Hyperbolic uncertainty estimator based fractional order sliding mode control framework for uncertain fractional order chaos stabilization and synchronization

• Published in: ISA transactions 2022-04, Vol.123, p.76-86
• Main Author: Deepika, Deepika
• Format: Article
• Language: English
• Subjects: Chaotic/hyper-chaotic systems; Fractional calculus; Sliding mode control (SMC); Uncertainties; Uncertainty and disturbance estimator (UDE)
• ISSN: 0019-0578; 1879-2022
• DOI: 10.1016/j.isatra.2021.05.036

This paper formulates a new fractional order (FO) integral terminal sliding mode control algorithms for the stabilization and synchronization of N-dimensional FO chaotic/hyper-chaotic systems, which are perturbed with unknown uncertainties. In order to render closed loop robustness, a novel efficient double hyperbolic functions based uncertainty estimator is developed for the estimation and mitigation of unknown uncertainties. Moreover, a double hyperbolic reaching law comprising of tangent hyperbolic and inverse sine hyperbolic functions is incorporated in the presented control techniques for the practical convergence of various chaotic system states and tracking errors to infinitesimally close to equilibrium. Examples such as FO Lu, FO Chen and FO Lorenz systems are taken to investigate robustness, finite time convergence, tracking accuracy and closed loop stability properties of the devised methodologies. Last but not least, comparative analysis is also carried out between the proposed and prior control techniques through various time domain performances such as settling time, error indices and measure of control energy. •Novel fractional order double hyperbolic integral terminal sliding mode control is developed.•Control of uncertain fractional order chaos is dealt.•Novel hyperbolic uncertainty estimator is also developed for estimation of unknown uncertainties.•Three examples are also validated along with comparative analysis with respect to prior techniques.