This paper is concerned with stablization of hybrid differential equations by intermittent control based on delay observations. By M-matrix theory and intermittent control strategy, we establish a sufficient stability criterion on intermittent hybrid stochastic differential equations. Meantime, we show that hybrid differential equations can be stabilized by intermittent control based on delay observations if the delay time $ \tau $ is bounded by $ \tau^* $. Finally, an example is presented to illustrate our theory.

In this paper, we investigate stabilisation of hybrid stochastic systems with time-varying delay by feedback control based on discrete-time state and mode observations with a time delay. By constructing a proper Lyapunov functional, the $H_{\mathrm{\infty }}$, asymptotic and exponential stability of the controlled systems are studied in the pth moment sense for p>1. Meanwhile, we obtain the upper bound on the duration τ between two consecutive state and mode observations. At last, two numerical examples are illustrated to support our theoretical results.

This paper is concerned with the more general nonlinear stochastic Volterra integral equations with doubly singular kernels, whose singular points include both $s=t$ and $s=0$. We propose a Galerkin approximate scheme to solve the equation numerically, and we obtain the strong convergence rate for the Galerkin method in the mean square sense. The rate is $min\{2-2({\alpha }_1+{\beta }_1),1-2({\alpha }_2+{\beta }_2)\}$ (where ${\alpha }_1,{\alpha }_2,{\beta }_1,{\beta }_2$ are positive numbers satisfying $0<{\alpha }_1+{\beta }_1<1$, $0<{\alpha }_2+{\beta }_2<\frac{1}{2}$), which improves the results of some numerical schemes for the stochastic Volterra integral equations with regular or weakly singular kernels. Moreover, numerical examples are given to support the theoretical result and explain the priority of the Galerkin method.

The wave of intelligent manufacturing has swept the world, and intelligent manufacturing has realized the interconnection of the physical world and the information world. With the deep integration of intelligent manufacturing, cognitive computing and cognitive science, the manufacturing industry presents a new manufacturing model, which is called cognitive manufacturing. Cognitive manufacturing, as the evolution stage of intelligent manufacturing, endows industrial manufacturing system with perception and judgment ability. In addition, it enables the machine to realize self-adaptation, self-organization and self-decision-making based on cognition, thus completing accurate execution. But the manufacturing system cannot be entirely controlled by machines without the involvement of human. Based on the new generation of intelligent manufacturing for human-information-physical system and human-computer synthetic-intelligent system. This paper compares and extends the relevant technical models of intelligent manufacturing and cognitive manufacturing. Furthermore, it presents a framework that integrates the cognitive ability of human and machine, putting forward a cognitive manufacturing system architecture of human-machine collaborative cognition, called Human-in-Cognition Manufacturing-Loop (HCML). Additionally, the connotation, key implementation technology and future development trend of the system are discussed in details, and the role of artificial intelligence in the system are introduced.