Research On Attack Schedule Against State Estimation In Cyber-physical Systems

Recently,the security issue of cyber-physical systems(CPS)has attracted much attention from different communities.In CPS,cyber threats emerge in many ways which can cause significant destruction to the system operation.In wireless CPS,adversaries can block the communications of useful information by channel jamming,incurring the so-called jamming attacks.In addition,remote state estimation through wireless channels is a representative application of wireless CPS.The major research aspects of the state estimation and the attacking problem,are investigated under single sensor and single channel case in most of the current work.The study of state estimation and attack schedule problem of the system with multiple sensors and each communication channel potentially jammed by jamming attack are interesting and meaningful aspects in CPS.Firstly,for the two-system case,we investigate the problem of optimal offline energy efficient jamming attack schedule subject to the energy constraints of attacker and generalize the obtained outcomes to a more common case of multiple channels and multiple sensors.Secondly,for the case of that each sensor can only observe partial states of the system,we formulate the problem of optimal offline jamming attack schedule with two sensors and put forward a stable state estimation algorithm at the remote estimator using the local estimation of the states.Thirdly,we consider energy efficient optimal online attack power schedule against remote state estimation of wireless CPS under constrained denial-of-service attacks based on channels' signal-to-interference-plus-noise ratio(SINR).Furthermore,energy harvesting sensor has attracted considerable amount of interest.Compared with conventional battery-powered sensors,the sensors equipped with an energy harvester can recharge their batteries by gaining the energy from external environment(e.g.,body heat,solar,wind,water,thermal or mechanical vibrations).Motivated by this,we finally consider the problem of optimal online transmission power allocation at an energy harvesting sensor for remote estimation in wireless CPS subject to energy constraint.The main research contents can be summarized as follows:(1)We focus on the wireless jamming attack and examine,from the standpoint of the attacker,the problem of optimal offline attack schedule that causes the largest performance degradation of the remote station estimation system,subject to attacker's energy constraint.Unlike some existing studies,we consider estimating multiple systems where sensors transmite data to the remote estimator through multiple independent wireless channels.Due to the attacker's radio constraint,we assume that it can only launch jamming attack at one of the channels at any time.We start with the two-system case and formulate the energy efficient jamming attack schedule problem as a nonlinear program.The optimal offline energy efficient schedule is theoretically derived and is shown dependent on the wireless channels' properties,energy budget of the attacker and dynamics of the systems to be estimated.Then,we extend the results to multi-system cases,and propose both an optimal offline schedule algorithm and an efficient algorithm of much lower complexity.Finally,we validate the theoretical results by numerical simulations.(2)For the jamming attack in wireless CPS,we investigate the problem of optimal offline jamming attack scheduling against remote state estimation.Specifically,we consider that two wireless sensors report data to a remote estimator through two wireless communication channels lying in two unoverlapping frequency bands,respectively.Meanwhile,an adversary can select one and only one channel at a time to execute jamming attack.We prove that the optimal offline attack schedule is continuously launching attack on one channel determined based on the system dynamics matrix.The theoretical results are validated by numerical simulations.(3)We consider energy efficient optimal online attack power schedule against remote state estimation of wireless CPS under constrained denial-of-service attacks based on channels' signal-to-interference-plus-noise ratio.We propose a wireless communication model with SINRs of channels,in which different attack powers can cause different dropout rates.The problem of optimal online attack power schedule that causes the largest performance degradation of the remote state estimation,subject to attacker's average energy constraint in multi-systems,is solved by formulating it as a Markov decision process(MDP).We show that an optimal deterministic and stationary policy exists and the optimal policy has a threshold structure.(4)We investigate optimal online transmission power allocation for an energy harvesting sensor against remote state estimation in wireless CPS.The sensor has access to an energy harvester,which can collect energy from the external environment and is an everlasting but unreliable energy source compared to conventional batteries.For the wireless dropping communication channel,the packet dropout rates depend on both the signal noise ratio and the transmission power used by the sensor.We formulate the problem of the optimal online transmission power allocation for the energy harvesting sensor as an infinite time-horizon Markov decision processes.By analyzing the MDP algorithm,we show that an optimal deterministic and stationary transmission power policy exists.Moreover,we show that the optimal policy has a threshold type structure.A numerical simulation is provided to illustrate the performance of the transmission power allocation algorithm.