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Cyber-physical systems (CPS) are required to satisfy safety constraints in various application domains such as robotics, industrial manufacturing systems, and power systems. Faults and cyber attacks have been shown to cause safety violations, which can damage the system and endanger human lives. Resilient architectures have been proposed to ensure safety of CPS under such faults and attacks via methodologies including redundancy and restarting from safe operating conditions. The existing resilient architectures for CPS utilize different mechanisms to guarantee safety, and currently, there is no common framework to compare them. Moreover, the analysis and design undertaken for CPS employing one architecture is not readily extendable to another. In this article, we propose a timing-based framework for CPS employing various resilient architectures and develop a common methodology for safety analysis and computation of control policies and design parameters. Using the insight that the cyber subsystem operates in one out of a finite number of statuses, we first develop a hybrid system model that captures CPS adopting any of these architectures. Based on the hybrid system, we formulate the problem of joint computation of control policies and associated timing parameters for CPS to satisfy a given safety constraint and derive sufficient conditions for the solution. Utilizing the derived conditions, we provide an algorithm to compute control policies and timing parameters relevant to the employed architecture. We also note that our solution can be applied to a wide class of CPS with polynomial dynamics and also allows incorporation of new architectures. We verify our proposed framework by performing a case study on adaptive cruise control of vehicles.

 

This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that operate in adversarial environments have typically been abstracted as stochastic games (SGs); however, because traditional SG models do not incorporate a notion of time, they cannot be used in a setting where the objective is time-sensitive. To address this, we introduce durational stochastic games (DSGs). DSGs generalize SGs to incorporate a notion of time and model the adversary’s abilities to tamper with the control input (actuator attack) and manipulate the timing information that is perceived by the CPS (timing attack). We define notions of spatial, temporal, and spatio-temporal robustness to quantify the amounts by which system trajectories under the synthesized policy can be perturbed in space and time without affecting satisfaction of the MITL objective. In the case of an actuator attack, we design computational procedures to synthesize controllers that will satisfy the MITL task along with a guarantee of its robustness. In the presence of a timing attack, we relax the robustness constraint to develop a value iteration-based procedure to compute the CPS policy as a finite-state controller to maximize the probability of satisfying the MITL task. A numerical evaluation of our approach is presented on a signalized traffic network to illustrate our results.

 

Increasingly large trip demands have strained urban transportation capacity, which consequently leads to traffic congestion and rapid growth of greenhouse gas emissions. In this work, we focus on achieving sustainable transportation by incentivizing passengers to switch from private cars to public transport. We address the following challenges. First, the passengers incur inconvenience costs when changing their transit behaviors due to delay and discomfort, and thus need to be reimbursed. Second, the inconvenience cost, however, is unknown to the government when choosing the incentives. Furthermore, changing transit behaviors raises privacy concerns from passengers. An adversary could infer personal information (e.g., daily routine, region of interest, and wealth) by observing the decisions made by the government, which are known to the public. We adopt the concept of differential privacy and propose privacy-preserving incentive designs under two settings, denoted as two-way communication and one-way communication. Under two-way communication, passengers submit bids and then the government determines the incentives, whereas in one-way communication, the government simply sets a price without acquiring information from the passengers. We formulate the problem under two-way communication as a mixed integer linear program and propose a polynomial-time approximation algorithm. We show the proposed approach achieves truthfulness, individual rationality, social optimality, and differential privacy. Under one-way communication, we focus on how the government should design the incentives without revealing passengers’ inconvenience costs while still preserving differential privacy. We formulate the problem as a convex program and propose a differentially private and near-optimal solution algorithm. A numerical case study using the Caltrans Performance Measurement System (PeMS) data source is presented as evaluation. The results show that the proposed approaches achieve a win-win situation in which both the government and passengers obtain non-negative utilities.