Synchronization in Networks of Identical Systems via Pinning: Application to Distributed Secondary Control of Microgrids

Motivated by the need for fast synchronized operation of power microgrids, we analyze the problem of single and multiple pinning in networked systems. We derive lower and upper bounds on the algebraic connectivity of the network with respect to the reference signal. These bounds are utilized to devise a suboptimal algorithm with polynomial complexity to find a suitable set of nodes to pin the network effectively and efficiently. The results are applied to secondary voltage pinning control design for a microgrid in islanded operation mode. Comparisons with existing single and multiple pinning strategies clearly demonstrates the efficacy of the obtained results.Comment: 11 pages, 9 figures, submitted to Transactions on Control Systems Technolog

Optimizing dynamical network structure for pinning control

Controlling dynamics of a network from any initial state to a final desired state has many applications in different disciplines from engineering to biology and social sciences. In this work, we optimize the network structure for pinning control. The problem is formulated as four optimization tasks: i) optimizing the locations of driver nodes, ii) optimizing the feedback gains, iii) optimizing simultaneously the locations of driver nodes and feedback gains, and iv) optimizing the connection weights. A newly developed population-based optimization technique (cat swarm optimization) is used as the optimization method. In order to verify the methods, we use both real-world networks, and model scale-free and small-world networks. Extensive simulation results show that the optimal placement of driver nodes significantly outperforms heuristic methods including placing drivers based on various centrality measures (degree, betweenness, closeness and clustering coefficient). The pinning controllability is further improved by optimizing the feedback gains. We also show that one can significantly improve the controllability by optimizing the connection weights

Structural engineering of evolving complex dynamical networks

Networks are ubiquitous in nature and many natural and man-made systems can be modelled as networked systems. Complex networks, systems comprising a number of nodes that are connected through edges, have been frequently used to model large-scale systems from various disciplines such as biology, ecology, and engineering. Dynamical systems interacting through a network may exhibit collective behaviours such as synchronisation, consensus, opinion formation, flocking and unusual phase transitions. Evolution of such collective behaviours is highly dependent on the structure of the interaction network. Optimisation of network topology to improve collective behaviours and network robustness can be achieved by intelligently modifying the network structure. Here, it is referred to as "Engineering of the Network". Although coupled dynamical systems can develop spontaneous synchronous patterns if their coupling strength lies in an appropriate range, in some applications one needs to control a fraction of nodes, known as driver nodes, in order to facilitate the synchrony. This thesis addresses the problem of identifying the set of best drivers, leading to the best pinning control performance. The eigen-ratio of the augmented Laplacian matrix, that is the largest eigenvalue divided by the second smallest one, is chosen as the controllability metric. The approach introduced in this thesis is to obtain the set of optimal drivers based on sensitivity analysis of the eigen-ratio, which requires only a single computation of the eigenvector associated with the largest eigenvalue, and thus is applicable for large-scale networks. This leads to a new "controllability centrality" metric for each subset of nodes. Simulation results reveal the effectiveness of the proposed metric in predicting the most important driver(s) correctly.     Interactions in complex networks might also facilitate the propagation of undesired effects, such as node/edge failure, which may crucially affect the performance of collective behaviours. In order to study the effect of node failure on network synchronisation, an analytical metric is proposed that measures the effect of a node removal on any desired eigenvalue of the Laplacian matrix. Using this metric, which is based on the local multiplicity of each eigenvalue at each node, one can approximate the impact of any node removal on the spectrum of a graph. The metric is computationally efficient as it only needs a single eigen-decomposition of the Laplacian matrix. It also provides a reliable approximation for the "Laplacian energy" of a network. Simulation results verify the accuracy of this metric in networks with different topologies. This thesis also considers formation control as an application of network synchronisation and studies the "rigidity maintenance" problem, which is one of the major challenges in this field. This problem is to preserve the rigidity of the sensing graph in a formation during motion, taking into consideration constraints such as line-of-sight requirements, sensing ranges and power limitations. By introducing a "Lattice of Configurations" for each node, a distributed rigidity maintenance algorithm is proposed to preserve the rigidity of the sensing network when failure in a sensing link would result in loss of rigidity. The proposed algorithm recovers rigidity by activating, almost always, the minimum number of new sensing links and considers real-time constraints of practical formations. A sufficient condition for this problem is proved and tested via numerical simulations. Based on the above results, a number of other areas and applications of network dynamics are studied and expounded upon in this thesis

Controllability of Social Networks and the Strategic Use of Random Information

This work is aimed at studying realistic social control strategies for social networks based on the introduction of random information into the state of selected driver agents. Deliberately exposing selected agents to random information is a technique already experimented in recommender systems or search engines, and represents one of the few options for influencing the behavior of a social context that could be accepted as ethical, could be fully disclosed to members, and does not involve the use of force or of deception. Our research is based on a model of knowledge diffusion applied to a time-varying adaptive network, and considers two well-known strategies for influencing social contexts. One is the selection of few influencers for manipulating their actions in order to drive the whole network to a certain behavior; the other, instead, drives the network behavior acting on the state of a large subset of ordinary, scarcely influencing users. The two approaches have been studied in terms of network and diffusion effects. The network effect is analyzed through the changes induced on network average degree and clustering coefficient, while the diffusion effect is based on two ad-hoc metrics defined to measure the degree of knowledge diffusion and skill level, as well as the polarization of agent interests. The results, obtained through simulations on synthetic networks, show a rich dynamics and strong effects on the communication structure and on the distribution of knowledge and skills, supporting our hypothesis that the strategic use of random information could represent a realistic approach to social network controllability, and that with both strategies, in principle, the control effect could be remarkable

A generalized simplicial model and its application

Higher-order structures, consisting of more than two individuals, provide a new perspective to reveal the missed non-trivial characteristics under pairwise networks. Prior works have researched various higher-order networks, but research for evaluating the effects of higher-order structures on network functions is still scarce. In this paper, we propose a framework to quantify the effects of higher-order structures (e.g., 2-simplex) and vital functions of complex networks by comparing the original network with its simplicial model. We provide a simplicial model that can regulate the quantity of 2-simplices and simultaneously fix the degree sequence. Although the algorithm is proposed to control the quantity of 2-simplices, results indicate it can also indirectly control simplexes more than 2-order. Experiments on spreading dynamics, pinning control, network robustness, and community detection have shown that regulating the quantity of 2-simplices changes network performance significantly. In conclusion, the proposed framework is a general and effective tool for linking higher-order structures with network functions. It can be regarded as a reference object in other applications and can deepen our understanding of the correlation between micro-level network structures and global network functions

Cooperation networks and innovation: A complex system perspective to the analysis and evaluation of a EU regional innovation policy programme

Recent developments in innovation theory and policy have led policymakers to assign particular importance to supporting networks of cooperation among heterogeneous economic actors, especially in production systems composed of small and medium enterprises. Such innovative policies call for parallel innovations in policy analysis, monitoring and assessment. Our analysis of a policy experiment aimed at supporting innovation networks in the Italian region of Tuscany intends to address some issues connected with the design, monitoring and evaluation of such interventions. Combining tools from ethnographic research and social networks analysis, we explore the structural elements of the policy programme, its macroscopic impact on the regional innovation system, and the success of individual networks in attaining their specific objectives. This innovative approach allows us to derive some general methodological suggestions for the design and evaluation of similar programmes.Innovation policy, cooperation networks, evaluation, regional development, SMEs production systems, complex systems