Sufficient Conditions For Consensus Research Articles

Leader-follower non-fragile consensus of delayed fractional-order nonlinear multi-agent systems

This paper addresses the leader-follower non-fragile consensus of nonlinear fractional-order (FO) multi-agent systems (FOMAS) with state time delay. The structured uncertainties occurring in both the plant and the controller are considered for the first time. Using the linear matrix inequality approach and the FO Razumikhin theorem, a delay- and order-dependent protocol is obtained to guarantee the leader-follower non-fragile consensus of the FOMAS with uncertain parameters. New sufficient conditions for the leader-follower non-fragile consensus of FO linear multi-agent systems are presented. The feasibility and effectiveness of the protocol proposed is verified with three numerical examples. Compared with the existing schemes, the approach reveals good robustness and can be extended to different kinds of consensus problems.

Mean‐square output consensus of heterogeneous multi‐agent systems with communication noises

This paper focuses on the mean-square output consensus of heterogeneous multi-agent systems, in which the communication noises are taken into consideration. Through internal model principle and control gain function, the novel state feedback and output feedback control strategies are designed for leaderless and a leader situation respectively to attenuate disturbances caused by communication noises. In addition, based on matrix theory and stochastic analysis, the sufficient condition for output consensus in the corresponding case is obtained. In the end, the simulations are used to confirm the correctness of the conclusion.

Research on consensus of multi-agent systems with and without input saturation constraints

In recent years, with the continuous development of multi-agent technology represented by unmanned aerial vehicle (UAV) swarm, consensus control has become a hot spot in academic research. In this paper, we put forward a discrete-time consensus protocol and obtain the necessary and sufficient conditions for the second-order consensus of the second-order multi-agent system with a fixed structure under the condition of no saturation input. The theoretical derivation verifies that the two eigenvalues of the Laplacian of the communication network matrix and the sampling period have an important effect on achieving consensus. Then we construct and verify sufficient conditions to achieve consensus under the condition of input saturation constraints. The results show that consensus can be achieved if velocity, position gain, and sampling period satisfy a set of inequalities related to the eigenvalues of the Laplacian matrix. Finally, the accuracy and validity of the theoretical results are proved by numerical simulations.

Research on Fault Tolerance Consistency of Multi - Agent Based on Event Triggering Mechanism

For the multi-agent system with directed topology, considering the possible actuator faults of any agent, the robust H ∞ fault-tolerant consensus controller design problem is studied when the system is disturbed by external finite energy. Firstly, a distributed event-triggered fault-tolerant consistency protocol is proposed, which is used to transform the fault-tolerant consistency of distributed multi-agent systems into the stability of time-delay systems. Secondly, by using Lyapunov stability theory, a sufficient condition for the fault-tolerant consensus of the multi-agent system is given for the actuator faults that may occur in any agent. A cooperative design method that saves network communication resources and realizes fault-tolerant consensus control is obtained, which makes all states of the fault multi-agent system asymptotically consistent and has a certain disturbance rejection performance. Finally, the feasibility and effectiveness of the proposed method are verified by simulation.

Event-triggered H-infinity finite-time consensus control for nonlinear second-order multi-agent systems with disturbances

The study considers the problem of finite-time event-triggered H-infinity consensus for second-order multi-agent systems (MASs) with intrinsic nonlinear dynamics and external bounded disturbances. Based on the designed triggering function, a distributed event-triggered control strategy is presented on the basis of the designed triggering function to ensure consensus in the system, which effectively reduces the data transmission. Then, sufficient conditions for the finite-time consensus with H-infinity performance level of the resulting event-triggered MAS are derived by utilizing the Lyapunov function and finite-time stability theory. Furthermore, Zeno behavior is proven to be excluded under the proposed event-triggered scheme. Finally, the validity of the proposed results is verified by numerical simulation.

Robust output consensus of discrete‐time networked negative imaginary systems

AbstractThis paper considers robust output consensus of discrete‐time networked homogeneous negative imaginary (NI) systems under ℓ2 external disturbances via integral quadratic constraints (IQCs). A necessary and sufficient condition for robust output consensus of discrete‐time networked NI systems without poles at ±1 is obtained by the IQC‐based discrete‐time NI (D‐NI) stability result. Moreover, the robust output consensus problem can be solved by designing an unstable controller whose poles are related to transmission zeros of D‐NI systems. The case of discrete‐time networked NI systems with poles at 1 is also studied. These main results are related to all eigenvalues of the Laplacian matrix of the network graph as well as the corresponding complementary IQCs at ±1 frequencies. Some corollaries are given by constructing appropriate IQC multipliers in order to simplify the main results. Finally, three examples are shown to explain the validity of the main results.

Well posedness and asymptotic consensus in the Hegselmann-Krause model with finite speed of information propagation

We consider a variant of the Hegselmann-Krause model of consensus formation where information between agents propagates with a finite speed c > 0 \mathfrak {c}>0 . This leads to a system of ordinary differential equations (ODE) with state-dependent delay. Observing that the classical well-posedness theory for ODE systems does not apply, we provide a proof of global existence and uniqueness of solutions of the model. We prove that asymptotic consensus is always reached in the spatially one-dimensional setting of the model, as long as agents travel slower than c \mathfrak {c} . We also provide sufficient conditions for asymptotic consensus in the spatially multidimensional setting.

Secure Event-Triggered Consensus Control of Linear Multiagent Systems Subject to Sequential Scaling Attacks.

This article investigates secure consensus of linear multiagent systems under event-triggered control subject to a scaling deception attack. Different from probabilistic models, a sequential scaling attack is considered, in which specific attack properties, such as the attack duration and frequency, are defined. Moreover, to alleviate the utilization of communication resources, distributed static and dynamic event-triggered control protocols are proposed and analyzed, respectively. This article aims at providing a resilient event-triggered framework to defend a kind of sequential scaling attack by exploring the relationship among the attack duration and frequency, and event-triggered parameters. First, the static event-triggered control is studied, and sufficient consensus conditions are derived, which impose constraints on the attack duration and frequency. Second, a state-based auxiliary variable is introduced in the dynamic event-triggered scheme. Under the proposed dynamic event-triggered control, consensus criteria involving triggering parameters, attack constraints, and system matrices are obtained. It proves that the Zeno behavior can be excluded. Moreover, the impacts of the scaling factor, triggering parameters, and attack properties are discussed. Finally, the effectiveness of the proposed event-triggered control mechanisms is validated by two examples.

Necessary and Sufficient Conditions for Consensus in Fractional-Order Multiagent Systems via Sampled Data Over Directed Graph

This paper studies the consensus in fractional-order multiagent systems over directed graph via sampled-data control method. A distributed control protocol using the sampled position and velocity data is designed. By virtue of the Mittag-Leffler function, Laplace transform, and matrix theory, some necessary and sufficient conditions associated with the sampling period, the fractional order, the coupling strengths, and the network structure to obtain consensus of the systems are obtained. Then, some detailed discussions are presented about how to select the sampling period and how to design the coupling strengths to attain the consensus of the systems, respectively. Lastly, some numerical simulation results are illustrated to reflect the availability of the theoretical analysis.

Output Consensus for Heterogeneous Linear Multiagent Systems With a Predictive Event-Triggered Mechanism.

In this paper, an output consensus problem for a heterogeneous linear multiagent system with a predictive event-triggered mechanism on directed graphs is investigated. An event-triggered consensus protocol is proposed by introducing an internal reference model for each agent to handle the heterogeneity existing in the system. With the proposed mechanism, each agent predicts its internal reference model's input by employing the estimate of the internal reference model's state differences between itself and its neighbor agents. As it considers the internal reference model's inputs of agents, the system requires far fewer event-triggered times to achieve consensus, leading to a significant reduction in communication cost among agents. A necessary and sufficient condition of the output consensus for the heterogeneous linear multiagent system is put forth. Furthermore, Zeno behavior can be ruled out for each agent. Some numerical examples are given to demonstrate the effectiveness of the proposed control mechanism.

Event-triggered Consensus Control of Nonlinear Multi-agent Systems based on First-order Hold

In this paper, consensus problem is studied for the first-order nonlinear multi-agent systems under directed topology, and a novel event-triggered consensus protocol is proposed. Different from the existing results with general zero-order hold, the first-order hold is adopted to construct the event-triggered control signal so as to reduce the triggering rate. By using Lyapunov stability method and matrix theory, a sufficient consensus condition is derived for the agents to reach the asymptotic consensus, and Zeno-behavior can be avoided. Finally, a numerical example is presented to demonstrate the effectiveness of our proposed protocol.

Consensus of discrete-time multi-agent systems with multiplicative uncertainties and delays

This paper studies the consensus problem of discrete-time single-integrator multi-agent systems with multiplicative uncertainties and bounded communication delays in switching networks. Some sufficient conditions for non-stochastic consensus are obtained by adopting the constant-gain protocol. For the case that the uncertainty is exponentially decaying (i.e. is with ), it is proved for any bounded delays, the consensus can be achieved if the switching topology is uniformly rooted. For the case that the uncertainty is polynomially decaying (i.e. is with ), under a precondition that the system state is bounded, a similar conclusion is also obtained. The convergence rate of the consensus protocol is quantified in terms of the decay rate of uncertainties. Simulation results are given to verify the correctness of the conclusion.

Positive Consensus in Fractional-Order Interval Networked Systems

This brief investigates the positive consensus of fractional-order interval networked systems with the order α meeting 0 <; α ≤ 1 and 1 <; α <; 2, respectively. Based on the theories of fractional stability and properties of Metzler matrix, by virtue of some rigorous theoretical analyses, the distributed control protocol is proposed and sufficient conditions of positive consensus for fractional-order interval networked systems with 0 <; α ≤ 1 are given, which have no connection with the order. What's more, the results can be extended to conditions without using the information of Laplacian matrix with respect to networked topology. Furthermore, sufficient conditions for the systems with 1 <; α <; 2 to reach positive consensus are presented in terms of linear matrix inequality. Finally, simulation examples are given to verify the effective of results.

Cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noises

This paper focuses on the mean square cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noise via pinning control technique. Network topology can take weaker conditions in each cluster but an extra balanced condition is also needed. A time-varying control gain will be introduced to eliminate the effect of stochastic noise. For the case of fixed topology, if the induced digraph of each cluster has a directed spanning tree, the sufficient conditions for the mean square cluster consensus can be obtained. For the case of Markovian switching topologies, if the induced digraph of union of the Laplacian matrix of each mode has a directed spanning tree, the mean square cluster consensus conclusion can be derived. Particularly, if the elements of transition probability of Markov chain are partly unknown, we can also obtain the same conclusion under the same conditions. Finally, two examples are given to illustrate our results.

Fixed-time consensus of heterogeneous multi-agent systems based on distributed observer

Fixed-time consensus of the heterogeneous multi-agent system, which consisting of first-order and second-order agents with a leader, is studied in this paper. A new control algorithm based on the distributed observer is proposed. By adopting the graph theory, matrix theory, control theory and Lyapunov stability method, some sufficient conditions for the fixed-time consensus and an upper bound of settling time are given. An example is presented to illustrate the potential correctness of the main results.

On Necessary and Sufficient Conditions for Exponential Consensus in Dynamic Networks via Uniform Complete Observability Theory

In this article, we deal with the consensus problem of multiple partial-state coupled linear systems, which are neutrally stable. These systems communicate over dynamic undirected networks, which change continuously and can be disconnected at any time. We develop an analysis framework from uniform complete observability theory to work out <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">the necessary and sufficient conditions</i> for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">if and only if</i> a jointly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\delta,T)$</tex-math></inline-formula> -connected condition and an observability condition relying only on system and input matrices are satisfied. A lower bound of the convergence rate is also provided. We figure out the proof by applying matrix analysis and linear functional analysis. A simulation example is presented to illustrate our theoretical findings.

Guaranteed Cost for an Event-Triggered Consensus Strategy for Interconnected Two Time-Scales Systems With Structured Uncertainty.

This article proposes the design of an event-triggered control strategy for consensus of interconnected two-time scales systems with structured uncertainty. The control design under consideration ensures also that consensus is achieved with an overall guaranteed cost. Since each system involves processes evolving on both fast and slow time scales, two Zeno-free event-triggered mechanisms are designed to independently decide the sampling and transmission instants for the slow and fast states, respectively. As the first step, we design an event-triggering consensus protocol in the ideal/nominal case when the interconnected systems are not affected by uncertainties and the interactions happen over a fixed interaction network. Next, the results are extended in order to take into account structured uncertainties affecting the systems' dynamics. At this step, we go further and we provide sufficient conditions for event-triggering consensus with a guaranteed overall cost. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.

Event-triggered consensus control for general second-order multi-agent systems

The consensus problem of multi-agent systems with general second-order dynamics is studied. A distributed event-triggering strategy is proposed to reduce the communication frequency of agents and the update frequency of event-triggering controller. Under the fixed topology, a consensus protocol and event-triggering function are designed for each agent. The sufficient conditions of consensus are obtained by the stability theory, and the theoretical proof of excluding Zeno behaviour is presented. Finally, a simulation example is given to illustrate the effectiveness of the obtained results.

Bipartite tracking consensus of linear multi‐agent systems with a dynamic leader under signed digraph

This study is concerned with the bipartite tracking consensus problem for linear multi-agent system over signed digraph, in which the leader agent owns a bounded control input that is unavailable to the followers. Compared with existing related works, the communication topology under consideration is allowed to be directed. Two kinds of distributed control protocols are proposed based on the relative states of neighbouring agents. By applying the graph theory, Lyapunov theory and adaptive control, some sufficient conditions for the bipartite tracking consensus are obtained. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed design methodology.

Exponential Consensus of Linear Systems Over Switching Network: A Subspace Method to Establish Necessity and Sufficiency.

In this article, the consensus problem of linear systems is revisited from a novel geometric perspective. The interaction network of these systems is assumed to be piecewise fixed. Moreover, it is allowed to be disconnected at any time but holds a quite mild joint connectivity property. The system matrix is marginally stable and the input matrix is not of full-row rank. By directly examining the subspace determined by the network, we first establish convergence by resorting to an observability condition. Then, according to joint connectivity, we are able to extend this convergence uniformly to the entire orthogonal complement of the consensus manifold. In this way, we work out the necessary and sufficient condition for exponential consensus. It turns out that, with a suitably designed feedback matrix, exponential consensus can be realized globally and uniformly if and only if a jointly (δ,T) -connected condition and an observability condition relying only on the system and input matrices are satisfied. We also characterize the lower bound of the convergence rate. Simple yet effective examples are presented to illustrate the findings.