Controllability and observability of CPSs under networked adversarial attacks

H ∞ Control for Time-Varying Cyber-Physical System Under Randomly Occurring Hybrid Attacks: The Output Feedback Case

“…Theorem 1: Given the attack attenuation level γ > 0 and the positive matrix W . For any nonzero ξ k , the closed-loop system (5) satisfies the H ∞ performance requirement (6) for any nonzero attack signal ξ k , if there exist two families of nonnegative definite matrices P k , S k (0 ≤ k ≤ N ) and a set of real-valued matricesK k satisfying (7) and the following backward recursive RDE:…”

“…are known real-valued time-varying matrices. Remark 1: Some previous researches have presented the model of sensor attacks and actuator attacks for linear timeinvariant system, and assumed that the attack signals have bounded energy in a finite-horizon [7], [15]. Inspired by these works, the time-varying CPS model subject to FDI attacks in sensors and actuators is given in (1), and the attack signals w i,k and a j,k are priori-unknown and energy bounded.…”

“…are stochastic and mutually independent variables which indicate the DoS attacks occurrence respectively when their value is 0, and are supposed to be the Bernoulli distributed white sequences with expectationsβ i . Remark 3: Actually, many literatures have been devoted efforts to study the control problems subject to the occurrence of FDI or DoS attacks [7], [11]. Additionally, random occurrence of DoS attacks which obey a probabilistic law are ineluctable due to unpredictable attack techniques and unstable network circumstances has been increasingly studied [6], [27], [30].…”

“…Since the future attack behavior is unpredictable, the worst performance of each sub-controller is considered, and the most secure sub-controller is designed to reconstruct the past attack profile in a certain time horizon when the energy of the attack signal is limited. The work [7] also focuses on the sensor and actuator attacks which can affect the dynamic characteristics of a linear time invariant system. The system has M controlled inputs from the actuators and P measured outputs from the sensors, which can be designed controllable and observable under attacks.…”

Leader‐following consensus of uncertain strict feedback multiagent systems subject to sensor and actuator attacks

“…To characterize the resilience of a control system in cyber‐physical systems (CPSs) against actuator attacks and sensor attacks, in Reference 43 new notions of controllability and observability are introduced to derive conditions under whether the state can be stabled and reconstructed by the existing control signal and measurements over a period of time. However, the condition in Reference 43 cannot be used to mitigate the attacks. The detailed control system configuration under adversarial attacks is shown in Figure 1.…”