Event-triggered pinning control of switching networks

This paper investigates event-triggered pinning control for the synchronization of complex networks of nonlinear dynamical systems. We consider networks described by time-varying weighted graphs and featuring generic linear interaction protocols. Sufficient conditions for the absence of Zeno behavior are derived and exponential convergence of a global normed error function is proven. Static networks are considered as a special case, wherein the existence of a lower bound for interevent times is also proven. Numerical examples demonstrate the effectiveness of the proposed control strategy

Robust Control

The need to be tolerant to changes in the control systems or in the operational environment of systems subject to unknown disturbances has generated new control methods that are able to deal with the non-parametrized disturbances of systems, without adapting itself to the system uncertainty but rather providing stability in the presence of errors bound in a model. With this approach in mind and with the intention to exemplify robust control applications, this book includes selected chapters that describe models of H-infinity loop, robust stability and uncertainty, among others. Each robust control method and model discussed in this book is illustrated by a relevant example that serves as an overview of the theoretical and practical method in robust control

Stability and Control in Complex Networks of Dynamical Systems

Stability analysis of networked dynamical systems has been of interest in many disciplines such as biology and physics and chemistry with applications such as LASER cooling and plasma stability. These large networks are often modeled to have a completely random (Erdös-Rényi) or semi-random (Small-World) topologies. The former model is often used due to mathematical tractability while the latter has been shown to be a better model for most real life networks. The recent emergence of cyber physical systems, and in particular the smart grid, has given rise to a number of engineering questions regarding the control and optimization of such networks. Some of the these questions are: How can the stability of a random network be characterized in probabilistic terms? Can the effects of network topology and system dynamics be separated? What does it take to control a large random network? Can decentralized (pinning) control be effective? If not, how large does the control network needs to be? How can decentralized or distributed controllers be designed? How the size of control network would scale with the size of networked system? Motivated by these questions, we began by studying the probability of stability of synchronization in random networks of oscillators. We developed a stability condition separating the effects of topology and node dynamics and evaluated bounds on the probability of stability for both Erdös-Rényi (ER) and Small-World (SW) network topology models. We then turned our attention to the more realistic scenario where the dynamics of the nodes and couplings are mismatched. Utilizing the concept of ε-synchronization, we have studied the probability of synchronization and showed that the synchronization error, ε, can be arbitrarily reduced using linear controllers. We have also considered the decentralized approach of pinning control to ensure stability in such complex networks. In the pinning method, decentralized controllers are used to control a fraction of the nodes in the network. This is different from traditional decentralized approaches where all the nodes have their own controllers. While the problem of selecting the minimum number of pinning nodes is known to be NP-hard and grows exponentially with the number of nodes in the network we have devised a suboptimal algorithm to select the pinning nodes which converges linearly with network size. We have also analyzed the effectiveness of the pinning approach for the synchronization of oscillators in the networks with fast switching, where the network links disconnect and reconnect quickly relative to the node dynamics. To address the scaling problem in the design of distributed control networks, we have employed a random control network to stabilize a random plant network. Our results show that for an ER plant network, the control network needs to grow linearly with the size of the plant network

Generation and escape of local waves from the boundary of uncoupled cardiac tissue

We aim to understand the formation of abnormal waves of activity from myocardial regions with diminished cell-to-cell coupling. In route to this goal, we studied the behavior of a heterogeneous myocyte network in which a sharp coupling gradient was placed under conditions of increasing network automaticity. Experiments were conducted in monolayers of neonatal rat cardiomyocytes using heptanol and isoproterenol as means of altering cell-to-cell coupling and automaticity respectively. Experimental findings were explained and expanded using a modified Beeler-Reuter numerical model. The data suggests that the combination of a heterogeneous substrate, a gradient of coupling and an increase in oscillatory activity of individual cells creates a rich set of behaviors associated with self-generated spiral waves and ectopic sources. Spiral waves feature a flattened shape and a pin-unpin drift type of tip motion. These intercellular waves are action-potential based and can be visualized with either voltage or calcium transient measurements. A source/load mismatch on the interface between the boundary and well-coupled layers can lock wavefronts emanating from both ectopic sources and rotating waves within the inner layers of the coupling gradient. A numerical approach allowed us to explore how: i) the spatial distribution of cells, ii) the amplitude and dispersion of cell automaticity, iii) and the speed at which the coupling gradient moves in space, affects wave behavior, including its escape into well-coupled tissue.Comment: 28 pages, 10 figures, submitted to Biophysical Journa

Event-triggered Consensus for Multi-agent Systems with Asymmetric and Reducible Topologies

This paper studies the consensus problem of multi-agent systems with asymmetric and reducible topologies. Centralized event-triggered rules are provided so as to reduce the frequency of system's updating. The diffusion coupling feedbacks of each agent are based on the latest observations from its in-neighbors and the system's next observation time is triggered by a criterion based on all agents' information. The scenario of continuous monitoring is first considered, namely all agents' instantaneous states can be observed. It is proved that if the network topology has a spanning tree, then the centralized event-triggered coupling strategy can realize consensus for the multi-agent system. Then the results are extended to discontinuous monitoring, where the system computes its next triggering time in advance without having to observe all agents' states continuously. Examples with numerical simulation are provided to show the effectiveness of the theoretical results

Event-triggered communication for passivity and synchronisation of multi-weighted coupled neural networks with and without parameter uncertainties

A multi-weighted coupled neural networks (MWCNNs) model with event-triggered communication is studied here. On the one hand, the passivity of the presented network model is studied by utilising Lyapunov stability theory and some inequality techniques, and a synchronisation criterion based on the obtained output-strict passivity condition of MWCNNs with eventtriggered communication is derived. On the other hand, some robust passivity and robust synchronisation criteria based on output-strict passivity of the proposed network with uncertain parameters are presented. At last, two numerical examples are provided to testify the effectiveness of the output-strict passivity and robust synchronisation results