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

Cyclical Mackey Glass Model for Oil Bull Seasonal

In this article, we propose an innovative way for modelling oil bull seasonals taking into account seasonal speculations in oil markets. Since oil prices behave very seasonally during two periods of the year (summer and winter), we propose a modification of Mackey Glass equation by taking into account the rhythm of seasonal frequencies. Using monthly data for WTI oil prices, Seasonal Cyclical Mackey Glass estimates indicate that seasonal interactions between heterogeneous speculators with different expectations may be responsible for pronounced swings in prices in both periods. Moreover, the seasonal frequency  / 3(referring to a period of 6 months) appears to be persistent over time.Oil bull seasonal, Seasonal speculations, Heterogeneous agents model, Seasonal Cyclical Mackey Glass models.

Chaos in economics and finance

In this article, we specify the different approaches followed by the economists and the financial economists in order to use chaos theory. We explain the main difference using this theory with other research domains like the mathematics and the physics. Finally, we present tools necessary for the economists and financial economists to explore this domain empirically.Chaos theory ; attractor ; Economy ; Finance ; estimation theory ; forecasting

Forecasting high waters at Venice Lagoon using chaotic time series analisys and nonlinear neural netwoks

Time series analysis using nonlinear dynamics systems theory and multilayer neural networks models have been applied to the time sequence of water level data recorded every hour at 'Punta della Salute' from Venice Lagoon during the years 1980-1994. The first method is based on the reconstruction of the state space attractor using time delay embedding vectors and on the characterisation of invariant properties which define its dynamics. The results suggest the existence of a low dimensional chaotic attractor with a Lyapunov dimension, DL, of around 6.6 and a predictability between 8 and 13 hours ahead. Furthermore, once the attractor has been reconstructed it is possible to make predictions by mapping local-neighbourhood to local-neighbourhood in the reconstructed phase space. To compare the prediction results with another nonlinear method, two nonlinear autoregressive models (NAR) based on multilayer feedforward neural networks have been developed. From the study, it can be observed that nonlinear forecasting produces adequate results for the 'normal' dynamic behaviour of the water level of Venice Lagoon, outperforming linear algorithms, however, both methods fail to forecast the 'high water' phenomenon more than 2-3 hours ahead.Publicad

Synchronization of Fractional-order Chaotic Systems with Gaussian fluctuation by Sliding Mode Control

This paper is devoted to the problem of synchronization between fractional-order chaotic systems with Gaussian fluctuation by the method of fractional-order sliding mode control. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode control technique is carried out to realize the synchronization of the given systems. One theorem about sliding mode controller is presented to prove the proposed controller can make the system synchronize. As a case study, the presented method is applied to the fractional-order Chen-L\"u system as the drive-response dynamical system. Simulation results show a good performance of the proposed control approach in synchronizing the chaotic systems in presence of Gaussian noise

Risk Control for Synchronizing a New Economic Model

Risk analysis in control problems is a critical but often overlooked issue in this research area. The main goal of this analysis is to assess the reliability of designed controllers and their impact on applied systems. The chaotic behavior of fractional-order economical systems has been extensively investigated in previous studies, leading to advancements in such systems. However, this chaotic behavior poses unpredictable risks to the economic system. This paper specifically investigates the reliability and risk analysis of chaotic fractional-order systems synchronization. Furthermore, we present a technique as a new mechanism to evaluate controller performance in the presence of obvious effects. Through a series of simulation studies, the reliability and risk associated with the proposed controllers are illustrated. Ultimately, we show that the suggested technique effectively reduces the risks associated with designed controllers