A novel fuzzy mixed H2/H∞ optimal controller for hyperchaotic financial systems

Abstract

Due to the importance of consumed control energy in financial systems, employing an optimal controller for these systems could be beneficial. Also, the presence of disturbances is undeniable in most of these systems. Hence, applying optimal mixed H2/H∞ control, which posses the positive features of both H∞ and H2 control, could bring up luminous results for these systems. However, in the literature, no attempt has been made to design this type of controller for chaotic financial systems. This issue motivated the current study. In this study, we present a type-2 fuzzy-based optimal mixed H2/H∞ control for a hyperchaotic financial system. In this approach, H∞ attenuates the effect of uncertainties and through H2 the consumed control energy is minimized. Also, since the proposed controller is equipped with a type-2 fuzzy observer, it can easily handle uncertainties and unknown functions. Via Lyapunov theorem, it is confirmed that all signals in the system are bounded. In the numerical simulation, firstly, a hyperchaotic financial system with coexisting attractors is investigated. The proposed controller is then applied to the financial system, and the proposed technique’s performance is assessed. Numerical simulations clearly confirm the theoretical claims about the effectiveness of the proposed methodology