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

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. (c) 2021 ISA. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper proposes a new fractional order integral terminal sliding mode control algorithm for the stabilization and synchronization of FO chaotic/hyper-chaotic systems. A novel double hyperbolic functions based uncertainty estimator is developed to estimate and mitigate unknown uncertainties. The presented control techniques incorporate a double hyperbolic reaching law to achieve convergence of system states and tracking errors. Examples and comparative analysis are provided to validate the proposed methodologies.