Control and synchronization of fractional‐order chaotic satellite systems using feedback and adaptive control techniques

Abstract

In this article, we present the basic concepts of fractional calculus and control and synchronization of fractional-order chaotic satellite system . Existence and uniqueness solutions of fractional-order satellite system are discussed and local stability of the system at the equilibrium points are studied. The lowest dimension of chaotic attractor of satellite system is 2.88 which is obtained through utilization of the fractional dynamics and computational simulation. Lyapunov exponents and bifurcation diagrams are drawn to measure the existence of chaos in the system. Feedback control method for chaos control in the fractional-order satellite system is achieved. Synchronization of two identical noninteger order chaotic satellite systems are achieved through adaptive control methodology.

Chaotic Dynamics and Chaos Control in a Fractional-Order Satellite Model and Its Time-Delay Counterpart

“…Theorem 1 (see [47]). If the nonlinear function θ(t, ξ(t), ξ(t − τ)) ∈ C([0, T], R n ) is Lipschitz continuous, then there exists a unique and continuous solution for general system (18).…”

“…erefore, chaotic dynamics were reported from natural phenomena arising from ecological, economical, physical, and engineering models [13][14][15][16]. Moreover, chaotic dynamics in engineering models involving fractional derivatives were reported in [17][18][19][20].…”

“…Moreover, in [41], Khan and Kumar reported some conditions for chaos synchronization in the IOS system with time delay. Furthermore, a fractional-order version of the IOS system, namely, the fractional-order satellite (FOS) model, was studied by Kumar et al [18].…”

Stability Analysis of Chaotic New Hamiltonian System Based on Henon-Heiles Model Using Adaptive Controlled Hybrid Projective Synchronization

“…In recent years, chaos synchronization of chaotic systems using various control techniques has become a fascinating and engaging area of study for the researchers and scientists. Many significant techniques are introduced and studied to control [22,2,8] and synchronization [24,12,25,9,10,17,3,7,11] of chaos occurring in dynamical systems.…”

“…Specifically, Hubler [6] in 1989 firstly introduced adaptive control method (ACM) in chaotic systems. Since then, many researches have been conducted using ACM [13,8,10,11]. Keeping the above discussions in view, our primal aim in this paper is to study hybrid projective synchronization (HPS) among identical newly described Hamiltonian chaotic systems [27] based on Hénon-Heiles model by ACM.…”