Resilient consensus control of nonlinear semi‐Markov multiagent systems with piecewise transition probabilities

This paper studies the mean square consensus problems of second-order continuous-time multi-agent systems with and without non-linear dynamics under the Markov switching topologies, respectively. Under the proposed consensus protocols, sufficient conditions for mean square consensus of multi-agent systems with noises are derived under Markov switching directed topologies, while necessary and sufficient conditions for mean square consensus of multi-agent systems without non-linear dynamics and noises are obtained under Markov switching directed topologies. Finally, simulation examples are given to show the effectiveness of the proposed methods.

Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems

This technical note studies the leader-following tracking consensus problem of a class of multi-agent systems where the dynamics of the leader is described by second-order systems. In order to track the states of the leader, observers for the followers are designed by fractional-order multi-agent systems where the relative velocity information is unavailable. It is interestingly found that the followers can track the leader with second-order dynamics even if the fractional order is less than two by only using the position information of the local neighbors, which is different from the existing results. A novel fractional-order observer is first proposed, whose order is surprisingly less than the original leader system. It is also shown that leader-following consensus can be ensured if some carefully selected followers are informed and the relative position-based protocols are appropriately designed with fractional order being between one and two. A necessary and sufficient condition for the leader-following consensus in multi-agent systems without control-input delay is proposed. The results are then extended to the case with constant control-input delay. It is found that, in both cases, the real and imaginary parts of the eigenvalues of the augmented Laplacian matrix of the topology play an important role in achieving consensus.

In this paper, a new compounded order multi-agent system is proposed. The multi-agent system consists of two groups with different orders. Also the input delay effect on the consensus of the multi-agent systems is investigated. The sufficient consensus conditions are discussed in the frequency domain by adopting Laplace transform. The delay bound of multi-agent system is derived and holds for different groups. Numerical example with different parameters is given to verify the efficiency of the results derived.

In this technical note, under widely used joint connectivity assumptions, some necessary and/or sufficient conditions for the heading consensus of autonomous multi-agent systems described by Vicsek's model are proposed. Further, more general nonaveraging protocols are studied for which necessary and/or sufficient conditions for the consensus are also given.

Second-order consensus in multi-agent dynamical systems with sampled position data

This paper proposes a method to design the coupling strengths in a multi-agent system in order to achieve consensus in arbitrary directed networks in the presence of input time-varying delays. A model transformation is carried out to convert the consensus problem into a stability one. Then, based on an appropriate Lyapunov-Krasovskii functional, sufficient conditions for consensus in multi-agent systems are derived, where the coupling strengths are given as variables of Linear Matrix Inequalities (LMI). The designed coupling strengths may enable consensus and also meet a specified convergence rate. Numerical simulations are provided to demonstrate the effectiveness of the proposed results.

This paper establishes some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems with directed topologies and time delays. First, theoretical analysis is carried out for the basic, but fundamentally important case where agents' second-order dynamics are governed by the position and velocity terms. A necessary and sufficient condition is derived to ensure second-order consensus and it is found that both the real and imaginary parts of the eigenvalues of the Laplacian matrix of the corresponding network topology play key roles in reaching consensus. Based on this result, a second-order consensus algorithm is constructed for the multi-agent system with communication delays. A necessary and sufficient condition is then proposed, which shows that consensus can be achieved in a multi-agent system whose topology contains a directed spanning tree if and only if the time delay is less than a critical value. Finally, simulation examples are given to verify the theoretical analysis.

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.

The existing results on consensus of multiagent systems are mainly based on homogeneous systems; that is, all agents have the same dynamic model. This paper focuses on consensus of heterogeneous multiagent systems, which consist of first-order and second-order integrator agents. Based on integral sliding mode control, the consensus protocols of heterogeneous multiagent systems with disturbances are investigated under the directed networks. Some sufficient conditions for finite-time consensus are obtained by utilizing Lyapunov stability theory. Finally, some examples verify the effectiveness of the proposed control schemes.

This brief studies the secure consensus problem of multiagent systems (MASs) via impulsive control under deception attacks. In most existing work, deception attackers are assumed to attack the agents rather than the communication channels, and the neighbors of the attacked agent receive the same tampered information from the attacked agent. The deception attacker is assumed to inject false data into the communication channels, and each neighbor of each agent may receive different tempered information from the same agent. Attacking the communication channels leads to an inconsistent dimension of the matrices in the controller, which brings difficulties in analyzing the convergence of MASs. To overcome the challenge, the extended diagonal matrix is proposed to analyze the effect of the deception attacks on the convergence of MASs, and sufficient conditions for the secure consensus are derived. The consensus error bound converges to a bounded area dependent on the total attack energy. Finally, a simulation example is given to verify the effectiveness of the results.

In this paper, we are concerned with the consensus of the forth-order discrete-time multiagent system in directed networks. First, by defining a group of new variables, the multiagent system is converted to the corresponding reduced order system. Based on the stability of the reduced order system, we discuss the consensus of the original multiagent system. Then, two necessary and sufficient conditions for the consensus of the forth-order discrete-time multiagent system are established by using the related knowledge of algebraic graph theory and matrix theory. Compared with the existing results, the obtained conditions of this paper are more extensive. In order to reduce the number of information exchange between agents, we use event-triggered mechanism to deal with the consensus of the multiagent system. Furthermore, Zeno behavior of multiagent system will not make an appearance due to the reasonable design of the triggering function. A numerical example is finally given to demonstrate the effectiveness of theoretical results.

An asymmetric Lyapunov-Krasovskii functional approach for event-triggered consensus of multi-agent systems with deception attacks

This paper studies consensus and \(H_\infty\) consensus problems for heterogeneous multi-agent systems composed of first-order and second-order integrator agents. We first rewrite the multi-agent systems into the corresponding reduced-order systems based on the graph theory and the reduced-order transformation. Then, the linear matrix inequality approach is used to consider the consensus of heterogeneous multi-agent systems with time-varying delays in directed networks. As a result, sufficient conditions for consensus and \(H_\infty\) consensus of heterogeneous multi-agent systems in terms of linear matrix inequalities are established in the cases of fixed and switching topologies. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results.

This paper investigates the consensus problem for heterogeneous multi-agent systems consisting of third-order and first-order agents. The interaction topology includes both fixed and switching cases. First, by a model transformation, heterogeneous multi-agent systems are converted into equivalent error systems. Then we analyze the consensus problem of the multi-agent systems by analyzing the stability problem of the error systems. For a fixed topology, a sufficient condition for consensus of heterogeneous multi-agent systems is obtained based on algebraic graph theory and linear system theory. For a switching topology, a necessary and sufficient condition for mean-square consensus of multi-agent systems is obtained based on algebraic graph theory and Markovian jump system theory. Finally, we give some simulation examples.