Robust observer-based stabilizer for perturbed nonlinear complex financial systems with market confidence and ethics risks by finite-time integral sliding mode control

In this paper, the finite-time stabilization of nonlinear chaotic financial system (NCFS) by considering market confidence and ethics risk has been investigated. In order to address the stabilization problem of NCFS in the presence of model uncertainties and external disturbances, a robust adaptive finite-time stabilizer has been designed based on a finite-time disturbance observer (FTDO). By utilization of the proposed FTDO, the exact estimation of imposed perturbations is achieved in the sense of finite-time stability, such that a better transient performance can be attained compared with Lyapunov parameter estimation methods. Furthermore, on the basis of proposed FTDO, the continuous control input is developed, so that it avoids the possible chattering effects, and as a result, a free-chattering terminal sliding mode control is achieved in order to drive the state errors of the financial system toward zero in finite time. The investigated adaptive observer-based control strategy can keep the original structure of the system and can be implemented to stabilize other chaotic systems including dynamical economic systems. Finally, via some numerical simulations, the efficiency and reliability of the proposed approach has been illustrated.

Automated summary

This paper investigates the finite-time stabilization of nonlinear chaotic financial system (NCFS) by designing a robust adaptive finite-time stabilizer based on a finite-time disturbance observer (FTDO). The FTDO allows for exact estimation of perturbations, leading to better transient performance compared to other methods. A continuous control input is developed based on the FTDO to avoid chattering effects and achieve a free-chattering terminal sliding mode control to drive state errors of the financial system towards zero in finite time. The proposed adaptive observer-based control strategy preserves the original structure of the system and can be applied to stabilize other chaotic systems, including dynamic economic systems. Through numerical simulations, the efficiency and reliability of the approach have been demonstrated.