Secure Control Of Cyber-Physical Systems Under Denial-of-Service Attacks

Recent years,as the popular of the communication and network technology in cyber-physical systems,the fragility of cyber-physical systems is more and more obvious and the cases that cyber-physical systems were attacked by malicious attackers become much more.Therefore,the security of cyber-physical systems is drawing more attention.In this paper,we study how can the attacked systems maintain the admissible system state at admissible level from the secure control point after the system performance degrade which is caused by the malicious adversaries by DoS attacks.The main contributions can be summarized into following three parts:1.We first model the cyber-physical systems under Denial-of-Service attacks as an singular system with time-varying delay which is caused by DoS attacks,and then we study the influence of the attacks on the stability of the cyber-physical systems by the linear matrix inequality.We transform the singular system with time-varying delay into a neutral system with time-varying delay.After that we construct a new LaypunovKrasovkii functional,and then obtain a delay-dependent stability criterion with better conservative by the Wirtinger-based integral inequality.We can derive the upper bound the time-varying delay from the stability criterion,and at the same time we regard the upper bound of the time varying delay as an index which can measure the maximum attack-tolerance of the cyber-physical systems.Finally,by the numerical example we demonstrate the effectiveness of the algorithm.2.We design a state feedback controller of the cyber-physical systems under DoS attacks.The system performance will degrade severely after the system is attacked by the malicious adversaries.In this part we design an state feedback controller to guarantee the system performance can maintain at admissible level.3.Now most researchers model the DoS attacks as an simple Bernoulli data dropout model.In this part,we give a new model of DoS attacks according to DoS attacks process which can characterize the influence of DoS attacks more precisely.Then,we model the cyber-physical systems under DoS attacks as an dynamic Stackelberg game with closed-loop information structure.In this Stackelberg game we assume the controller as leader and attacker as follower.We define the cost function of these two players according to their realistic energy request,respectively.After giving the cost function of the players,we obtain the necessary condition of the existence of the optimal solution of players by the improved minimum principle and get the sufficient condition by focal times theory.Finally we can get the optimal control strategy of the cyber-physical systems under DoS attacks.