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In this article, a fixed-time adaptive fault-tolerant control approach is presented for the attitude tracking of rigid spacecraft subject to inertia uncertainties, external disturbances, and actuator faults. The designed controller is developed as a combination of the fixed-time integral sliding mode control and parametric adaptation technique. The fixed-time integral sliding mode controller has no singularity problem naturally by constructing a novel integral sliding mode surface based on the bi-limit homogeneous method. Moreover, the parametric adaptation technique is incorporated to estimate the total uncertainty indirectly. Benefiting from this development, the designed controller is smooth with no obvious chattering phenomenon and does not require any information on the upper bound of the total uncertainty. The attitude and angular velocity tracking errors under the designed controller can regulate to the minor fields about zero in fixed time. A remarkable feature of the designed controller is that it is not only robust against inertia uncertainties and external disturbances, but also insensitive to multiple types of actuator faults. Finally, simulation results show the effectiveness and merits of the presented control approach. • Fixed-time adaptive fault-tolerant control approach for attitude tracking of rigid spacecraft. • Combination of fixed-time integral sliding mode control and parametric adaptation technique. • Novel integral sliding mode surface based on bi-limit homogeneous method eliminates singularity problem. • Smooth controller with no chattering phenomenon, regulates tracking errors to minor fields around zero in fixed time. • Robust against inertia uncertainties and external disturbances. [ABSTRACT FROM AUTHOR]

This paper focuses primarily on the predefined-time stability for a class of fixed-time stable systems, with the least upper bound of the settling time as an explicit parameter. It is mathematically proved that the systems under consideration herein can reach stability within any preassigned time, rather than the overestimation of convergence time found in previous fixed-time stability. Comparisons show that our studied system is more general than some classical ones, and that many existing results can be derived. As an application of the exposed stability analysis, static and adaptive predefined-time control algorithms are designed to study the average consensus problem for nonlinear leaderless multi-agent systems. Particularly, the adaptive control protocol guarantees predefined-time consensus without requiring the global topology information of the systems under consideration. Numerical simulations are provided throughout to support our theoretical results. [ABSTRACT FROM AUTHOR]

In today's sophisticated world, where financial systems play an increasingly important role, the application of controllers through management strategies is of crucial importance, given their vital role. An analysis of the synchronization of economic systems can provide a valuable insight into the financial synchronous development of different countries or regions around the world. In this paper, an adaptive fixed-time control strategy is presented for the function projective synchronization of drive-response hyperchaotic economic systems with unknown parameters and external perturbations. The developed controller is constructed by combining the fixed-time control approach and parametric adaptation technique. Specifically, the adaptive adjusting mechanisms are designed to estimate the unknown parameters and external perturbations, respectively. Stability investigation shows that the function projective synchronization errors under the developed controller can stabilize to the minor fields about zero in fixed time. A key feature of the developed controller is its high insensitive to unknown parameters and strong robustness against external perturbations. Finally, the effectiveness and merits of the presented control strategy are examined by simulation scenarios. • Introducing a novel adjustable fixed-time control strategy • Development of a robust controller by combining a fixed-time control approach with a parametric adaptation technique • Design of an adaptive adjusting mechanism to robust estimation of unknown time-varying parameters and external perturbations [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]