Properties Of Laplacian Matrix Research Articles

Nonfragile consensus of nonlinear multiagent systems with intrinsic delays via aperiodic memory sampled‐data control

AbstractThis paper focuses on the consensus issue of nonlinear multiagent systems (MASs) with intrinsic time‐varying delays via the nonfragile and aperiodic memory sampled‐data control scheme. An improved continuous Lyapunov–Krasovskii functional (LKF) with some two‐sided looped‐functional terms is introduced, in which several free‐weighting‐matrices are not necessarily positive definite. Furthermore, based on the property of Laplacian matrix, the consensus issue of original MASs can be investigated directly without transforming into error systems. Then, several sufficient criteria for the consensus of MASs are presented by means of the recently developed generalized integral inequality and the constructed LKF. Next, the required nonfragile controller gain is obtained by resorting to linear matrix inequalities and the maximal length of sampling period is derived as well. Finally, two illustrative examples are employed to exhibit the effectiveness and feasibility of the proposed consensus protocol.

Dynamic H∞ Consensus of Higher-Order Nonlinear Multi-Agent Systems With General Directed Topology

This paper investigates the leaderless <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem of multi-agent systems with higher-order Lipschitz dynamics and external disturbance. The topology is assumed to be directed. Distributed controllers using only relative outputs information of the adjacent agents are constructed. In order to deal with the non-symmetric property of the associated Laplacian matrix of directed topology, some properties of Laplacian matrix are introduced. By introducing an appropriate state transformation, the <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> consensus problem is converted to a low-dimensional system stability problem which is solved using Lyapunov stability analysis method. The effectiveness of the proposed control design is demonstrated through simulation examples.

Output feedback control for bipartite consensus of nonlinear multi-agent systems with disturbances and switching topologies

The bipartite consensus protocol for nonlinear multi-agent system (MAS) subject to switching interaction graphs and external disturbances is addressed in this paper. The coordination goal of this paper is to present a static output feedback control design such that the bipartite consensus of the considered MAS can be achieved with prescribed mixed H∞ and passive performance. We consider undirected structurally balanced signed network topologies to express the cooperative and competitive interaction between neighboring agents. To achieve the desired objective of this paper, the problem under consideration is first transformed into a stabilization problem by using the properties of Laplacian matrix. Then utilizing Lyapunov stability theory, the desired bipartite consensus conditions are developed for the resulting model in terms of linear matrix inequalities. Ultimately, a numerical example is provided to verify the robustness of the considered static output feedback control design.

Distributed optimization of general linear multi-agent systems with external disturbance

In this paper, we consider the distributed optimization problems with linear coupling constraint of general homogeneous and heterogeneous linear multi-agent systems under weighted-balanced and strongly connected digraphs. In order to control all agents converge to the optimal output, we propose distributed control laws, therein, the optimal output can make the global cost function reach minimum. Then we guarantee the convergence of the proposed algorithms by the properties of Laplacian matrix and Lyapunov stability theorem. Furthermore, we extend the result of heterogeneous linear multi-agent system to the case that dynamics of agents are subject to external disturbances, and prove that the algorithm designed by internal model principle can make all agents reach the optimal output exactly. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms.

Distributed leaderless impulsive consensus of non-linear multi-agent systems with input saturation

This paper aims to propose dynamic consensus protocols for a class of non-linear saturated multi-agent systems. Due to the existence of non-linear dynamics of each agent, the system does not satisfy the condition named asymptotically null controllable with bounded controls (ANCBC). As a result, the widely-adopted method of low-gain feedback to solve consensus control problems for linear multi-agent systems with input saturation cannot be used. To step back, even if the system is linear and meets the ANCBC condition, the existing low-gain method or that combined with adaptive method can only make the system eventually reach zero consensus, which is unable to bring the system to dynamic consensus. In addition, from the view of energy conservation, this study proposes the impulsive control method to reduce the energy consumption of the controller. By taking advantages of the stability theory of impulsive systems, as well as the properties of Laplacian matrix and convex hull, corresponding distributed dynamic consensus protocols are proposed. Still, the shape reference set is introduced to assess the attraction domain of the leaderless MASs. Finally, the performance of the proposed anti-saturation impulsive control algorithm is demonstrated by extensive numerical experiments.

Distributed Power Management for Dynamic Economic Dispatch in the Multimicrogrids Environment

In the multimicrogrids environment, this brief proposes a distributed power management strategy to minimize a sum of generation costs function subject to generator constraints, which includes the supply-demand balance constraint, the individual constraint, the capacity constraint, and the ramp-rate constraint. First, under the framework of discontinuous dynamical system, a distributed primal–dual consensus algorithm is discussed. Then, using the property of Laplacian matrix, it is proven that the algorithm is any-time, which indicates that supply-demand balance is not disturbed. Based on theory of dynamical system, the proposed algorithm is proven to be stable, and the optimization capabilities of the distributed primal–dual consensus algorithm are also discussed. Finally, case studies based on IEEE 30-bus, IEEE-57 bus, and IEEE 300-bus system show the effectiveness and performance of the proposed distributed primal–dual consensus algorithm.

Model-Free Fault Tolerant Control for a Class of Complex Dynamical Networks With Derivative Couplings.

This paper studies the fault tolerant synchronization control for a class of derivative coupled complex dynamical networks (CDNs). Different from the existing results, each subsystem model is assumed to be completely unknown and the coupling terms are mismatched with the control input. Within this framework, a novel model-free fault tolerant controller is designed. Under the proposed control law, the synchronization errors of CDNs are proved to asymptotically converge to zero, which means that the synchronization is successfully achieved. Especially, by combining an important spectral decomposition technique and some properties of Laplacian matrix, a data-based algorithm is provided to derive the controller parameter. In addition, the proposed method is also valid for the CDNs with unknown coupling weights. Finally, examples on circuit systems are given to verify the theoretical results, and some circuit realizations of the proposed control law are implemented based on the circuit theory.

Containment Control of Linear Multiagent Systems With Aperiodic Sampling and Measurement Size Reduction.

The containment control problem for generally linear multiagent systems with aperiodic sampling intervals and measurement size reduction is considered in this paper. Under the assumption that the sampling interval changes from a finite set, an improved protocol is proposed, such that a larger sampling interval can be obtained to achieve containment. By using the properties of Laplacian matrix and the newly developed protocol, the containment control problem is transformed into the stability problem of a discrete-time switched linear system. A sufficient condition is obtained that ensures all the followers converge to the convex hull formed by the state of leaders, and such a sufficient condition is presented in terms of linear matrix inequalities, which are independent of the node of network. To further reduce the communication among agents, a switching-type measurement size reduction scheme is introduced. An optimization problem is proposed for the corresponding controller design. Finally, two simulation studies are conducted to show the effectiveness and advantage of the proposed control algorithms.

Asynchronous containment control for discrete-time second-order multi-agent systems with time-varying delays

The asynchronous containment control problem of second-order discrete-time multi-agent systems with time-varying delays is investigated. Asynchrony in this paper means that each agent updates state information via its clock that is independent of those of the other agents’, and the time sequence over which each agent updates its state information is not necessarily equispaced. An asynchronous distributed control protocol is designed to realize local control strategies for the second-order discrete-time multi-agent system. By utilizing the proposed protocol and properties of Laplacian matrix, the asynchronous containment control problem of second-order multi-agent systems is equivalently transformed into a stability problem of synchronous error system. Based on the nonnegative matrix theory and graph theory, a necessary and sufficient condition is obtained to make all the followers asymptotically converge to the convex hull formed by the stationary leaders. Finally, some simulation examples are presented for illustration.

Consensus of switched multi-agent systems under quantised measurements

ABSTRACTThis paper deals with the quantised consensus problem for switched multi-agent system which is composed of continuous-time and discrete-time subsystems. We adopt the distributed consensus protocols based on the quantised relative state measurements of agents. By using the properties of Laplacian matrix, it is shown that the switched multi-agent system can reach consensus exponentially with logarithmic quantiser under arbitrary switching. It is also proved that the distance between the states of any pair of neighbouring agents just converges to a bounded set when uniform quantisers are utilised. Simulation examples are presented to illustrate the effectiveness of the theoretical results.

Consensus analysis of multi‐agent systems under switching topologies by a topology‐dependent average dwell time approach

This study addresses the consensus problem for a class of any order multi-agent systems under switching topologies which could include kinds of unconsensusable topologies. The consensus problem, depending on structure properties and the corresponding topology, is researched with fixed structure properties under directed switching topologies. By the properties of Laplacian matrix, the consensus problem for multi-agent systems is converted into the stability problem of the corresponding switched systems with a Laplacian-like matrix. Some sufficient conditions for consensus are presented by using the dwell time approach. Finally, numerical examples and the results of computer simulation are given to verify the theoretical analysis.

Containment control of continuous-time linear multi-agent systems with aperiodic sampling

In this paper, the containment control problem of continuous-time linear multi-agent systems is investigated. An aperiodic sampled-data based protocol is induced by using neighboring information with uncertainly time-varying sampling intervals. By utilizing the proposed protocol and properties of Laplacian matrix, the containment control problem of continuous-time linear multi-agent systems is equivalently transformed into a stability problem of discrete-time linear systems. The stability analysis is based on the robustness of related discrete-time systems against perturbation caused by the variation of sampling intervals. By using small-gain theorem, sufficient conditions are obtained to guarantee the stability of uncertain discrete-time systems. Furthermore, two special cases are given to illustrate the method proposed in this paper. The theoretical results are verified by some simulations.

Leader-following control of multiple nonholonomic systems over directed communication graphs

This paper considers the leader-following control problem of multiple nonlinear systems with directed communication topology and a leader. If the state of each system is measurable, distributed state feedback controllers are proposed using neighbours’ state information with the aid of Lyapunov techniques and properties of Laplacian matrix for time-invariant communication graph and time-varying communication graph. It is shown that the state of each system exponentially converges to the state of a leader. If the state of each system is not measurable, distributed observer-based output feedback control laws are proposed. As an application of the proposed results, formation control of wheeled mobile robots is studied. The simulation results show the effectiveness of the proposed results.