Multi-objective Active Control Policy Design for Commensurate and Incommensurate Fractional Order Chaotic Financial Systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.In this paper, an active control policy design for a fractional order (FO) financial system is attempted, considering multiple conflicting objectives. An active control template as a nonlinear state feedback mechanism is developed and the controller gains are chosen within a multi-objective optimization (MOO) framework to satisfy the conditions of asymptotic stability, derived analytically. The MOO gives a set of solutions on the Pareto optimal front for the multiple conflicting objectives that are considered. It is shown that there is a trade-off between the multiple design objectives and a better performance in one objective can only be obtained at the cost of performance deterioration in the other objectives. The multi-objective controller design has been compared using three different MOO techniques viz. Non Dominated Sorting Genetic Algorithm-II (NSGA-II), epsilon variable Multi-Objective Genetic Algorithm (ev-MOGA), and Multi Objective Evolutionary Algorithm with Decomposition (MOEA/D). The robustness of the same control policy designed with the nominal system settings have been investigated also for gradual decrease in the commensurate and incommensurate fractional orders of the financial system

Synchronization of Time Delayed Fractional Order Chaotic Financial System

The research on a time delayed fractional order financial chaotic system is a hot issue. In this paper, synchronization of time delayed fractional order financial chaotic system is studied. Based on comparison principle of linear fractional equation with delay, by using a fractional order inequality, a sufficient condition is obtained to guarantee the synchronization of master-slave systems. An example is exploited to show the feasibility of the theoretical results

Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters

This paper investigates the modified function projective synchronization between fractional-order chaotic systems, which are partially linear financial systems with uncertain parameters. Based on the stability theory of fractional-order systems and the Lyapunov matrix equation, a controller is obtained for the synchronization between fractional-order financial chaotic systems. Using the controller, the error systems converged to zero as time tends to infinity, and the uncertain parameters were also estimated so that the phenomenon of parameter distortion was effectively avoided. Numerical simulations demonstrate the validity and feasibility of the proposed method

Controlling Hyperchaotic Finance System with Combining Passive and Feedback Controllers

In this paper, a novel control method that combines passive, linear feedback, and dislocated feedback control methods is proposed and applied to the control of the four-dimensional hyperchaotic finance system which has been introduced and controlled with the linear feedback and speed feedback control methods by Yu, Cai, and Li (2012). The stability of the hyperchaotic finance system at its equilibrium points is ensured on the basis of a Lyapunov function. Computer simulations are used for verifying all the theoretical analyses visually. In the simulations, the proposed control method is also compared with the speed feedback and linear feedback control methods to observe its effectiveness. Finally, the comparative findings are discussed

The law of value : a contribution to the classical approach to economic analysis

This thesis contributes to our understanding of the relationship between the material activity of human labour and the monetary forms of an economy by examining the theoretical foundations of the classical approach to economic analysis, in particular the objective costs-of-production approach to economic value. The classical labour theory of value suffers from two related problems: David Ricardo's problem of an invariable measure of value and Karl Marx's transformation problem. This thesis proposes to resolve both problems by constructing a more general labour theory of value. The more general theory provides a new perspective on related issues in the classical theory, including Marx's classification of money-capital as an irrational commodity, the meaning and significance of Piero Sraffa's standard commodity and Luigi Pasinetti's restriction of the labour theory to a normative role. According to the classical account of capitalist competition the scramble for profit causes market prices to "gravitate" to natural prices. This thesis proposes a nonlinear dynamic model of classical gravitation in which prices and labour costs converge to a state of mutual consistency in equilibrium. The dynamic model, combined with a general labour theory of value, establishes a lawful relation between prices and labour costs, which reconstructs Marx's version of the classical "law of value"

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Making the Local: Anthropology & the Suburban Citizen

Through anthropology at the edge, this thesis looks at how social projects form in dialogic relation to the ‘other’ as they meet and contest the meaning, values and forms of the material world. This PhD emerged between two social projects who aimed to make better suburbs. One, the Adaptable Suburbs Project (ASP) aimed to release the “untapped potential” of suburbs through a methodology of architectural analysis that combined different data sources. An online mapping platform aimed to collect oral testimonies from residents to reveal the “meaning, values, symbols” of the built environment. The location of a mountain, destroyed by a giant, was added by a group of local enthusiasts - the “Seething Villagers”. Playing with notions of history, myth and “fact”, Seethingers create events and “stupid” stories to create meaningful communities which “allow people to shine”. The story was refused by the ASP as the historical “fact” compromised the communicative ideal of deliberative democracy that underpinned the mapping project. Both social projects, one making better through academically informed planning policy at a national level, the other through forming “resilient” communities at a local level, met again in a council meeting. Here one social project, - Seethingers, as local citizens - articulated the values and meanings of the built environment through the framework of the other in order to object to planning application. It is here where the effects of the refusal were felt again. Producing efficacious knowledge and articulations about the world takes “work”. This thesis asks what sorts of subjectivities emerge at the edge of social projects, in moments of contestations, and what is lost in this process? Subjectivities emerge, not from the centre of a social project, but from the edge where it is always meeting the other. This thesis examines (and is) the material transfer of knowledge of ‘the other’ and its social, ethical and political implications