Robust synchronization of four-dimensional chaotic finance systems with unknown parametric uncertainties

• Published in: Automatika Vol. 65; no. 1; pp. 217 - 234
• Main Authors: Shafiq, Muhammad, Ahmad, Israr
• Format: Journal Article
• Language: English
• Published: Ljubljana Taylor & Francis Ltd 02.01.2024; Taylor & Francis Group
• Subjects: Adaptive control; adaptive controller; chaos synchronization; Chaos theory; Closed loops; Computer simulation; Control systems design; Controllers; Disturbances; Economic development; Economic factors; Economic growth; Finance; Hyperchaotic finance system; Lyapunov stability theory; Robust control; Stability analysis; Synchronism; Systems stability; Uncertainty
• ISSN: 0005-1144; 1848-3380
• DOI: 10.1080/00051144.2023.2295204

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.