Trading the stability of finite zeros for global stabilization of nonlinear cascade systems

This paper analyzes the stabilizability properties of nonlinear cascades in which a nonminimum phase linear system is interconnected through its output to a stable nonlinear system. It is shown that the instability of the zeros of the linear system can be traded with the stability of the nonlinear system up to a limit fixed by the growth properties of the cascade interconnection term. Below this limit, global stabilization is achieved by smooth static state feedback. Beyond this limit, various examples illustrate that controllability of the cascade may be lost, making it impossible to achieve large regions of attractions.

Global stability of Hopfield neural networks

This paper gives a condition for the global stability of a continuous-time hopfield neural network when its activation function maybe not monotonically increasing.

Global change alters the stability of food webs

Recent research has generally shown that a small change in the number of species in a food web can have consequences both for community structure and ecosystem processes. However 'change' is not limited to just the number of species in a community, but might include an alteration to such properties as precipitation, nutrient cycling and temperature. How such changes might affect species interactions is important, not just through the presence or absence of interactions, but also because the patterning of interaction strengths among species is intimately associated with community stability. Interaction strengths encompass such properties as feeding rates and assimilation efficiencies, and encapsulate functionally important information with regard to ecosystem processes. Interaction strengths represent the pathways and transfer of energy through an ecosystem. We review the best empirical data available detailing the frequency distribution of interaction strengths in communities. We present the underlying (but consistent) pattern of species interactions and discuss the implications of this patterning. We then examine how such a basic pattern might be affected given various scenarios of 'change' and discuss the consequences for community stability and ecosystem functioning.

Global Systemic Risk and International Regulatory Coordination: Squaring Sovereignty and Financial Stability

In recent years much attention has been given to systemic risk and maintaining financial stability. Much of the focus, rightly, has been on market failures and the role of regulation in addressing them. This article looks at the role of domestic policies and government actions as sources of global instability. The global financial system is built upon global markets controlled by national financial and macroeconomic policies. In this context, regulatory asymmetries, diverging policy preferences, and government failures add a further dimension to global systemic risk not present at the national level.
Systemic risk is a result of the interplay between two independent variables: an underlying trigger event, in this analysis a domestic policy measure, and a transmission channel. The solution to systemic risk requires tackling one of these variables. In a domestic setting, the centralization of regulatory power into one single authority makes it easier to balance the delicate equilibrium between enhancing efficiency and reducing instability. However, in a global financial system in which national financial policies serve to maximize economic welfare, regulators will be confronted with difficult policy and legal tradeoffs.
We investigate the role that financial regulation plays in addressing domestic policy failures and in controlling the danger of global financial interdependence. To do so we analyse global financial interconnectedness, and explain its role in transmitting instability; we investigate the political economy dynamics at the origin of regulatory asymmetries and government failures; and we discuss the limits of regulation.

Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of precast concrete multi-storey buildings

This study deals with the reduction of the stiffness in precast concrete structural elements of multi-storey buildings to analyze global stability. Having reviewed the technical literature, this paper present indications of stiffness reduction in different codes, standards, and recommendations and compare these to the values found in the present study. The structural model analyzed in this study was constructed with finite elements using ANSYS® software. Physical Non-Linearity (PNL) was considered in relation to the diagrams M x N x 1/r, and Geometric Non-Linearity (GNL) was calculated following the Newton-Raphson method. Using a typical precast concrete structure with multiple floors and a semi-rigid beam-to-column connection, expressions for a stiffness reduction coefficient are presented. The main conclusions of the study are as follows: the reduction coefficients obtained from the diagram M x N x 1/r differ from standards that use a simplified consideration of PNL; the stiffness reduction coefficient for columns in the arrangements analyzed were approximately 0.5 to 0.6; and the variation of values found for stiffness reduction coefficient in concrete beams, which were subjected to the effects of creep with linear coefficients from 0 to 3, ranged from 0.45 to 0.2 for positive bending moments and 0.3 to 0.2 for negative bending moments.

On the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability Analysis

A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds up the required Krylov subspace iterations and has the capability of converging to specific parts of the global spectrum. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the performance of the present method could be dramatically improved with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

Global Stability Analysis of a Compressible Turbulent Flow around a High-Lift Configuration

The purpose of this work is to analyze a complex high lift configuration for which significant regions of separated flow are present. Current state of the art methods have some diffculty to predict the origin and the progression of this separated flow when increasing the angle of attack. The mechanisms responsible for the maximum lift limit on multi-element wing con?gurations are not clear; this stability analysis could help to understand the physics behind the phenomenon and to find a relation between the flow separation and the instability onset. The methodology presented herein consists in the computation of a steady base flow solution based on a finite volume discretization and a proposal of the solution for a generalized eigenvalue problem corresponding to the perturbed and linearized problem. The eigenvalue problem has been solved with the Arnoldi iterative method, one of the Krylov subspace projection methods. The described methodology was applied to the NACA0012 test case in subsonic and in transonic conditions and, finally, for the first time to the authors knowledge, on an industrial multi-component geometry, such as the A310 airfoil, in order to identify low frequency instabilities related to the separation. One important conclusion is that for all the analyzed geometries, one unstable mode related to flow separation appears for an angle of attack greater than the one correspondent to the maximum lift coe?cient condition. Finally, an adjoint study was carried out in order to evaluate the receptivity and the structural sensitivity of the geometries, giving an indication of the domain region that could be modified resulting in the biggest change of the flowfield.

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

In this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier?Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart?Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

Global Stability Analysis of Turbulent Transonic Flows on Airfoil geometries

La aparición de inestabilidades en un flujo es un problema importante que puede afectar a algunas aplicaciones aerodinámicas. De hecho existen diferentes tipos de fenómenos no-estacionarios que actualmente son tema de investigación; casos como la separación a altos ángulos de ataque o el buffet transónico son dos ejemplos de cierta relevancia. El análisis de estabilidad global permite identificar la aparición de dichas condiciones inestables, proporcionando información importante sobre la región donde la inestabilidad es dominante y sobre la frecuencia del fenómeno inestable. La metodología empleada es capaz de calcular un flujo base promediado mediante una discretización con volúmenes finitos y posteriormente la solución de un problema de autovalores asociado a la linealización que aparece al perturbar el flujo base. El cálculo numérico se puede dividir en tres pasos: primero se calcula una solución estacionaria para las ecuaciones RANS, luego se extrae la matriz del Jacobiano que representa el problema linealizado y finalmente se deriva y se resuelve el problema de autovalores generalizado mediante el método iterativo de Arnoldi. Como primer caso de validación, la técnica descrita ha sido aplicada a un cilindro circular en condiciones laminares para detectar el principio de las oscilaciones de los vórtices de von Karman, y se han comparado los resultados con experimentos y cálculos anteriores. La parte más importante del estudio se centra en el análisis de flujos compresibles en régimen turbulento. La predicción de la aparición y la progresión de flujo separado a altos ángulos de ataque se han estudiado en el perfil NACA0012 en condiciones tanto subsónicas como supersónicas y en una sección del ala del A310 en condiciones de despegue. Para todas las geometrías analizadas, se ha podido observar que la separación gradual genera la aparición de un modo inestable específico para altos ángulos de ataque siempre mayores que el ángulo asociado al máximo coeficiente de sustentación. Además, se ha estudiado el problema adjunto para obtener información sobre la zona donde una fuerza externa provoca el máximo cambio en el campo fluido. El estudio se ha completado calculando el mapa de sensibilidad estructural y localizando el centro de la inestabilidad. En el presente trabajo de tesis se ha analizado otro importante fenómeno: el buffet transónico. En condiciones transónicas, la interacción entre la onda de choque y la capa límite genera una oscilación de la posición de la onda de choque y, por consiguiente, de las fuerzas aerodinámicas. El conocimiento de las condiciones críticas y su origen puede ayudar a evitar la oscilación causada por estas fuerzas. Las condiciones para las cuales comienza la inestabilidad han sido calculadas y comparadas con trabajos anteriores. Por otra parte, los resultados del correspondiente problema adjunto y el mapa de sensibilidad se han obtenido por primera vez para el buffet, indicando la región del dominio que sera necesario modificar para crear el mayor cambio en las propiedades del campo fluido. Dado el gran consumo de memoria requerido para los casos 3D, se ha realizado un estudio sobre la reducción del domino con la finalidad de reducirlo a la región donde está localizada la inestabilidad. La eficacia de dicha reducción de dominio ha sido evaluada investigando el cambio en la dimensión de la matriz del Jacobiano, no resultando muy eficiente en términos del consumo de memoria. Dado que el buffet es un problema en general tridimensional, el análisis TriGlobal de una geometría 3D podría considerarse el auténtico reto futuro. Como aproximación al problema, un primer estudio se ha realizado empleando una geometría tridimensional extruida del NACA00f2. El cálculo del flujo 3D y, por primera vez en casos tridimensionales compresibles y turbulentos, el análisis de estabilidad TriGlobal, se han llevado a cabo. La comparación de los resultados obtenidos con los resultados del anterior modelo 2D, ha permitido, primero, verificar la exactitud del cálculo 2D realizado anteriormente y también ha proporcionado una estimación del consumo de memoria requerido para el caso 3D. ABSTRACT Flow unsteadiness is an important problem in aerodynamic applications. In fact, there are several types of unsteady phenomena that are still at the cutting edge of research in the field; separation at high angles of attack and transonic buffet are two important examples. Global Stability Analysis can identify the unstable onset conditions, providing important information about the instability location in the domain and the frequency of the unstable phenomenon. The methodology computes a base flow averaged state based on a finite volume discretization and a solution for a generalized eigenvalue problem corresponding to the perturbed linearized equations. The numerical computation is then performed in three steps: first, a steady solution for the RANS equation is computed; second, the Jacobian matrix that represents the linearized problem is obtained; and finally, the generalized eigenvalue problem is derived and solved with an Arnoldi iterative method. As a first validation test, the technique has been applied on a laminar circular cylinder in order to detect the von Karman vortex shedding onset, comparing the results with experiments and with previous calculations. The main part of the study focusses on turbulent and compressible cases. The prediction of the origin and progression of separated flows at high angles of attack has been studied on the NACA0012 airfoil at subsonic and transonic conditions and for the A310 airfoil in take-off configuration. For all the analyzed geometries, it has been found that gradual separation generates the appearance of one specific unstable mode for angles of attack always greater than the ones related to the maximum lift coefficient. In addition, the adjoint problem has been studied to suggest the location of an external force that results in the largest change to the flow field. From the direct and the adjoint analysis the structural sensitivity map has been computed and the core of the instability has been located. The other important phenomenon analyzed in this work is the transonic buffet. In transonic conditions, the interaction between the shock wave and the boundary layer leads to an oscillation of the shock location and, consequently, of the aerodynamic forces. Knowing the critical operational conditions and its origin can be helpful in preventing such fluctuating forces. The instability onset has then been computed and compared with the literature. Moreover, results of the corresponding adjoint problem and a sensitivity map have been provided for the first time for the buffet problem, indicating the region that must be modified to create the biggest change in flow field properties. Because of the large memory consumption required when a 3D case is approached, a domain reduction study has been carried out with the aim of limiting the domain size to the region where the instability is located. The effectiveness of the domain reduction has been evaluated by investigating the change in the Jacobian matrix size, not being very efficient in terms of memory consumption. Since buffet is a three-dimensional problem, TriGlobal stability analysis can be seen as a future challenge. To approximate the problem, a first study has been carried out on an extruded three-dimensional geometry of the NACA0012 airfoil. The 3D flow computation and the TriGlobal stability analysis have been performed for the first time on a compressible and turbulent 3D case. The results have been compared with a 2D model, confirming that the buffet onset evaluated in the 2D case is well detected. Moreover, the computation has given an indication about the memory consumption for a 3D case.

Capital 2.0 capital formation and legal risk in a new global economic order from fiat to exit: including case studies of the proposed transatlantic trade and investment partnership between the United States and the European Union and the financing relation between the United States and the People’s Republic of China

Following the intrinsically linked balance sheets in his Capital Formation Life Cycle, Lukas M. Stahl explains with his Triple A Model of Accounting, Allocation and Accountability the stages of the Capital Formation process from FIAT to EXIT. Based on the theoretical foundations of legal risk laid by the International Bar Association with the help of Roger McCormick and legal scholars such as Joanna Benjamin, Matthew Whalley and Tobias Mahler, and founded on the basis of Wesley Hohfeld’s category theory of jural relations, Stahl develops his mutually exclusive Four Determinants of Legal Risk of Law, Lack of Right, Liability and Limitation. Those Four Determinants of Legal Risk allow us to apply, assess, and precisely describe the respective legal risk at all stages of the Capital Formation Life Cycle as demonstrated in case studies of nine industry verticals of the proposed and currently negotiated Transatlantic Trade and Investment Partnership between the United States of America and the European Union, TTIP, as well as in the case of the often cited financing relation between the United States and the People’s Republic of China. Having established the Four Determinants of Legal Risk and its application to the Capital Formation Life Cycle, Stahl then explores the theoretical foundations of capital formation, their historical basis in classical and neo-classical economics and its forefathers such as The Austrians around Eugen von Boehm-Bawerk, Ludwig von Mises and Friedrich von Hayek and most notably and controversial, Karl Marx, and their impact on today’s exponential expansion of capital formation. Starting off with the first pillar of his Triple A Model, Accounting, Stahl then moves on to explain the Three Factors of Capital Formation, Man, Machines and Money and shows how “value-added” is created with respect to the non-monetary capital factors of human resources and industrial production. Followed by a detailed analysis discussing the roles of the Three Actors of Monetary Capital Formation, Central Banks, Commercial Banks and Citizens Stahl readily dismisses a number of myths regarding the creation of money providing in-depth insight into the workings of monetary policy makers, their institutions and ultimate beneficiaries, the corporate and consumer citizens. In his second pillar, Allocation, Stahl continues his analysis of the balance sheets of the Capital Formation Life Cycle by discussing the role of The Five Key Accounts of Monetary Capital Formation, the Sovereign, Financial, Corporate, Private and International account of Monetary Capital Formation and the associated legal risks in the allocation of capital pursuant to his Four Determinants of Legal Risk. In his third pillar, Accountability, Stahl discusses the ever recurring Crisis-Reaction-Acceleration-Sequence-History, in short: CRASH, since the beginning of the millennium starting with the dot-com crash at the turn of the millennium, followed seven years later by the financial crisis of 2008 and the dislocations in the global economy we are facing another seven years later today in 2015 with several sordid debt restructurings under way and hundred thousands of refugees on the way caused by war and increasing inequality. Together with the regulatory reactions they have caused in the form of so-called landmark legislation such as the Sarbanes-Oxley Act of 2002, the Dodd-Frank Act of 2010, the JOBS Act of 2012 or the introduction of the Basel Accords, Basel II in 2004 and III in 2010, the European Financial Stability Facility of 2010, the European Stability Mechanism of 2012 and the European Banking Union of 2013, Stahl analyses the acceleration in size and scope of crises that appears to find often seemingly helpless bureaucratic responses, the inherent legal risks and the complete lack of accountability on part of those responsible. Stahl argues that the order of the day requires to address the root cause of the problems in the form of two fundamental design defects of our Global Economic Order, namely our monetary and judicial order. Inspired by a 1933 plan of nine University of Chicago economists abolishing the fractional reserve system, he proposes the introduction of Sovereign Money as a prerequisite to void misallocations by way of judicial order in the course of domestic and transnational insolvency proceedings including the restructuring of sovereign debt throughout the entire monetary system back to its origin without causing domino effects of banking collapses and failed financial institutions. In recognizing Austrian-American economist Schumpeter’s Concept of Creative Destruction, as a process of industrial mutation that incessantly revolutionizes the economic structure from within, incessantly destroying the old one, incessantly creating a new one, Stahl responds to Schumpeter’s economic chemotherapy with his Concept of Equitable Default mimicking an immunotherapy that strengthens the corpus economicus own immune system by providing for the judicial authority to terminate precisely those misallocations that have proven malignant causing default perusing the century old common law concept of equity that allows for the equitable reformation, rescission or restitution of contract by way of judicial order. Following a review of the proposed mechanisms of transnational dispute resolution and current court systems with transnational jurisdiction, Stahl advocates as a first step in order to complete the Capital Formation Life Cycle from FIAT, the creation of money by way of credit, to EXIT, the termination of money by way of judicial order, the institution of a Transatlantic Trade and Investment Court constituted by a panel of judges from the U.S. Court of International Trade and the European Court of Justice by following the model of the EFTA Court of the European Free Trade Association. Since the first time his proposal has been made public in June of 2014 after being discussed in academic circles since 2011, his or similar proposals have found numerous public supporters. Most notably, the former Vice President of the European Parliament, David Martin, has tabled an amendment in June 2015 in the course of the negotiations on TTIP calling for an independent judicial body and the Member of the European Commission, Cecilia Malmström, has presented her proposal of an International Investment Court on September 16, 2015. Stahl concludes, that for the first time in the history of our generation it appears that there is a real opportunity for reform of our Global Economic Order by curing the two fundamental design defects of our monetary order and judicial order with the abolition of the fractional reserve system and the introduction of Sovereign Money and the institution of a democratically elected Transatlantic Trade and Investment Court that commensurate with its jurisdiction extending to cases concerning the Transatlantic Trade and Investment Partnership may complete the Capital Formation Life Cycle resolving cases of default with the transnational judicial authority for terminal resolution of misallocations in a New Global Economic Order without the ensuing dangers of systemic collapse from FIAT to EXIT.

Modeling, stability analysis and control of microgrid

With the increase in the level of global warming, renewable energy based distributed generators (DGs) will increasingly play a dominant role in electricity production. Distributed generation based on solar energy (photovoltaic and solar thermal), wind, biomass, mini-hydro along with use of fuel cells and micro turbines will gain considerable momentum in the near future. A microgrid consists of clusters of load and distributed generators that operate as a single controllable system. The interconnection of the DG to the utility/grid through power electronic converters has raised concern about safe operation and protection of the equipments. Many innovative control techniques have been used for enhancing the stability of microgrid as for proper load sharing. The most common method is the use of droop characteristics for decentralized load sharing. Parallel converters have been controlled to deliver desired real power (and reactive power) to the system. Local signals are used as feedback to control converters, since in a real system, the distance between the converters may make the inter-communication impractical. The real and reactive power sharing can be achieved by controlling two independent quantities, frequency and fundamental voltage magnitude. In this thesis, an angle droop controller is proposed to share power amongst converter interfaced DGs in a microgrid. As the angle of the output voltage can be changed instantaneously in a voltage source converter (VSC), controlling the angle to control the real power is always beneficial for quick attainment of steady state. Thus in converter based DGs, load sharing can be performed by drooping the converter output voltage magnitude and its angle instead of frequency. The angle control results in much lesser frequency variation compared to that with frequency droop. An enhanced frequency droop controller is proposed for better dynamic response and smooth transition between grid connected and islanded modes of operation. A modular controller structure with modified control loop is proposed for better load sharing between the parallel connected converters in a distributed generation system. Moreover, a method for smooth transition between grid connected and islanded modes is proposed. Power quality enhanced operation of a microgrid in presence of unbalanced and non-linear loads is also addressed in which the DGs act as compensators. The compensator can perform load balancing, harmonic compensation and reactive power control while supplying real power to the grid A frequency and voltage isolation technique between microgrid and utility is proposed by using a back-to-back converter. As utility and microgrid are totally isolated, the voltage or frequency fluctuations in the utility side do not affect the microgrid loads and vice versa. Another advantage of this scheme is that a bidirectional regulated power flow can be achieved by the back-to-back converter structure. For accurate load sharing, the droop gains have to be high, which has the potential of making the system unstable. Therefore the choice of droop gains is often a tradeoff between power sharing and stability. To improve this situation, a supplementary droop controller is proposed. A small signal model of the system is developed, based on which the parameters of the supplementary controller are designed. Two methods are proposed for load sharing in an autonomous microgrid in rural network with high R/X ratio lines. The first method proposes power sharing without any communication between the DGs. The feedback quantities and the gain matrixes are transformed with a transformation matrix based on the line R/X ratio. The second method involves minimal communication among the DGs. The converter output voltage angle reference is modified based on the active and reactive power flow in the line connected at point of common coupling (PCC). It is shown that a more economical and proper power sharing solution is possible with the web based communication of the power flow quantities. All the proposed methods are verified through PSCAD simulations. The converters are modeled with IGBT switches and anti parallel diodes with associated snubber circuits. All the rotating machines are modeled in detail including their dynamics.

Local adjustment and global adaptation of control periods for QoC management of control systems

Linking real-time schedulability directly to the Quality of Control (QoC), the ultimate goal of a control system, a hierarchical feedback QoC management framework with the Fixed Priority (FP) and the Earliest-Deadline-First (EDF) policies as plug-ins is proposed in this paper for real-time control systems with multiple control tasks. It uses a task decomposition model for continuous QoC evaluation even in overload conditions, and then employs heuristic rules to adjust the period of each of the control tasks for QoC improvement. If the total requested workload exceeds the desired value, global adaptation of control periods is triggered for workload maintenance. A sufficient stability condition is derived for a class of control systems with delay and period switching of the heuristic rules. Examples are given to demonstrate the proposed approach.