Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

Abstract

In this paper, we use sliding mode control integrated with an interval type-2 fuzzy system for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the Sliding Mode Control (SMC), an interval fuzzy type-2 logic controller is used. In addition, an adaptive interval type-2 fuzzy inference approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic system. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy approximators. The stability analysis for the proposed control scheme is provided, and simulation results compare the performance of interval type-2 fuzzy and type-1 fuzzy con-M. Roopaei ( ) · trollers to verify the effectiveness of the proposed method.

Generalized predictive control based on fuzzy sliding-mode control strategy and fuzzy PI controller for synchronization of uncertain chaotic systems

“…The imperfect performance of FSMC is caused by a problem called control chattering. There are many attempts to reduce the chattering impact of FSMC [16] [14], but these improvements make the use of this kind of controller more complex. Fuzzy PI controller is better in the sense that its results are achieved without using any improvement.…”

“…This kind of controllers needs improvements, and for each problem, a specific algorithm must be designed. In many cases, advanced control methods lend a helping hand to classical control approaches in order to fix some problems [14]- [16]. The outcome of this combination is new controllers called hybrid or complex controllers, which are more flexible than classical control approaches, but less flexible than advanced control methods.…”

Fuzzy modeling for chaotic systems via interval type-2 T–S fuzzy model with parametric uncertainty

“…In recent years, type-2 fuzzy logic systems have received much attention from the control community as a powerful tool for nonlinear control. Researchers in [22][23][24][25][26][27] have proposed a type-2 fuzzy logic system (FLS) to deal with uncertain grades of membership using type-2 fuzzy sets. Melin and et al [28] have designed optimal controllers for autonomous mobile robots.…”

Projective Synchronization Scheme Based on Fuzzy Controller for Uncertain Multivariable Chaotic Systems

“…A Lyapunov approach is adopted to carry out the parameter adaptation design, the convergence and the stability analysis involved in the proposed synchronization system. Compared to works in [19,24,29,[36][37][38][46][47][48], the main contributions of this chapter lie in the following:…”