Wangli He

Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control

This paper studies leader-follower synchronization in heterogeneous dynamic networks via distributed impulsive control. The goal is to drive the followers to approximately synchronize with the leader within a nonzero error bound, referred to as quasi-synchronization. Some fundamental and yet challenging problems are addressed : (1) How to obtain a tight quasi-synchronization error bound; (2) How many and which nodes should be controlled; (3) How to design the coupling strength, to select the pinned nodes and to determine the impulse intervals to optimize the error bound or to achieve quasi-synchronization within a prescribed error bound. First, some general quasi-synchronization conditions are derived with explicit expressions of the error bound. Second, the pinning strategy and the coupling strength in achieving quasi-synchronization are explored and expressed in term of impulse intervals. It is interesting to find that a large coupling strength will destroy synchrony, in contrast to continuous pinning control. Furthermore, the common requirement that the leader has a directed path to every node is needed only in the case that the impulse intervals can be arbitrarily small. A new concept, referred to as impulse pinning controllability, is introduced to the case that impulses cannot take place too frequently. Third, an optimization of the error bound is discussed and formulated. Under a prescribed error bound, the design problem of the coupling strength, pinned nodes and impulse intervals is solved. Finally, three examples are given to verify the theoretical results.

Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control ☆

Abstract This paper investigates the problem of network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control. First, by taking network-induced delays into account, a nonlinear system with delayed impulses is formulated. Then, a general consensus criterion is derived and several special cases of network-induced delays and network topologies are discussed. Moreover, sufficient conditions on the design of the sampling period, pinned nodes and the coupling strength are provided. The effects of the coupling strength and pinning strategy are further explored for multi-agent systems with an undirected communication graph. Finally, two examples are given to verify the theoretical results.

Leader-Following Consensus of Nonlinear Multiagent Systems With Stochastic Sampling

This paper is concerned with sampled-data leader-following consensus of a group of agents with nonlinear characteristic. A distributed consensus protocol with probabilistic sampling in two sampling periods is proposed. First, a general consensus criterion is derived for multiagent systems under a directed graph. A number of results in several special cases without transmittal delays or with the deterministic sampling are obtained. Second, a dimension-reduced condition is obtained for multiagent systems under an undirected graph. It is shown that the leader-following consensus problem with stochastic sampling can be transferred into a master-slave synchronization problem with only one master system and two slave systems. The problem solving is independent of the number of agents, which greatly facilitates its application to large-scale networked agents. Third, the network design issue is further addressed, demonstrating the positive and active roles of the network structure in reaching consensus. Finally, two examples are given to verify the theoretical results.

Lag Quasi-Synchronization of Coupled Delayed Systems With Parameter Mismatch

This paper is concerned with lag synchronization of two coupled delayed systems with parameter mismatch. Due to parameter mismatch, complete lag synchronization can not be achieved. Therefore, a new lag quasi-synchronization scheme is proposed to ensure that coupled systems are in a state of lag synchronization with an error level. Several simple criteria are derived and the error level is estimated by applying a generalized Halanary inequality and matrix measure. Three examples are given to illustrate the effectiveness of the proposed lag quasi-synchronization scheme. It is shown that as the coupling strength increases, the estimated error level is close to the simulated one, which well supports theoretical results.

Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control

This paper investigates pinning synchronization of coupled neural networks with both current-state coupling and distributed-delay coupling via impulsive control. A novel impulse pinning strategy involving pinning ratio is proposed and a general criterion is derived to ensure an array of neural networks with two different topologies synchronizes with the desired trajectory. In order to handle the difficulties of high-dimension criteria, some inequality techniques and matrix decomposition methods through simultaneous diagonalization of two matrices are introduced and low-dimensional criteria are obtained. Finally, an illustrative example is given to show the effectiveness of the proposed method.

Synchronization analysis of heterogeneous dynamical networks

This paper investigates the synchronization problem over heterogeneous dynamical networks, in which nonidentical dynamical systems coexist. By introducing a virtual target, synchronization with an error level, called quasi-synchronization, is analyzed in asymmetric and symmetric networks, respectively. Some sufficient quasi-synchronization conditions are presented and explicit expressions of error levels are derived to estimate the synchronization error. Finally, two networks with six different Chuas circuits are provided to verify the theoretical results.

Dynamic Optimization of Industrial Processes With Nonuniform Discretization-Based Control Vector Parameterization

This paper proposes a novel scheme of nonuniform discretizetion-based control vector parameterization (ndCVP, for short) for dynamic optimization problems (DOPs) of industrial processes. In our ndCVP scheme, the time span is partitioned into a multitude of uneven intervals, and incremental time parameters are encoded, along with the control parameters, into the individual to be optimized. Our coding method can avoid handling complex ordinal constraints. It is proved that ndCVP is a natural generalization of uniform discretization-based control vector parameterization (udCVP). By integrating ndCVP into hybrid gradient particle swarm optimization (HGPSO), a new optimization method, named ndCVP-HGPSO for short, is formed. By application in four classic DOPs, simulation results show that ndCVP-HGPSO is able to achieve similar or even better performances with a small number of control intervals; while the computational overheads are acceptable. Furthermore, ndCVP and udCVP are compared in terms of two situations: given the same number of control intervals and given the same number of optimization variables. The results show that ndCVP can achieve better performance in most cases.

Multiagent Systems on Multilayer Networks: Synchronization Analysis and Network Design

This paper is concerned with the synchronization of multiagent systems connected via different types of interactions, known as multilayer networks. Additive coupling and Markovian switching coupling are proposed to capture the layered connections with two kinds of mathematical models constructed. First, based on simultaneously diagonalization of multiple Laplacian matrices, a general criterion is derived, ensuring that the synchronization problem with additive coupling can be decoupled. Then, an alternative condition is presented, which is related to the number of layers, regardless of the number of agents. With the derived criteria, a concept of joint synchronization region is introduced and further discussed as a network design problem. Synchronization with Markovian switching layers is also analyzed in parallel, exemplified by some special cases of two-layer networks. Finally, a group of cellular neural networks coupled by two-layer connections are chosen to illustrate the effectiveness of the theoretical results.

Event-Triggered Communication for Leader-Following Consensus of Second-Order Multiagent Systems

This paper is concerned with leader-following consensus of second-order multiagent systems with nonlinear dynamics. First, to save the limited communication resources, a new event-triggered control protocol is delicately developed without requiring continuous communication among the follower agents. Then, by employing the Lyapunov functional method and the Kronecker product technique, a novel sufficient criterion with less conservation is derived to guarantee the leader-following consensus while excluding the Zeno behavior. Furthermore, for the first time, an algorithm to actively adjust the leader adjacency matrix is presented, which efficiently expands the application range of some existing criteria. An example is finally given to illustrate the effectiveness of theoretical results.

Synchronization of heterogeneous dynamical networks via distributed impulsive control

This paper studies global synchronization between a heterogeneous dynamical network and a known target trajectory via distributed impulsive control. Synchronization with an error level, called quasi-synchronization, is analyzed by utilizing the time-varying Lyapunov function. Some sufficient quasi-synchronization conditions are presented and explicit expressions of error levels are derived. Furthermore, the effects of the pinning control matrix and the coupling strength are explored. Unlike the continuous pinning feedback control, it is shown that a large coupling strength will destroy synchronization in the present of impulsive controller, which is also verified by our simulations.