This paper studies the sensor placement problem in a networked control system for improving its security against cyber-physical attacks. The problem is formulated as a zero-sum game between an attacker and a detector. The attacker's decision is to select f nodes of the network to attack whereas the detector's decision is to place f sensors to detect the presence of the attack signals. In our formulation, the attacker minimizes its visibility, defined as the system L2 gain from the attack signals to the deployed sensors' outputs, and the detector maximizes the visibility of the attack signals. The equilibrium strategy of the game determines the optimal locations of the sensors. The existence of Nash equilibrium for the attacker-detector game is studied when the underlying connectivity graph is a directed or an undirected tree. When the game does not admit a Nash equilibrium, it is shown that the Stackelberg equilibrium of the game, with the detector as the game leader, can be computed efficiently. Our results show that, under the optimal sensor placement strategy, an undirected topology provides a higher security level for a networked control system compared with its corresponding directed topology.

We propose a game-theoretic framework for improving the resilience of multi-agent consensus dynamics in the presence of a strategic attacker. In this game, the attacker selects a set of network nodes to inject the attack signals. The attacker's objective is to minimize the required energy for steering the consensus towards its desired direction. This energy is captured by the trace of controllability Gramian of the system when the input is the attack signal. The defender improves the resilience of dynamics by adding self-feedback loops to certain nodes of the system and its objective is to maximize the trace of controllability Gramian. The Stackelberg equilibrium of the game is studied with the defender as the game leader. When the underlying network topology is a tree and the defender can select only one node, we show that the optimal strategy of the defender is determined by a specific distance-based network centrality measure, called network's f-center. In addition, we show that the degree-based centralities solutions may lead to undesirable payoffs for the defender. At the end, we discuss the case of multiple attack and defense nodes on general graphs.

Network control systems (NCSs) heavily rely on information and communication technologies for sharing information between sensors and controllers as well as controllers and actuators. When estimation, control or actuation tasks in a NCS are performed by an untrusted party, sharing information might result in the leakage of private information. The current paper reviews some of the recent results on the privacy-aware decision-making problems in NCSs. In particular, we focus on static and dynamic decision-making problems wherein privacy is measured using information-theoretic notions. We also review the applications of these problems in smart buildings and smart grids. 

A malicious attacker with access to the sensor channel in a feedback control system can severely affect the physical system under control, while simultaneously being hard to detect. A properly designed anomaly detector can restrict the impact of such attacks, however. Anomaly detectors with an internal state (stateful detectors) have gained popularity because they seem to be able to mitigate these attacks more than detectors without a state (stateless detectors). In the analysis of attacks against control systems with anomaly detectors, it has been assumed that the attacker has access to the detector's internal state, or designs its attack such that it is not detected regardless of the detector's state. In this paper, we show how an attacker can realize the first case by breaking the confidentiality of a stateful detector state evolving with linear dynamics, while remaining undetected and imitating the statistics of the detector under nominal conditions. The realization of the attack is posed in a convex optimization framework using the notion of Kullback-Leibler divergence. Further, the attack is designed such that the maximum mean estimation error of the Kalman filter is maximized at each time step by exploiting dual norms. A numerical example is given to illustrate the results.

We consider an extension of the Rescorla-Wagner model which bridges the gap between conditioning and learning on a neural-cognitive, individual psychological level, and the social population level. In this model, the interaction among individuals is captured by a Markov process. The resulting human-social behavior model is a recurrent iterated function system which behaves differently from the classical Rescorla-Wagner model due to randomness. A sufficient condition for the convergence of the forward process starting with arbitrary initial distribution is provided. Furthermore, the ergodicity properties of the internal states of agents in the proposed model are studied.

This paper presents a learning-based approach for disturbance attenuation for a non-linear dynamical system with event-based observer and model predictive control (MPC). Using the empirical risk minimization (ERM) method, we can obtain a learning error bound which is function of the number of samples, learning parameters, and model complexity. It enables us to analyze the closed-loop stability in terms of the learning property, where the state estimation error by the ERM learning is guaranteed to be bounded. Simulation results underline the learning's capability, the control performance and the event-triggering efficiency in comparison to the conventional event-triggered control scheme.

Quantized inter-agent communications in game-theoretic and distributed optimization algorithms generate uncertainty that affects the asymptotic and transient behavior of such algorithms. This chapter uses the information-theoretic notion of differential entropy power to establish universal bounds on the maximum exponential convergence rates of primal-dual and gradient-based Nash seeking algorithms under quantized communications. These bounds depend on the inter-agent data rate and the local behavior of the agents’ objective functions, and are independent of the quantizer structure. The presented results provide trade-offs between the speed of exponential convergence, the agents’ objective functions, the communication bit rates, and the number of agents and constraints. For the proposed Nash seeking algorithm, the transient performance is studied and an upper bound on the average time required to settle inside a specified ball around the Nash equilibrium is derived under uniform quantization. Furthermore, an upper bound on the probability that the agents’ actions lie outside this ball is established. This bound decays double exponentially with time.

We analyze the behavior of a large number of strategic drivers traveling er an urban traffic network using the mean-field game framework. We sume an incentive mechanism for congestion mitigation under which each iver selecting a particular route is charged a tax penalty that is fine in the logarithm of the number of agents selecting the same ute. We show that the mean-field approximation of such a rge-population dynamic game leads to the so-called linearly solvable rkov decision process, implying that an open-loop epsilon-Nash uilibrium of the original game can be found simply by solving a nite-dimensional linear system.

We consider the platoon matching problem for a set of trucks with the same origin, but different destinations. It is assumed that the vehicles benefit from traveling in a platoon for instance through reduced fuel consumption. The vehicles belong to different fleet owners and their strategic interaction is modeled as a non-cooperative game where the vehicle actions are their departure times. Each truck has a preferred departure time and its utility function is defined as the difference between its benefit from platooning and the cost of deviating from its preferred departure time. We show that the platoon matching game is an exact potential game. An algorithm based on best response dynamics is proposed for finding a Nash equilibrium of the game. At a Nash equilibrium, vehicles with the same departure time are matched to form a platoon. Finally, the total fuel reduction at the Nash equilibrium is studied and compared with that of a cooperative matching solution where a common utility function for all vehicles is optimized.