Synthesis of Covert Actuator Attackers for Free

In this paper, we shall formulate and address a problem of covert actuator attacker synthesis for cyber-physical systems that are modelled by discrete-event systems. We assume the actuator attacker partially observes the execution of the closed-loop system and is able to modify each control command issued by the supervisor on a specified attackable subset of controllable events. We provide straightforward but in general exponential-time reductions, due to the use of subset construction procedure, from the covert actuator attacker synthesis problems to the Ramadge-Wonham supervisor synthesis problems. It then follows that it is possible to use the many techniques and tools already developed for solving the supervisor synthesis problem to solve the covert actuator attacker synthesis problem for free. In particular, we show that, if the attacker cannot attack unobservable events to the supervisor, then the reductions can be carried out in polynomial time. We also provide a brief discussion on some other conditions under which the exponential blowup in state size can be avoided. Finally, we show how the reduction based synthesis procedure can be extended for the synthesis of successful covert actuator attackers that also eavesdrop the control commands issued by the supervisor.Comment: The paper has been accepted for the journal Discrete Event Dynamic System

The Global Attractors For The Higher-order Kirchhoff-type Equation With Nonlinear Strongly Damped Term

The paper studies the longtime behavior of solutions to the initial boundary value problem for a class of Higher-order Kirchhoff models: For strong nonlinear damping and , we make assumptions (H1)-(H3). are nonlinear function specified later , we make assumptions (G1)-(G3). Under of the proper assume, the main results are existence and uniqueness of the solution are proved , and deal with the global attractors in natural energy space

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Exponential attractor for the Higher-order Kirchhoff-type equation with nonlinear strongly damped term

We investigate the existence of exponential attractor for the Higher-order Kirchhoff-type equation with nonlinear strongly damped term: .For strong nonlinear damping σ(s) and φ(s) ,we assumptions .Under of the proper assume H1-H3, we first prove the squeezing property of the nonlinear semigroup associated with this equation, then the existence of exponential attractor is proved