A bus-off attack is a denial-of-service (DoS) attack which exploits error handling in the controller area network (CAN) to induce an honest node to disconnect itself from the CAN bus. This paper develops a stochastic transmission policy as a countermeasure for the controller-transmitter pair against the bus-off attack. We model this as a non-zero-sum linear-quadratic-Gaussian game between the controller-transmitter pair and the attacker. We derive Nash equilibria of the game for two different information structures of the attacker. We show that the attacker has a dominant attack strategy under both information structures. Under the dominant attack strategy, we show that the optimal control policy is linear in the system state. We further identify a necessary and a sufficient conditions on the transmission policy to have bounded average cost. The theoretical results are complemented by a detailed case study of a bus-off attack on a vehicular adaptive cruise control model.

We develop a new algorithm, based on approximate dynamic programming, to efficiently schedule the charging processes of a large number of electric vehicles (EVs) with flexibility, which allows the EV charging service provider to charge the EVs between their minimum and target state of charge (SoC) within a time window. We assume that the charging demands have known distributions and the charging process of EVs can be scheduled preemptively. We model the scheduling problem as a dynamic program with state-dependent constraints and solve it utilizing the fitted value iteration. We propose a multi-stage decoupled algorithm to reduce the dimensions in the fitted value iteration to reduce the computation complexity, and provide sufficient conditions for achieving optimality.