This research presents a new fractional-order discrete-time susceptible-infected-recovered (SIR) epidemic model with vaccination. The dynamical behavior of the suggested model is examined analytically and numerically. Through using phase attractors, bifurcation diagrams, maximum Lyapunov exponent and the 0−1 test, it is verified that the newly introduced fractional discrete SIR epidemic model vaccination with both commensurate and incommensurate fractional orders has chaotic behavior. The discrete fractional model gives more complex dynamics for incommensurate fractional orders compared to commensurate fractional orders. The reasonable range of commensurate fractional orders is between $\gamma$ = 0.8712 and $\gamma$ = 1, while the reasonable range of incommensurate fractional orders is between ${\gamma }_2$ = 0.77 and ${\gamma }_2$ = 1. Furthermore, the complexity analysis is performed using approximate entropy ($ApEn$) and $C_0$ complexity to confirm the existence of chaos. Finally, simulations were carried out on MATLAB to verify the efficacy of the given findings.

This paper proposes a novel neural adaptive fixed-time control approach for the attitude stabilization and vibration suppression of flexible spacecraft. First, the neural network (NN) was introduced to identify the lumped unknown term involving uncertain inertia, external disturbance, torque saturation, and elastic vibrations. Then, the proposed controller was synthesized by embedding the NN compensation into the fixed-time backstepping control framework. Lyapunov analysis showed that the proposed controller guaranteed the stabilization of attitude and angular velocity to the adjustable small neighborhoods of zero in fixed time. The proposed controller is not only robust against uncertain inertia and external disturbance, but also insensitive to elastic vibrations of the flexible appendages. At last, the excellent stabilization performance and good vibration suppression capability of the proposed control approach were verified through simulations and detailed comparisons.

This article addresses the challenging problem of fixed-time output-constrained synchronization for master–slave chaotic financial systems with unknown parameters and perturbations. A fixed-time neural adaptive control approach is originally proposed with the aid of the barrier Lyapunov function (BLF) and neural network (NN) identification. The BLF is introduced to preserve the synchronization errors always within the predefined output constraints. The NN is adopted to identify the compound unknown item in the synchronization error system. Unlike the conventional NN identification, the concept of indirect NN identification is employed, and only a single adaptive learning parameter is required to be adjusted online. According to the stability argument, the proposed controller can ensure that all error variables in the closed-loop system regulate to the minor residual sets around zero in fixed time. Finally, simulations and comparisons are conducted to verify the efficiency and benefits of the proposed control strategy. It can be concluded from the simulation results that the proposed fixed-time neural adaptive controller is capable of achieving better synchronization performance than the compared linear feedback controller.

In this article, a neural integral sliding mode control strategy is presented for the finite-time fault-tolerant attitude tracking of rigid spacecraft subject to unknown inertia and disturbances. First, an integral sliding mode controller was developed by originally constructing a novel integral sliding mode surface to avoid the singularity problem. Then, the neural network (NN) was embedded into the integral sliding mode controller to compensate the lumped uncertainty and replace the robust switching term. In this way, the chattering phenomenon was significantly suppressed. Particularly, the mechanism of indirect neural approximation was introduced through inequality relaxation. Benefiting from this design, only a single learning parameter was required to be adjusted online, and the computation burden of the proposed controller was extremely reduced. The stability argument showed that the proposed controller could guarantee that the attitude and angular velocity tracking errors were regulated to the minor residual sets around zero in a finite time. It was noteworthy that the proposed controller was not only strongly robust against unknown inertia and disturbances, but also highly insensitive to actuator faults. Finally, the effectiveness and advantages of the proposed control strategy were validated using simulations and comparisons.