Dynamic network model of banking system stability

This paper presents a dynamic model of banking interactions, which uses interbank connections to study the stability of the banking system. The dynamic model extends previous work on network models of the banking system taking inspiration from large scale, complex, interconnected systems studied within the domain of engineering. The banking system is represented as a network where nodes are individual banks and the links between any two banks consist of interbank loans and borrowing. The dynamic structure of the model is represented as a set of differential equations, which, to the best of our knowledge, is an original characteristic of our approach. This dynamic structure not only allows us to analyse systemic risk but also to incorporate an analysis of control mechanisms. Uncertainty is introduced in the system by applying stochastic shocks to the bank deposits, which are assigned as an exogenous signal. The behaviour of the system can be analysed for different initial conditions and parameter sets. This paper shows some preliminary results under different combinations of bank reserve ratios, bank capital sizes and different degrees of bank inter-connectedness. The results show that both reserve ratio and link rate have a positive effect on the stability of the system in the presence of moderate shocks. However, for high values of the shocks, high reserve ratios may have a detrimental effect on the survival of banks. In future work, we will apply strategies from the domain of control engineering to the dynamic model to characterise more formally the stability of the banking network

Fuzzy Distributed Cooperative Tracking For A Swarm Of Unmanned Aerial Vehicles With Heterogeneous Goals

Copyright © 2015 Taylor & Francis This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Systems Science on 29 December 2015, available online: http://www.tandfonline.com/10.1080/00207721.2015.1126380This article proposes a systematic analysis for a tracking problem which ensures cooperation amongst a swarm of UAVs, modelled as nonlinear systems with linear and angular velocity constraints, in order to achieve different goals. A distributed Takagi-Sugeno (TS) framework design is adopted for the representation of the nonlinear model of the dynamics of the UAVs. The distributed control law which is introduced is composed of both node and network level information. Firstly feedback gains are synthesised using a Parallel Distributed Compensation (PDC) control law structure, for a collection of isolated UAVs; ignoring communications among the swarm. Then secondly, based on an alternation-like procedure, the resulting feedback gains are used to determine Lyapunov matrices which are utilised at network level to incorporate into the control law the relative differences in the states of the vehicles, and to induce cooperative behaviour. Eventually stability is guaranteed for the entire swarm. The control synthesis is performed using tools from linear control theory: in particular the design criteria are posed as Linear Matrix Inequalities (LMIs). An example based on a UAV tracking scenario is included to outline the efficacy of the approach.Engineering and Physical Sciences Research Council (EPSRC

Synchronization and local convergence analysis of networks with dynamic diffusive coupling

In this paper, we address the problem of achieving synchronization in networks of nonlinear units coupled by dynamic diffusive terms. We present two types of couplings consisting of a static linear term, corresponding to the diffusive coupling, and a dynamic term which can be either the integral or the derivative of the sum of the mismatches between the states of neighbouring agents. The resulting dynamic coupling strategy is a distributed proportional-integral (PI) or a proportional-derivative (PD) law that is shown to be effective in improving the network synchronization performance, for example, when the dynamics at nodes are nonidentical. We assess the stability of the network by extending the classical Master Stability Function approach to the case where the links are dynamic ones of PI/PD type. We validate our approach via a set of representative examples including networks of chaotic Lorenz and networks of nonlinear mechanical systems

Distributed Robust Stability Analysis of Interconnected Uncertain Systems

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic constraints. This approach yields a sparse linear matrix inequality which can be decomposed into a set of smaller, coupled linear matrix inequalities. This allows us to solve the analysis problem efficiently and in a distributed manner. We also show that the decomposed problem is equivalent to the original robustness analysis problem, and hence our method does not introduce additional conservativeness.Comment: This paper has been accepted for presentation at the 51st IEEE Conference on Decision and Control, Maui, Hawaii, 201

Multiplex PI-Control for Consensus in Networks of Heterogeneous Linear Agents

In this paper, we propose a multiplex proportional-integral approach, for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Sufficient conditions for convergence are derived that depend upon the structure of the network, the parameters characterizing the control layers and the node dynamics. The effectiveness of the theoretical results is illustrated using a power network model as a representative example.Comment: 13 pages, 6 Figures, Preprint submitted to Automatic

Voltage Stabilization in Microgrids via Quadratic Droop Control

We consider the problem of voltage stability and reactive power balancing in islanded small-scale electrical networks outfitted with DC/AC inverters ("microgrids"). A droop-like voltage feedback controller is proposed which is quadratic in the local voltage magnitude, allowing for the application of circuit-theoretic analysis techniques to the closed-loop system. The operating points of the closed-loop microgrid are in exact correspondence with the solutions of a reduced power flow equation, and we provide explicit solutions and small-signal stability analyses under several static and dynamic load models. Controller optimality is characterized as follows: we show a one-to-one correspondence between the high-voltage equilibrium of the microgrid under quadratic droop control, and the solution of an optimization problem which minimizes a trade-off between reactive power dissipation and voltage deviations. Power sharing performance of the controller is characterized as a function of the controller gains, network topology, and parameters. Perhaps surprisingly, proportional sharing of the total load between inverters is achieved in the low-gain limit, independent of the circuit topology or reactances. All results hold for arbitrary grid topologies, with arbitrary numbers of inverters and loads. Numerical results confirm the robustness of the controller to unmodeled dynamics.Comment: 14 pages, 8 figure