the theoretical analysis is confirmed by some numerical examples.

Distributed Dynamic Self-Triggered Control for Uncertain Complex Networks With Markov Switching Topologies and Random Time-Varying Delay

This paper studies the synchronization of complex networks with probabilistic interval delay and Markov switching topologies by using a novel dynamic self-triggered control (DSTC) scheme. Employing the probability distribution information of the input time-delay, the control protocol is transformed into a new rule with stochastic parameters. Also, a more general case of switching topologies, Markov switching topologies with partial information on transition rate, is discussed. By introducing a free-connection weighting matrix scheme and using the stability theory, a less conservative synchronization result is derived. It is shown by a numerical example that the DSTC method can reduce the sampling frequency apparently, and the tolerable delay upper bound can also be relaxed. In addition, continuous communication and the Zeno-behavior can be avoided.

Improved Consensus Conditions for Multi-Agent Systems With Uncertain Topology: The Generalized Transition Rates Case

This paper is dedicated to addressing the consensus issues for a class of multi-agent systems (MASs) subjected to Markovian switching interaction topology and time-varying input delay. In line with this consideration, we first propose a modified reciprocally convex inequality, named as delay-dependent reciprocally convex inequality to obtain a tighter upper bound about the time-derivative of Lyapunov-Krasovskii functional. As a result, an improved condition with less conservatism stated elegantly in terms of linear matrix inequalities is established such that the MASs with Markovian switching topology and time varying input delay can approach the unified state. Further, the general cases of Markovian switching topology where each transition rate is completely unknown or just its estimate value is known are systematically investigated as well. Moreover, to make our results more meaningful, several comparison results concerning the admissible input delay against other related ones are also presented, which yield that our consensus conditions significantly improve the existing ones advocated thus far. Finally, we verify the validity, the effectiveness, and the practical applicability of our results in the simulation examples.

On reachable set estimation of multi-agent systems

In this paper, the problem of reachable set estimation of multi-agent systems (MASs) is investigated. For the ease of application, balanced communication topology with a directed spanning tree and non-zero initial condition are considered. Based on the Lyapunov method and orthogonal transformation technique, sufficient conditions are established in terms of linear matrix inequalities to guarantee that the reachable set of MASs is bounded by a compact ellipsoid. Moreover, by employing some useful skills from stochastic analysis, the result is then extended to the problem for MASs under Markovian switching topologies. The effectiveness of the obtained results is illustrated by two numerical examples.

Cooperative output regulation problem of discrete-time linear multi-agent systems with Markov switching topologies

This paper studies the cooperative output regulation problem of discrete-time linear multi-agent systems subject to Markov switching topologies.To cope with the problem that some followers cannot directly obtain the state information of the leader and themselves, the distributed state feedback control algorithm and output feedback control algorithm are designed based on the Markov state compensators of the leader and followers, respectively. Then, the corresponding sufficient conditions for solving the cooperative output regulation problem of multi-agent systems with unstable and stable exosystem are proposed, respectively. Finally, numerical simulations are provided to verify the effectiveness of the designed algorithms.

Synchronization of Markovian complex networks with input mode delay and Markovian directed communication via distributed dynamic event-triggered control

In this study, distributed dynamic event-triggered controller containing Markov switching topologies is proposed in Markovian Complex Networks (MCNs). It is proved that the Zeno-behavior is avoided. Considering that the time delay and the controller vary with different modes in practical applications, two terms of the controller are designed to contain Markov switching. And mode-dependent Lyapunov–Krasovskii functions (LKFs) are constructed, whereby the time-varying delay with Markov switching in the controller is perfectly processed. And by constructing a pair of LKFs, some summation terms containing the transition probability are eliminated. In addition, two synchronization criteria for MCNs with input mode delay and Markovian directed communication are established. Finally, numerical simulations are given to illustrate the effectiveness of the proposed method.

Observer-based memory consensus for nonlinear multi-agent systems with output quantization and Markov switching topologies

This paper focuses on the issue of observer based memory consensus design for nonlinear multi-agent systems (MASs) with quantization effects and Markov switching topologies. Notably, an observer based memory consensus protocol with quantization in measurement output is proposed to achieve the consensus of considered nonlinear MASs. Throughout this paper, undirected graph is used to describe the interaction between the neighboring agents. By using Lyapunov technique together with the algebraic graph theory properties, a group of new sufficient conditions is derived in the form of linear matrix inequalities (LMIs) to obtain the consensus of considered nonlinear MASs. Especially, the controller and observer gain matrices are obtained by solving the derived LMIs. Finally, two numerical examples are provided to establish the capability of proposed observer-based consensus protocol.

Bipartite Synchronization of coupled system with Markov switching topology

In this paper, we investigate the leaderless bipartite synchronization problem about nonlinear systems with time delay under Markov switching topologies. We first deal with the strongly connected part of the coupled system. Then, by utilizing the consensus trajectory of the strongly connected agents, we transform the consensus problem into a stable problem. A mild condition about switching topology is proposed which just require the union graph has a spanning tree. We also propose a novel method to deal with the error system. Then, sufficient conditions are presented to make all the systems achieve bipartite synchronization under ergodic Makrov switching topology. At last, an example is given to verify our theory.

Finite-time synchronization of stochastic multi-links dynamical networks with Markovian switching topologies

In this paper, finite-time synchronization of stochastic multi-links dynamical networks with Markovian switching topologies (SMDNM) via intermittent control is discussed. Different from previous literature, topological structure of multi-links complex networks is Markovian switching and each switching subnetwork is not required to contain a directed spanning tree or to be strongly connected. Meanwhile, a novel quantized aperiodically intermittent control is designed and the coupling function is nonlinear. Based on a new differential inequality and Kirchhoff’s Matrix Tree Theorem, a synchronization criterion is derived to ensure finite-time synchronization of SMDNM within a finite time which is closely related to the topology of the network. Moreover, we apply theoretical results to oscillators systems and a synchronization criterion is presented. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the proposed methodology.

Consensus via event-triggered strategy of nonlinear multi-agent systems with Markovian switching topologies

The consensus problem via event-triggered strategy of nonlinear multi-agent systems (MASs) with Markovian switching topologies is addressed in this paper. To simplify information transmission, a distributed event-triggered mechanism (ETM) is designed. By combining the Markovian switching topologies and ETM, an appropriate consensus control protocol is presented. Considering the impact of delay on systems stability, the system model is transformed by the delay system approach. By choosing a Lyapunov–Krasovskii function and applying linear matrix inequalities technique, sufficient conditions are obtained to ensure the consensus stability with H∞ norm bound of the MASs. A numerical simulation is given to confirm the effectiveness of the designed method.

Scaled consensus of multi-agent systems with switching topologies and communication noises

This paper concerns with the mean square scaled consensus for multi-agent systems(MAS) with Markovian switching topologies and communication noises. A time-homogeneous Markov process governs the switching and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain in control protocol which can reduce the effect of communication noises. It is shown that the effect of Markovian switching topologies mainly depends on the union of topologies associated with the positive recurrent states of Markov process. Then necessary and sufficient criteria can be established to guarantee the mean square scaled consensus under the action of distributed protocols. Moreover, the LV operator for semi-Markovian switching topologies case is derived and we can extend our result to the cases that the elements of transition rates matrix are partly unknown and the topological structure is semi-Markovian switching. Finally, an example is conducted to demonstrate the validity of our results.

Necessary and Sufficient Conditions for Consensus of Continuous-Time Multiagent Systems With Markovian Switching Topologies and Communication Noises.

This paper investigates the mean square consensus problem for continuous-time multiagent systems with randomly switching topologies and noises. The switching is governed by a time-homogeneous Markov process, and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain which can reduce the effect of communication noises. It is shown that the effect of Markovian switching topologies mainly depends on the union of topologies associated with the positive recurrent states of the Markov process. Then, necessary and sufficient conditions can be obtained under a control protocol with time-varying gain. Moreover, we extend our result to the cases where the topological structure is semi-Markovian switching and the elements of transition rate matrix are partly unknown. Finally, we give an example to illustrate the validity of our results.

Analysis of linear asynchronous hybrid stochastic systems and its application to multi-agent systems with Markovian switching topologies

ABSTRACTThis paper studies the stability and stabilisation of a class of asynchronous hybrid stochastic systems described by linear Markov jump systems with asynchronous parameters induced by hysteretic mode and input delay. By exploring the essential properties of the Markov chain and developing novel Lyapunov function/functional based approaches, we derive sufficient conditions in terms of sizes of the delays ensuring the mean square asymptotical stability of the systems. Interestingly, the Lyapunov functional based approach further leads to the mean square stability criteria that depend only on the drift part and allow an arbitrary large delay for the diffusion part, which is different from the Lyapunov-Razumikhin based results. The theoretical results are applied to solve the consensus problems of multi-agent systems with Markovian switching topologies and input delay. Numerical examples demonstrate the established results.

Distributed formation control for multiple quadrotor UAVs under Markovian switching topologies with partially unknown transition rates

This paper addresses distributed formation control for a group of quadrotor unmanned aerial vehicles (UAVs) under Markovian switching topologies with partially unknown transition rates. 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. Extended high gain observers (EHGOs) are constructed with a two-time-scale format to deal with the issue of nonlinear input coefficients, so that there could be a higher estimation precision of the system uncertainties. To impel multiple quadrotor UAVs to achieve a predesigned formation shape, a modified integral sliding mode (ISM) control protocol is proposed here with a multi-time-scale structure, which allows independent analysis of the dynamics in each time scale. The stability proof for the system state space origin is derived from the singular perturbation method and Lyapunov stability theory. In addition, the introduced ISM controller can deal with the time varying desired references with the bounded accelerations and is robust to the disturbances. Finally, simulations on six quadrotor UAVs are given to verify the effectiveness of the theoretical results.

Event-Based Distributed Filtering Over Markovian Switching Topologies

In this paper, we consider the distributed filtering problem for continuous-time stochastic systems over sensor networks subject to Markovian switching topologies. Due to limited communication energy and bandwidth, an event-based communication scheme is proposed with the aim to decrease the transmission frequency. An individual triggering condition is put forward to regulate the communication rates for each component of the system state in order to better reflect the engineering requirements. The aim of this paper is to design a distributed filter over sensor networks with Markovian switching topologies such that the dynamics of the estimation error is exponentially mean-square bounded. It is shown that, with the proposed event-based distributed filtering algorithm, the exponential mean-square boundedness of the estimation errors is guaranteed if the sensor network is distributively detectable and the combined communication topology is strongly connected. A numerical example is presented to illustrate the usefulness of the developed algorithm.

Finite-time cluster synchronization for a class of fuzzy cellular neural networks via non-chattering quantized controllers

This paper considers the finite-time cluster synchronization (FTCS) of coupled fuzzy cellular neural networks (FCNNs) with Markovian switching topology, discontinuous activation functions, proportional leakage, and time-varying unbounded delays. Novel quantized controllers without the sign function are designed to avoid the chattering and save communication resources. Under the framework of Filippov solution, several sufficient conditions are derived to guarantee the FTCS by constructing new Lyapunov–Krasovskii functionals and utilizing M-matrix methods. The new analytical techniques skillfully overcome the difficulties caused by time-varying delays and cope with the uncertainties of both Filippov solution and Markov jumping, which enable us determine the settling time explicitly. Numerical simulations demonstrate the effectiveness of the theoretical analysis.

H∞ Consensus Control for Heterogeneous Multi-Agent via Output under Markov Switching Topologies

The paper investigates H ∞ consensus problem of heterogeneous multi-agent systems including agents with first- and second-order integrators in the presence of disturbance and communication time delays under Markov switching topologies. Based on current messages, outdated information stored in memory and communication time delay information from neighbors, a more general kind of distributed consensus algorithm is proposed, which is faster consensus convergence. By applying stochastic stability analysis, model transformation techniques and graph theory, sufficient conditions of mean square consensus and H ∞ consensus are obtained, respectively. Finally, simulation examples are given to illustrate the effectiveness of obtained theoretical results.

New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies

This paper studies the stochastic exponential synchronization problem for uncertain chaotic neural networks (UCNNs) with probabilistic faults (PFs) and randomly occurring time-varying parameters uncertainties(ROTVPUs). To reflect more realistic control behaviors, a new stochastic reliable nonuniform sampling controller with Markov switching topologies is designed for the first time. First, by taking into full account more information on sawtooth structural sampling pattern, time delay and its variation, a novel loose-looped Lyapunov–Krasovskii functional (LLLKF) is developed via introducing matrices-refined-function and adjustable parameters. Second, with the aid of novel LLLKF and relaxed Wirtinger-based integral inequality (RWBII), new synchronization algorithms are established to guarantee that UCNNs are synchronous exponentially under probabilistic actuator and sensor faults. Third, based on the proposed optimization algorithm, the desired reliable sampled-data controller can be achieved under more larger exponential decay rate. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the designed algorithms.

Novel aperiodically intermittent stability criteria for Markovian switching stochastic delayed coupled systems.

This paper concerns th moment exponential stability of stochastic coupled systems with multiple time-varying delays, and Markovian switching topologies via intermittent control. Compared with previous research results, the mathematical model of this kind of stochastic coupled systems with multiple time-varying delays and Markovian switching topologies is studied for the first time. The intermittent control designed in this paper is aperiodical, which is more general in practice. Moreover, the restriction between control width and time delays is removed. By constructing a new differential inequality on delayed dynamical systems with Markovian switching topologies and combining the graph-theoretic approach with M-matrix theory, two sufficient criteria are derived to guarantee th moment exponential stability of systems. Moreover, the exponential convergence rate has a close relationship with the maximum ratio of the rest width to the aperiodical time span (the sum of the control width and the rest width). Finally, we employ the theoretical results to study the exponential stability of stochastic coupled oscillators with multiple time-varying delays and Markovian switching topologies. Meanwhile, a numerical example is presented to illustrate the effectiveness and feasibility of the proposed results.

Event-TriggeredH∞Filtering for Multiagent Systems with Markovian Switching Topologies

This paper is concerned with the problem of event-triggeredH∞filtering for multiagent systems with Markovian switching topologies and network-induced delay. An event-triggered mechanism is given to ease the information transmission. Consider that the network topology is directed in this paper, which represents the communication links among agents. Due to the existence of network-induced delay, the time-delay approach is adopted, which can effectively deal with filtering error system. By constructing a Lyapunov-Krasovskii functional and employing linear matrix inequality technique, sufficient conditions are established to ensure the filtering error system to achieve asymptotically stable withH∞performance index. A simulation example is given to illustrate the effectiveness of the proposed method.