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Irregular and complex behavior in the financial system can disrupt stability and smooth economic growth. It causes randomness within the system, generating chaos; hindering synchronization behaviour. Achieving smooth and rapid synchronization between two coupled hyperchaotic finance (HF) systems with lessened fluctuation of input and output signals is vital for continuing financial stability and fostering economic growth, a challenge addressed in this article. The paper proposes a novel time-efficient nonlinear control (TENLC) technique and investigates HF systems synchronization using the drive-response system (DRS) arrangement. The proposed TENLC strategy realizes fast and smooth synchronization behaviour between two coupled HF systems, reducing closed-loop state-variable trajectory oscillations. The controller is designed to retain the nonlinear components within the closed-loop system and does not depend on the system's parameters, simplifying the design and analysis process. The Lyapunov stability technique confirms the closed-loop's global stability at the origin. Proofs of mathematical analysis and computer-based simulation results validate the theoretical findings, showing that the presented TENLC strategy converges the state error trajectories to zero in a short transient time with lessened fluctuations for all signals. The comparative computer-based simulation analysis confirms that the presented TENLC approach outperforms other synchronization control techniques. [ABSTRACT FROM AUTHOR]

ABSTRACTThe inherent randomness in economic factors causes complex and irregular behaviour that affects financial system stability and economic growth. Such chaotic behaviour can make it difficult to synchronize financial systems. The chaotic finance system synchronization precision maintains financial stability and economic growth. In this paper, the controller design procedure assumes that the financial system is exposed to unknown bounded exogenous disturbances and model uncertainties. This research proposes a novel direct adaptive control strategy that achieves robust synchronization of two identical four-dimensional finance chaotic (FDFC) systems. The proposed controller establishes a faster, smoother synchronization error vector convergence to zero. The controller design procedure does not eliminate the closed-loop's nonlinear terms and is independent of the financial system parameters. These controller's attributes accomplish the closed-loop robust performance. Further, this controller uses real-time estimates of unknown model uncertainties and bounds to compensate for unknown exogenous disturbances. Computer simulation results and proofs of theoretical analysis based on the Lyapunov stability theory confirm that the proposed control technique compels the error vector trajectories to the origin in a short transient time with less active oscillations for all signals. The paper includes comparative computer simulations for verifying the theoretical findings.

The inherent randomness in economic factors causes complex and irregular behaviour that affects financial system stability and economic growth. Such chaotic behaviour can make it difficult to synchronize financial systems. The chaotic finance system synchronization precision maintains financial stability and economic growth. In this paper, the controller design procedure assumes that the financial system is exposed to unknown bounded exogenous disturbances and model uncertainties. This research proposes a novel direct adaptive control strategy that achieves robust synchronization of two identical four-dimensional finance chaotic (FDFC) systems. The proposed controller establishes a faster, smoother synchronization error vector convergence to zero. The controller design procedure does not eliminate the closed-loop's nonlinear terms and is independent of the financial system parameters. These controller's attributes accomplish the closed-loop robust performance. Further, this controller uses real-time estimates of unknown model uncertainties and bounds to compensate for unknown exogenous disturbances. Computer simulation results and proofs of theoretical analysis based on the Lyapunov stability theory confirm that the proposed control technique compels the error vector trajectories to the origin in a short transient time with less active oscillations for all signals. The paper includes comparative computer simulations for verifying the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper considers the local stabilization problem for a hyperchaotic finance system by using a time-delayed feedback controller based on discrete-time observations. The quadratic system theory is employed to represent the nonlinear finance system and a piecewise augmented discontinuous Lyapunov-Krasovskii functional is constructed to analyze the stability of the closed-loop system. By further incorporating some advanced integral inequalities, a stabilization criterion is proposed by means of the feasibility of a set of linear matrix inequalities under which the hyperchaotic finance system can be asymptotically stabilized for any initial condition satisfying certain constraint. As the by-product, a simplified criterion is also obtained for the case without time delay. Moreover, the optimization problems with respect to the domain of attraction are specially discussed, which are transformed into the minimization problems subject to linear matrix inequalities. Finally, numerical simulations are provided to illustrate the effectiveness of the derived results.

This paper considers the $ H_\infty $ control problem for a hyperchaotic system with energy-bounded disturbance under the delayed feedback controller. Using the quadratic system theory, an augmented Lyapunov functional, some integral inequalities and rigorous mathematical derivations, a sufficient condition is first established by using linear matrix inequalities under which the closed-loop system can achieve some desirable performances including the boundedness, the $ H_\infty $ performance and the asymptotic stability. Subsequently, several convex optimization problems are formulated to obtain the optimal performance indices. Finally, numerical simulations are presented to illustrate the effectiveness of the obtained results.

This paper considers the H ∞ control problem for a hyperchaotic system with energy-bounded disturbance under the delayed feedback controller. Using the quadratic system theory, an augmented Lyapunov functional, some integral inequalities and rigorous mathematical derivations, a sufficient condition is first established by using linear matrix inequalities under which the closed-loop system can achieve some desirable performances including the boundedness, the H ∞ performance and the asymptotic stability. Subsequently, several convex optimization problems are formulated to obtain the optimal performance indices. Finally, numerical simulations are presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: This work presents an accurate algorithm for solving the chaotic control (optimal and adaptive control) problems of hyperchaotic finance system. A modification of the spectral homotopy analysis method technique is proposed for solving the hyperchaotic finance system and the extreme conditions obtained from the Pontryagin minimum principle. The proposed method is based on implementing the spectral homotopy analysis method on a sequence of multiple intervals thereby increasing its radius of convergence to yield highly accurate method that is referred to as the piecewise spectral homotopy analysis method. Finally, piecewise spectral homotopy analysis method is used to solve the problem of Lyapunov stabilization of the hyperchaotic finance system. Numerical simulations are given to illustrate and verify effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]