Theoretical and practical applications of fuzzy fractional integral sliding mode control for fractional-order dynamical system

Abstract

This paper proposes a fuzzy fractional integral sliding mode control for synchronizing fractionalorder dynamical systems with mismatched fractional orders. It is applied to synchronize the fractional-order modified coupled dynamos chaotic systems. Synchronization between two identical fractional order, different fractional orders, integer order and fractional-order modified coupled dynamos chaotic systems have been demonstrated. For practical applications, these derived synchronized fractional-order chaotic systems are utilized to develop a novel cryptosystem for an image encryption and decryption. Numerical simulations are provided to verify the significance of theoretical analysis.

A Review on Variable-Order Fractional Differential Equations: Mathematical Foundations, Physical Models, Numerical Methods and Applications

“…Dynamic-order fractional dynamic system. In recent years, the usage of fractional order dynamical systems play a vital role in real-world applications, including for examples, the affine cipher using date of birth fuzzy [77], fractional integral sliding mode control [10], fractional order modified Duffing systems [39], fractional order King Cobra chaotic system [75], digital cryptography [74], and authenticated encryption scheme [76]. Hence, we investigate the fractional order dynamical systems which have great application potentials in real-world engineering fields.…”

Robust Control of Disturbed Fractional‐Order Economical Chaotic Systems with Uncertain Parameters

“…, and φ 4 (•) can have different dimensions, and it is easy to know that the uncertain terms considered in system (19) stand for a large range of system uncertainties. us, the economical model considered in some recent literature, for example, [10,16,18,[37][38][39], is a special case of our model (19). Our objective here is to design a proper controller u i (t) such that the state vector ζ(t) could track the desired signal…”

Adaptive Neural Network Control of Chaotic Fractional-Order Permanent Magnet Synchronous Motors Using Backstepping Technique

“…Therefore, such oscillations should be effectively suppressed. For this reason, various methods have been developed to stabilize non-linear chaotic systems, in which fractional order chaos control has also been focused, such as OGY type [25], feedback type [26][27][28], dynamic surface type [29], sliding mode type [30][31][32][33], backstepping type [34,35], etc.…”