This paper considers optimal attack attention allocation on remote state estimation in multi-systems. Suppose there are M independent systems, each of which has a remote sensor monitoring the system and sending its local estimates to a fusion center over a packet-dropping channel. An attacker may generate noises to exacerbate the communication channels between sensors and the fusion center. Due to capacity limitation, at each time the attacker can exacerbate at most N of the M channels. The goal of the attacker side is to seek an optimal policy maximizing the estimation error at the fusion center. The problem is formulated as a Markov decision process (MDP) problem, and the existence of an optimal deterministic and stationary policy is proved. We further show that the optimal policy has a threshold structure, by which the computational complexity is reduced significantly. Based on the threshold structure, a myopic policy is proposed for homogeneous models and its optimality is established. To overcome the curse of dimensionality of MDP algorithms for general heterogeneous models, we further provide an asymptotically (as M and N go to infinity) optimal solution, which is easy to compute and implement. Numerical examples are given to illustrate the main results.

This paper considers a remote state estimation problem, where a sensor measures the state of a linear discrete-time process and has computational capability to implement a local Kalman filter based on its own measurements. The sensor sends its local estimates to a remote estimator over a communication channel that is exposed to a Denial-of-Service (DoS) attacker. The DoS attacker, subject to limited energy budget, intentionally jams the communication channel by emitting interference noises with the purpose of deteriorating estimation performance. In order to maximize attack effect, following the existing answer to "when to attack the communication channel", in this paper we manage to solve the problem of "how much power the attacker should use to jam the channel in each time". For the static attack energy allocation problem, when the system matrix is normal, we derive a sufficient condition for when the maximum number of jamming operations should be used. The associated jamming power is explicitly provided. For a general system case, we propose an attack power allocation algorithm and show the computational complexity of the proposed algorithm is not worse than O(T), where T is the length of the time horizon considered. When the attack can receive the real-time ACK information, we formulate a dynamic attack energy allocation problem, and transform it to a Markov Decision Process to find the optimal solution.

This paper studies the joint design over an infinite horizon of the transmission power controller and remote estimator for state estimation over fading channels. A sensor observes a dynamic process and sends its observations to a remote estimator over a wireless fading channel characterized by a time-homogeneous Markov chain. The successful transmission probability depends on both the channel gains and the transmission power used by the sensor. The transmission power control rule and the remote estimator should be jointly designed, aiming to minimize an infinite-horizon cost consisting of the power usage and the remote estimation error. We formulate the joint optimization problem as an average cost belief-state Markov decision process and prove that there exists an optimal deterministic and stationary policy. We then show that when the monitored dynamic process is scalar or the system matrix is orthogonal, the optimal remote estimates depend only on the most recently received sensor observation, and the optimal transmission power is symmetric and monotonically increasing with respect to the norm of the innovation error.

This paper investigates the stability of Kalman filtering over Gilbert-Elliott channels where random packet drops follow a time-homogeneous two-state Markov chain whose state transition is determined by a pair of failure and recovery rates. First of all, we establish a relaxed condition guaranteeing peak-covariance stability described by an inequality in terms of the spectral radius of the system matrix and transition probabilities of the Markov chain. We further show that the condition can be interpreted using a linear matrix inequality feasibility problem. Next, we prove that the peak-covariance stability implies mean-square stability, if the system matrix has no defective eigenvalues on the unit circle. This connection between the two stability notions holds for any random packet drop process. We prove that there exists a critical curve in the failure-recovery rate plane, below which the Kalman filter is mean-square stable and no longer mean-square stable above. Finally, a lower bound for this critical failure rate is obtained making use of the relationship we establish between the two stability criteria, based on an approximate relaxation of the system matrix.

In power system operation, the economic dispatch problem (EDP) aims to minimize the total generation cost while meeting the demand and satisfying generator capacity limits. This paper proposes an algorithm based on the gradient push-sum method to solve the EDP in a distributed manner over communication networks potentially with time-varying topologies and communication delays. This paper shows that the proposed algorithm is guaranteed to solve the EDP if the time-varying directed communication network is uniformly jointly strongly connected. Moreover, the proposed algorithm is also able to handle arbitrarily large but bounded time-varying delays on communication links. Numerical simulations are used to illustrate and validate the proposed algorithm.

Driven by smart grid technologies, a great effort has been made in developing distributed energy resources (DERs) in recent years for improving reliability and efficiency of distribution systems. Emerging DERs require effective and efficient control and coordination in order to harvest their potential benefits. In this paper, we consider optimal DER coordination problem, where the goal is to minimize the total generation cost while meeting total demand and satisfying individual generator output limit. This paper develops a distributed algorithm for solving the optimal DER coordination problem over lossy communication networks with packet-dropping communication links. Under the assumption that the underlying communication network is strongly connected with a positive probability and the packet drops are independent and identically distributed, we show that the proposed algorithm is able to solve the optimal DER coordination problem even in the presence of packet drops. Numerical simulation results are used to validate and illustrate the proposed algorithm.

We propose distributed static and dynamic event-triggered control laws to solve the consensus problem for multiagent systems with output saturation. Under the condition that the underlying graph is undirected and connected, we show that consensus is achieved under both event-triggered control laws if and only if the average of the initial states is within the saturation level. Numerical simulations are provided to illustrate the effectiveness of the theoretical results and to show that the control laws lead to reduced need for inter-agent communications.

We consider the problem of multiple sensor scheduling for remote state estimation of multiple process over a shared link. In this problem, a set of sensors monitor mutually independent dynamical systems in parallel but only one sensor can access the shared channel at each time to transmit the data packet to the estimator. We propose a stochastic event-based sensor scheduling in which each sensor makes transmission decisions based on both channel accessibility and distributed event-triggering conditions. The corresponding minimum mean squared error estimator is explicitly given. Considering information patterns accessed by sensor schedulers, time-based ones can be treated as a special case of the proposed one. By ultilizing real-time information, the proposed schedule outperforms the time-based ones in terms of the estimation quality. Resorting to solving a Markov decision process (MDP) problem with an average cost criterion, we can find optimal parameters for the proposed schedule. As for practical use, a greedy algorithm is devised for parameter design, which has rather low computational complexity. We also provide a method to quantify the performance gap between the schedule optimized via MDP and any other schedules.

In this paper, we study neural cognition in social network. A stochastic model is introduced and shown to incorporate two well-known models in Pavlovian conditioning and social networks as special case, namely Rescorla-Wagner model and Friedkin-Johnsen model. The interpretation and comparison of these model are discussed. We consider two cases when the disturbance is independent identically distributed for all time and when the distribution of the random variable evolves according to a Markov chain. We show that the systems for both cases are mean square stable and the expectation of the states converges to consensus.

State estimation is a core objective in cyber-physical systems. In the state estimation problem over linear systems, the Kalman filter is the standard solution. The filter is the format on which the solutions to subsequent estimation problems are based. Among these problems are the estimation problem in the presence of packet drops and estimation problem involving event-based triggers. We study in this paper both phenomena simultaneously. In an attempt to find the Kalman-like filter, which proves the Gaussianity of the state and offers a set of update equations, our paper shows that no such filter exists. More precisely, one cannot find an event-based trigger such that under possible packet drops, the state variable remains a Gaussian variable. This conclusion can be reasonably extended to a more general setting.