Single‐channel predefined‐time synchronisation of chaotic systems

Abstract

Chaos has attracted the interest of the research community due to its applications in secure communication, and in the study of complex systems in physics, engineering and other applied sciences. In the particular case of secure communication, fast synchronisation is a requirement to avoid any loss of information at the initial stage, when the signalisation data is transmitted. With the aim of providing fast and precise synchronisation, a novel algorithm is proposed in this paper, such that, by considering just one channel of communication, a dynamic observer synchronises with a chaotic system in predefined‐time. The proposal is based on the equivalent control concept of sliding mode theory, and the stability of the synchronisation is demonstrated in the Lyapunov framework. A simulation study is carried out to highlight the reliability of the proposed scheme.

Predefined‐time backstepping control for a nonlinear strict‐feedback system

“…The proposed algorithm (19) is directly studied on a high‐order nonlinear strict‐feedback system with disturbance in (8). It can be seen that system (8) is more general than the first‐order systems, the second‐order systems, or the high‐order chain of integrators in traditional predefined‐time control studies 5‐14,17,21 The proposed algorithm (19) always takes effect on t ≥ 0.…”

“…No unbounded term is involved when the time tends to T 1 compared with traditional predefined‐time methods 18‐20 If the initial output tracking error satisfies y (0) − y d (0) ≠ 0 and the time‐varying tuning function ρ (t) is selected as (14), then according to (26), the upper bound of settling time T 1 is also exactly the system settling time under the proposed algorithm (19), so T 1 is not conservatively estimated compared with traditional predefined‐time algorithms 3‐14 The only parameter in algorithm (19) is the predefined‐time T 1 .…”

“…On the basis of Lyapunov‐like conditions for ensuring dynamic systems to exhibit predefined‐time stability or predefined‐time boundedness, many predefined‐time controllers were designed for various systems, for example, nonlinear second‐order systems, 6‐8 nonholonomic systems, 9 chaotic systems, 10,11 rigid spacecrafts, 12 robotic manipulators 13,14 as well as first‐order and second‐order multi‐agent systems 15,16 . However, the predefined‐time controllers derived on the basis of Lyapunov analysis 3‐14 may provide conservative estimate of upper bounds of system convergence time, especially for high‐order systems. The real convergence time may be much smaller than the estimated upper bound.…”

Predefined-Time Modified Function Projective Synchronization for Multiscroll Chaotic Systems via Sliding Mode Control Technology

“…Additionally, in the process of secure communication, the designer expects the encoded message can be recovered within any sufficiently short time given in advance. It is necessary to consider the concept of predefined-time stability control technique, applying which an upper bound (sometimes the least upper bound) of convergence (settling) time is directly involved in the design of the controller as a preassigned tuning gain [17][18][19][20]. In chaotic secure communication, if the synchronization scheme is designed based on the above control technique, the encrypted message will be decrypted within a predetermined time which is independent of the initial state.…”

Predefined-Time Polynomial-Function-Based Synchronization of Chaotic Systems via a Novel Sliding Mode Control

“…On the other hand, synchronization time is another important indicator to measure the performance of the communication scheme since the encoded message cannot be recovered before the synchronisation is established. In the case of secure communication, fast synchronisation is required to avoid any loss of information at the initial stage [13]. Compared with asymptotic control, finite-time control has many advantages such as fast convergence, high accuracy and strong robustness.…”