We propose an open-loop and a closed-loop stochastic event-triggered sensor schedule for remote state estimation. Both schedules overcome the essential difficulties of existing schedules in recent literature works where, through introducing a deterministic event-triggering mechanism, the Gaussian property of the innovation process is destroyed which produces a challenging nonlinear filtering problem that cannot be solved unless approximation techniques are adopted. The proposed stochastic event-triggered sensor schedules eliminate such approximations. Under these two schedules, the minimum mean squared error (MMSE) estimator and its estimation error covariance matrix at the remote estimator are given in a closed-form. The stability in terms of the expected error covariance and the sample path of the error covariance for both schedules is studied. We also formulate and solve an optimization problem to obtain the minimum communication rate under some estimation quality constraint using the open-loop sensor schedule. A numerical comparison between the closed-loop MMSE estimator and a typical approximate MMSE estimator with deterministic eventtriggered sensor schedule, in a problem setting of target tracking, shows the superiority of the proposed sensor schedule.

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Ensuring the security of control systems against integrity attacks is a major challenge. Due to the events of Stuxnet, replay attacks in particular have been considered by the research community. Replaying previous measurements of a system in steady state allows an adversary to generate statistically correct virtual outputs which can bypass traditional detectors. The adversary can then inject destabilizing inputs to cause damage to the plant. The method of injecting secret noisy control inputs, or physical watermarking, has recently been proposed to detect replay attacks. However, the proposed watermarking design methods assume that the adversary does not use his potential access to real time communication channels to create stealthy virtual outputs to send to the defender. In this paper, we formulate an attack model for an adversary who uses knowledge of the system as well as access to a subset of real time control inputs and sensor outputs to construct stealthy virtual outputs. A robust physical watermark and detector to counter such an adversary is proposed. 53rd IEEE Conference on Decision and Control

Maintaining the security of control systems in the presence of integrity attacks is a significant challenge. In literature, several possible attacks against control systems have been formulated including replay, false data injection, and zero dynamics attacks. The detection and prevention of these attacks may require the defender to possess a particular subset of trusted communication channels. Alternatively, these attacks can be prevented by keeping the system model secret from the adversary. In this paper, we consider an adversary who has the ability to modify and read all sensor and actuator channels. To thwart this adversary, we introduce external states dependent on the state of the control system, with linear timevarying dynamics unknown to the adversary. We also include sensors to measure these states. The presence of unknown timevarying dynamics is leveraged to detect an adversary who simultaneously aims to identify the system and inject stealthy outputs. Potential attack strategies and bounds on the attacker's performance are provided.

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