| With the development of computer technology,communication technology,and control technology,people are no longer satisfied with the expansion of existing system functions,but they put forward new demands for informationization and intelligence of various embedded systems.Under the guidance of these demands,cyber-physical system(CPS)comes into being.CPS is a novel intelligent system,and it realizes the deep integration of computation,communication,and control functions.At present,CPS has been widely applied in security-critical fields such as national defense,smart grids,and aerospace,which is vulnerable to cyber attacks,once being attacked,CPS functions may be damaged or fail,which will further result in security accidents.Therefore,its trustworthiness faces serious challenges.To evaluate CPS trustworthiness,generalized stochastic Petri Nets(GSPN)are utilized to the modeling and analytics of the trustworthiness of CPS according to the characteristics of CPS,and the initial trustworthiness of CPS can be obtained;To study the evolution process of CPS trustworthiness,nonlinear dynamics theories and methods are introduced to establish the propagation model of malware in CPS,and the evolution mechanism of CPS trustworthiness is revealed by studying its dynamic behaviors.The main research contents of this thesis are as follow s:(1)Based on the system trustworthiness theory,the concept of CPS trustworthiness is expounded,and CPS trustworthiness measurement method and steps are proposed.First,according to characteristics of CPS and security threats it faces,CPS trustworthiness metrics are established,and the CPS trustworthiness model is constructed with the use of GSPN.Second,according to the isomorphism of GSPN and continuous time Markov chain,the reachability diagram and isomorphism Markov chain of the model can be obtained;Finally,the steady-state probability and transient probability of Markov chain are calculated to obtain values of trustworthiness metrics,and the trustworthiness of CPS is quantitatively evaluated,which lays a foundation for the analysis of the CPS trustworthiness evolution mechanism and other subsequent works.(2)A malware propagation model with two infection rates is constructed,and a CPS trustworthiness evolution dynamics model is established on the basis.First,equilibriums and the basic regeneration number of the malware propagation model are obtained,and the stability of equilibriums is analyzed and the stability conditions are obtained.Second,by analyzing the stability of equilibriums,it is proved that transcritical bifurcation occurs in the model.Through in-depth analytics of the dynamic behaviors of the model,the trustworthiness evolution mechanism of CPS is revealed.Finally,on the basis of the above analytics,the dynamic behaviors of the model are verified by simulations,and the evolution process of CPS trustworthiness is visually demonstrated.This thesis provides a new idea for CPS trustworthiness evaluation method by evaluating the CPS trustworthiness and analyzing its evolution process,and it has certain theoretical and practical significance for controlling the propagation of malware in CPS and improving CPS trustworthiness. |
