Finite-time adaptive consensus of a class of multi-agent systems

This paper studies the finite-time consensus (FTC) of second-order multi-agent systems (MASs), where the event-triggered strategy is adopted. Firstly, a new protocol is designed to solve the FTC problem for the MASs under consideration. Then, by using Lyapunov theory and graph theory, the sufficient conditions are obtained to guarantee the FTC of the MASs. Meanwhile, a lower-bounded inter-event time is given to exclude the Zeno behavior. Finally, a numerical simulation is presented to demonstrated the effectiveness of the theoretical results.

For network graphs, numerous graph features are intimately linked to eigenvalues of the Laplacian matrix, such as connectivity and diameter. Thus, it is very important to solve eigenvalues of the Laplacian matrix for graphs. Similarly, for higher-order networks, eigenvalues of combinatorial Laplacian matrices are also important for invariants of graphs. However, for large-scale networks, it is difficult to calculate eigenvalues of the Laplacian matrix directly because it is either very difficult to obtain the whole network structure or requires a lot of computing resources. Therefore, this article makes the following contributions. Firstly, this paper proposes a random walk approach for estimating the bounds of the greatest eigenvalues of Laplacian matrices for large-scale networks. Considering the relationship between the spectral moments of the adjacency matrix and the closed paths in the network, we utilize the relationship between the adjacency matrix and the Laplacian matrix to establish the relationship between the Laplacian matrix and the closed paths. Then, we employ equiprobable random walks to sample the large graph to obtain the small graph. Through algebraic topology knowledge, we obtain the bounds of the largest eigenvalue of the Laplacian matrix of the large graph by using Laplacian spectral moments of the small graph. Secondly, for high-order networks, this paper proposes a method based on random walks and graph transformations. The graph transformation we propose mainly converts graphs with second-order simplices into ordinary weighted graphs, thereby transforming the problem of solving the spectral moments of the second-order combined Laplacian matrix into solving the spectral moments of the adjacency matrix. Then, we use the aforementioned random walk method to solve bounds of the greatest eigenvalue of the second-order combinatorial Laplacian matrix. Finally, by comparing the proposed method with existing algorithms in synthetic and real networks, its accuracy and superiority are demonstrated.

In this note, we investigate cooperative robust consensus problem for a class of linear heterogeneous multi-agent systems (MASs) with parameter uncertainty in agents. All the agents can have nonidentical dynamic dimensions. By combining the communication network, a distributed dynamic compensator is established based on only the measurable output information of the exosystem, which provides an estimated value of the state of the exosystem for each agent. The distributed dynamic output feedback protocol (DDOFP) is proposed by utilizing the exosystem compensator, through which the cooperative robust consensus is achieved under switching topology by following output regulation framework. Here, we introduce the stabilization scheme for a class of liner switched systems to analyse the closed-loop stability, which avoids the dependence on the eigenvalues of Laplacian matrix, such that it is a fully distributed control strategy without any global information. Finally, the simulation example is illustrated to verify the feasibility and effectiveness of the theory results.

Finite-time event-triggered consensus control for high-speed train with gradient resistance

A multi-level finite element nodal ordering using algebraic graph theory

In this article, the adaptive finite-time consensus problem is discussed for uncertain nonlinear multiagent systems. In contrast with the correlative literature, the systems permit multiple uncertainties (not only in control coefficients but also in inherent nonlinearities), and typically the consensus protocol is pursued in a fully distributed fashion (independent from any global information of network topology). This essentially challenges the realization of the finite-time consensus. To overcome the challenge, a new continuous fully distributed protocol is proposed by combining adaptive techniques such that the finite-time consensus of the systems under investigation is achieved. Remarkably, a dynamic high gain, rather than multiple ones in the related literature, is adequate to resist two kinds of uncertainties and to guarantee the fully distributed fashion of the consensus protocol. Moreover, the adaptive finite-time consensus protocol is specified on the scenario of leader-following multiagent systems. Simulation results of three interaction topologies are acquired to illustrate the validity and the wider applicability of the proposed protocol.

Finite-time robust consensus of nonlinear disturbed multiagent systems via two-layer event-triggered control

Second-order consensus of multi-agent systems with nonlinear dynamics via impulsive control

Finite-time consensus of multi-agent systems with continuous time-varying interaction topology

Finite-time consensus of neutrally stable multi-agent systems in the presence of input saturation

In this article, we study the finite-time consensus in probability for stochastic multi-agent systems. First, we give the nonlinear consensus protocol for multi-agent systems with Gaussian white noise, and define the concept of finite-time consensus in probability. Second, we prove that multi-agent systems can achieve the finite-time consensus in probability under five different kinds of communication topologies by using graph theory, stochastic Lyapunov theory and probability theory. Finally, some simulation examples are provided to illustrate the effectiveness of the theoretical results.

In this paper, we develop control algorithms for addressing second-order consensus problems in intrinsically second-order nonlinear multi-agent dynamical systems with switching topologies. The proposed adaptive controller applies a leader-following strategy in which all agents are assumed to be informed of the leader's state. Another feature of this work which specifically distinguishes it from others is that the proposed controller uses undirected and directed graphs to accommodate for a full range of possible graph information topologies without limitations of bidirectional communication.

In this article, for second-order multiagent systems with uncertain disturbances, the finite-time leader-follower consensus problem has been investigated. First, by considering that the leader's states are only available to part of the followers, a distributed estimator is constructed to estimate the state tracking errors between the leader and each follower. Then, an estimator-based control scheme is proposed under the event-triggered strategy to achieve finite-time leader-follower consensus. Besides, the event-triggered intervals are with a positive lower bound such that the Zeno behavior can be avoided. Note that the system is discontinuous under the event-triggered mechanism; thus, a nonsmooth analysis is performed. Numerical simulations are presented to demonstrate the effectiveness of our theoretical results.

A novel finite-time consensus technique is derived for second-order linear multi-agent systems with input saturation constraints. The hyperbolic tangent–based saturation function is presented for achieving input saturation while reducing the chattering issue of classical saturation functions. The leader-following consensus controller with a single saturation function is constructed to address the issue of saturation level partition between position feedback and velocity feedback. Theoretically, the property of finite-time consensus, bounded input, and smoothness of a closed-form system are proved by the Lyapunov theory in detail. Numerical simulations are conducted to exhibit the effectiveness of the proposed method fully.

The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results.