This article is concerned with the problem of the stealth attack strategy design for T–S fuzzy cyber–physical systems (CPSs). Virtual systems that reflect the attacker’s target are established, in which the parameter matrices of virtual systems rely on the different regions where the premise variables (PVs) of the T–S fuzzy CPS and the piecewise fuzzy observer are located at different past instants. Unlike the existing attack policies, a piecewise attack strategy is designed based on the established virtual systems, while the existing ones are required to be nonpiecewise. Furthermore, the $H_{-}/H_{\infty }$ scheme is applied to maximize the impact of the attack on the estimation performance (EP) of the observer while avoiding detected by the detector. A simulation example is applied to verify the effectiveness and advantages of the designed attack scheme.

This article studies the problem of the optimal stealth attack strategy design for linear cyber-physical systems (CPSs). Virtual systems that reflect the attacker's target are constructed, and a linear attack model with varying gains is designed based on the virtual models. Unlike the existing optimal stealth attack strategies that are designed based on sufficient conditions, necessary and sufficient conditions are, respectively, established to achieve the optimal attack performance while maintaining stealth in virtue of the solvability of certain coupled recursive Riccati difference equations (RDEs). Under those conditions, an optimal stealth attack strategy is constructed by an offline algorithm. A simulation example is applied to verify the effectiveness of the presented technical scheme.

This paper aims at the phenomenon of the fractured rock column in underground engineering which is prone to collapse when subjected to ground pressure. Uniaxial compression test and particle flow code (PFC2D) are used to analyze the influence of crack dip angle on the mechanical properties, crack propagation, and the failure mode of red sandstone. From the results, it is observed that the stress–strain curve of the precracked red sandstone can be divided into five stages, and there is a critical stress value in the stage of accelerated crack propagation and unstable fracture of the rock sample. Further, the peak strength, maximum strain, and the elastic modulus of the precracked red sandstone increase with the increase of crack dip angle, and the ultimate failure mode of rock sample changes from the “ladder” type failure to slope uneven failure. Furthermore, from PFC2D simulation, it is found that the tensile microcracks contribute more towards the failure of rock samples than the shear cracks. The contact force chain is very weak at the places where the precracks and macroshear planes are formed. This indicates that the original contact force is weakened due to particle fracture. Therefore, the bearing capacity of the precracked rock samples decreases with the increase in load. From the simulation results, it is found that the displacement at the shear plane of the rock sample is large, and the shear dilatation occurs. With the increase in load, the specimen falls off and is ejected. This is due to the weakening of the contact force between the internal particles. Thereafter, it fractures to produce microcracks, which gradually converge, thus providing a prerequisite for the transformation of elastic strain energy into kinetic energy.