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Despite the existence of promising methods for controlling complex systems, there is still a need for further advancement in controlling and synchronizing fractional systems. This is even more monumental when it comes to practical applications with faults and physical constraints present in their control actuators. To address this issue, the current study proposes a new control technique that utilizes a recurrent neural network-based finite-time super-twisting algorithm for fractional-order systems. The proposed controller is enhanced with an intelligent observer to account for faults and limitations that may be present in the control actuator of the fractional-order systems. The proposed method allows the system to be regulated even in the presence of control input constraints and faults. Moreover, the proposed technique guarantees that the closed-loop system will converge in a finite amount of time. The control design is explained in detail, and its finite-time stability is proven. To evaluate the performance of the controller, we applied it to two different fractional-order systems that were subject to control input limitations and faults. The outcomes of the proposed approach were then compared with those obtained using a state-of-the-art technique for fractional-order systems to further validate the effectiveness of our proposed approach. • A controller proposed for fractional systems using recurrent neural network-based finite-time super-twisting algorithm. • Controller enhanced with intelligent observer to handle faults and limitations in control actuators. • Proposed method enables system regulation despite control input constraints and faults. • Guaranteed finite-time convergence of closed-loop system. • Performance evaluated on two fractional-order systems, outperforming state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

• Spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. • A new chattering-free robust sliding mode controller with a neural network observer is proposed. • Based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. • Numerical results demonstrate the chattering-free and effective performance of the proposed control method. An immense body of research has focused on chaotic systems, mainly because of their interesting applications in a wide variety of fields. A comprehensive understanding and synchronization of chaotic systems play pivotal roles in practical applications. To this end, the present study investigates a multi-stable fractional-order chaotic system. Firstly, some dynamical features of the system are described, and the chaotic behaviour of the system is verified. Then, both spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. Besides, the combination of a new chattering-free robust sliding mode controller with a neural network observer is proposed for the synchronization of the fractional-order system. With the neural network estimator, unknown functions of the system are obtained, and the effects of disturbances are completely taken into account. Also, based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. Lastly, the proposed control technique is applied to the fractional-order system. Numerical results demonstrate the chattering-free and effective performance of the proposed control method for uncertain systems in the presence of unknown time-varying external disturbances. [ABSTRACT FROM AUTHOR]

In this article, a fixed-time neural control methodology is presented for the output-constrained synchronization of second-order chaotic systems with unknown parameters and perturbations. The presented controller is synthesized under the fixed-time backstepping control framework. In the virtual control law design, the barrier Lyapunov function (BLF) is introduced to tackle the output constraints. In the actual control law design, the neural network (NN) is embedded to identify the total unknown item. Stability argument shows that the resultant closed-loop system is practically fixed-time stable. A distinctive feature of the presented controller is that it is capable of stabilizing the synchronization errors in fixed time while ensuring the output constraints can always be satisfied simultaneously. The efficiency and superiority of the presented control methodology are examined through two simulated examples. • A fixed-time neural control methodology • Output-constrained synchronization of second-order chaotic systems • Fixed-time backstepping control framework [ABSTRACT FROM AUTHOR]

It is well known that the satellite attitude motion exhibits the chaotic phenomenon. This article addresses the challenging problem of chaotic attitude synchronization and anti-synchronization for master-slave satellites under unknown moments of inertia and disturbance torques. First, a fixed-time adaptive synchronization controller is designed by combining the fixed-time control technique and adaptive control technique. The parametric adaptation laws are adopted to identify the unknown parameters in the synchronization error system. Benefiting from the adaptive identifications, the proposed controller is highly robust to unknown moments of inertia and disturbance torques. The practical fixed-time stability of the resulting closed-loop system is strictly achieved. The proposed controller can guarantee all error variables in the closed-loop system regulate to the small residual sets around zero in fixed time. Then, a fixed-time adaptive anti-synchronization controller is developed in a similar way. Finally, simulations studies are conducted to demonstrate the effectiveness and excellent control performance of the proposed controllers. [ABSTRACT FROM AUTHOR]