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In this study, the stability of a hierarchical network with delayed output is discussed by applying a kind of optimal periodic control. To reduce the number of the nodes of the original hierarchical network, an aggregation algorithm is first presented to take some nodes with the same information as an aggregated node. Furthermore, the stability of the original hierarchical network can be guaranteed by the optimal periodic control of the aggregated hierarchical network. Then, an optimal control scheme is proposed to reduce the bandwidth waste in information transmission. In the control scheme, the time sequence is separated into two parts: the deterministic segment and the dynamic segment. With the optimal control scheme, two targets are achieved: 1) the outputs of the original and aggregated hierarchical system are both asymptotically stable and 2) the nodes with slow convergent rate can catch up with the convergence speeds of other nodes. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed hierarchical control framework for energy storage systems (ESSs) in DC microgrid clusters, which achieves voltage regulation and current sharing for ESSs in each microgrid as well as the whole microgrid cluster. The primary control stage adopts a droop controller which only requires local information while the secondary control stage provides correction terms for ESSs within microgrids. The tertiary control stage samples the pinned ESSs in different microgrids with low sampling rate to provide the voltage setpoint, which ensures global current sharing among microgrid cluster. The corresponding multilayered event-triggered consensus algorithm for clusters is proposed to reduce the communication cost generated by operation of the distributed controller. Both the control framework and the consensus algorithm can be extended for satisfying higher dimensional regulation needs. The controller is validated in a DC microgrid cluster through simulation under different scenarios, and the results illustrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

It is well known that the frequency synchronization of complex power networks is a prerequisite for stable operation. This paper investigates the global frequency synchronization in power networks via coordinating novel controllers on both the generator-side and the load-side. The designed controllers compute the monitored information from the generator-side and load-side simultaneously, and transmit the processed signals to steer the generators and load buses for maintaining frequency stability. In particular, the generator (load)-side buses can communicate with the load (generator)-side buses, not limited to the same side. Furthermore, nonlinear switching control protocols are proposed to analyze the frequency stability for overcoming the deficiency that the conventional linearized methods can only guarantee the local stability in or near an equilibrium state. The global stability region is rigorously proven, in which the sufficient conditions are derived for achieving global frequency synchronization of power systems. Finally, a prevailing modified Western System Coordinating Council (WSCC) 9-bus system and the widely-used IEEE 39-bus system are selected to validate the effectiveness and feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

This article addresses the bounded synchronization of heterogeneous complex dynamical networks. Different from most existing criteria which deal with only global bounded synchronization, a general theorem is established for analyzing both the local and global bounded synchronization of a class of heterogeneous networks in a unified approach. By developing a joint-diagonalization-like technique, several easy-to-use bounded synchronization criteria with low-dimensional linear matrix inequalities are derived based on the general theorem. Particularly, an estimate of the synchronization error and the admissible initial values are given. Examples are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

The evolution of the target system (leader) in pinning-controlled complex networks may need to be regulated by some control inputs for performing various practical tasks, e.g., obstacle avoidance, tracking highly maneuverable target, and so on. Motivated by this observation, we shall investigate the global pinning synchronization problems for complex switching networks for which the target system is subject to nonzero control inputs. First, using the idea of unit vector function method, a discontinuous coupling law is designed. With the aid of stability theory for switched systems, it is theoretically shown that synchronization in the network under this discontinuous coupling law can be achieved by choosing sufficiently large coupling strengths if the average dwell time (ADT) is bounded below by a positive constant. Second, we use the boundary layer method to design a continuous-coupling law. It has been theoretically shown that the synchronization error is ultimately uniformly bounded (UUB) under this continuous-coupling law. The chattering effect is also avoided in real implementation by using this continuous-coupling law. Furthermore, for networks with unknown external disturbances and unmodeled dynamics, neuro-adaptive-based coupling laws are designed to ensure that the synchronization error of the networks with undirected switching communication topologies under these laws is UUB. The obtained theoretical results are finally validated by performing numerical simulation on coupling Chua’s circuit systems. [ABSTRACT FROM AUTHOR]

Multi-layer networks, which incorporate multiple subsystems and different kinds of interactions, are recently believed to have a stronger ability in modelling various real-world systems than traditional single-layer complex networks. Motivated by this observation, we try to show how to achieve node-to-node synchronization and complete synchronization in multi-layer networks under directed switching communication topologies, where the nodes have Lur’e type dynamics. First, by using the multiple Lyapunov stability theory, we show that node-to-node synchronization in two-layer networks can be achieved by choosing sufficiently large coupling strength as well as suitable feedback gain matrix if the average dwell time is bounded below by some positive constants. The result is then extended to the case of multiple layers. Furthermore, if the inner communication topologies of each layer have a directed spanning tree with a common root, we show complete synchronization in the considered network can be achieved if the control parameters and the average dwell time are appropriately chosen. Finally, the theoretical results are validated through performing numerical simulations on Chua’s circuit with double scroll attractors. [ABSTRACT FROM AUTHOR]

Multi-agent systems are ubiquitous in the real-world and have received an increasing attention by many researchers worldwide. A multi-agent system is composed of many agents interconnected by a communication network. This paper aims to further investigate the flocking and preserving connectedness in multi-agent nonholonomic systems with proximity graphs, in which the positions and the relative distances are not available to the distributed controllers. Several sufficient conditions are derived to resolve the above problem based on the kinematic model and the dynamic model, respectively. These sufficient conditions indicate that, for any given distinct initial positions and connected initial graph, there always exist gains of the linear protocols to preserve the connectedness of the graph and realize flocking. Moreover, under an additional condition on initial heading angles, the similar result is obtained for a nonlinear protocol with the form of Kuramoto model. Finally, numerical simulations are given to validate the above theoretical results. [ABSTRACT FROM PUBLISHER]

This paper studies the global pinning synchronization problem for a class of complex networks with switching directed topologies. The common assumption in the existing related literature that each possible network topology contains a directed spanning tree is removed in this paper. Using tools from $M$ -matrix theory and stability analysis of the switched nonlinear systems, a new kind of network topology-dependent multiple Lyapunov functions is proposed for analyzing the synchronization behavior of the whole network. It is theoretically shown that the global pinning synchronization in switched complex networks can be ensured if some nodes are appropriately pinned and the coupling is carefully selected. Interesting issues of how many and which nodes should be pinned for possibly realizing global synchronization are further addressed. Finally, some numerical simulations on coupled neural networks are provided to verify the theoretical results. [ABSTRACT FROM PUBLISHER]

This paper addresses the global \cal H\infty pinning synchronization problem for a class of directed networks with aperiodic sampled-data communications. Important yet challenging issues of how many and which nodes should be pinned for realizing global synchronization in a fixed directed network without external disturbances are first discussed. By using a combined tool from the input-delay approach and free-weighting matrices technique, some sufficient synchronizability conditions are then derived for such networks. Furthermore, a multi-step algorithm is designed to estimate the upper bound of the maximum allowable sampling intervals for achieving synchronization. Theoretical results are then extended to global \cal H\infty pinning synchronization in fixed and switched directed networks with external disturbances, showing that a finite \cal H\infty performance index can be guaranteed under some suitable conditions. Finally, numerical simulations are performed to demonstrate the effectiveness of the analytical results. [ABSTRACT FROM PUBLISHER]