It is often appealing to assume that existing solutions can be directly applied to emerging engineering domains. Unfortunately, careful investigation of the unique challenges presented by new domains ...exposes its idiosyncrasies, thus often requiring new approaches and solutions. In this paper, we argue that the "smart" grid, replacing its incredibly successful and reliable predecessor, poses a series of new security challenges, among others, that require novel approaches to the field of cyber security. We will call this new field cyber-physical security. The tight coupling between information and communication technologies and physical systems introduces new security concerns, requiring a rethinking of the commonly used objectives and methods. Existing security approaches are either inapplicable, not viable, insufficiently scalable, incompatible, or simply inadequate to address the challenges posed by highly complex environments such as the smart grid. A concerted effort by the entire industry, the research community, and the policy makers is required to achieve the vision of a secure smart grid infrastructure.
Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable ...communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.
In this paper we consider the problem of infinite-horizon sensor scheduling for estimation in linear Gaussian systems. Due to possible channel capacity, energy budget or topological constraints, it ...is assumed that at each time step only a subset of the available sensors can be selected to send their observations to the fusion center, where the state of the system is estimated by means of a Kalman filter. Several important properties of the infinite-horizon schedules will be presented in this paper. In particular, we prove that the infinite-horizon average estimation error and the boundedness of a schedule are independent of the initial covariance matrix. We further provide a constructive proof that any feasible schedule with finite average estimation error can be arbitrarily approximated by a bounded periodic schedule. We later generalized our result to lossy networks. These theoretical results provide valuable insights and guidelines for the design of computationally efficient sensor scheduling policies.
Sensor networks are gaining a central role in the research community. This paper addresses some of the issues arising from the use of sensor networks in control applications. Classical control theory ...proves to be insufficient in modeling distributed control problems where issues of communication delay, jitter, and time synchronization between components are not negligible. After discussing our hardware and software platform and our target application, we review useful models of computation and then suggest a mixed model for design, analysis, and synthesis of control algorithms within sensor networks. We present a hierarchical model composed of continuous time-trigger components at the low level and discrete event-triggered components at the high level.
We study the economic impact of a potential class of integrity cyber attacks, named false data injection attacks, on electric power market operations. In particular, we show that with the knowledge ...of the transmission system topology, attackers may circumvent the bad data detection algorithms equipped in today's state estimator. This, in turn, may be leveraged by attackers for consistent financial arbitrage such as virtual bidding at selected pairs of nodes. This paper is a first attempt to formalize the economic impact of malicious data attacks on real-time market operations. We show how an attack could systematically construct a profitable attacking strategy, in the meantime being undetected by the system operator. Such a result is also valuable for the system operators to examine the potential economic loss due to such cyber attack. The potential impact of the false data injection attacks is illustrated on real-time market operations of the IEEE 14-bus system.
This technical note concerns control applications over lossy data networks. Sensor data is transmitted to an estimation-control unit over a network and control commands are issued to subsystems over ...the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this context, the discrete-time linear quadratic gaussian (LQG) optimal control problem is considered. In Schenato , a complete analysis was carried out for the case that sensor measurements and control inputs are delivered into a single packet to the estimator and to the actuators respectively. Here, a nontrivial generalization for MIMO systems is presented under the assumption that each sensor and each actuator exchange data with the control unit in an independent way by using their own data packet (no aggregation). In such a framework, it is shown that the separation principle still holds in the case where packet arrivals are acknowledged by the receiver. Moreover, the optimal LQG control is a linear function of the state that explicitly depends on the loss probabilities of the actuator channels. Such a dependence is not present in the single channel case considered in mean-square. In the infinite horizon case, stability conditions on the packet arrival probabilities are provided in terms of linear matrix inequalities (LMIs).
This paper considers control and estimation problems where the sensor signals and the actuator signals are transmitted to various subsystems over a network. In contrast to traditional control and ...estimation problems, here the observation and control packets may be lost or delayed. The unreliability of the underlying communication network is modeled stochastically by assigning probabilities to the successful transmission of packets. This requires a novel theory which generalizes classical control/estimation paradigms. The paper offers the foundations of such a novel theory. The central contribution is to characterize the impact of the network reliability on the performance of the feedback loop. Specifically, it is shown that for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g., TCP-like protocols), there exists a critical threshold of network reliability (i.e., critical probabilities for the successful delivery of packets), below which the optimal controller fails to stabilize the system. Further, for these protocols, the separation principle holds and the optimal LQG controller is a linear function of the estimated state. In stark contrast, it is shown that when there is no acknowledgement of successful delivery of control packets (e.g., UDP-like protocols), the LQG optimal controller is in general nonlinear. Consequently, the separation principle does not hold in this circumstance
The paper studies the asymptotic behavior of discrete time Random Riccati Equations (RRE) arising in Kalman filtering when the arrival of the observations is described by a Bernoulli independent and ...identically distributed (i.i.d.) process. We model the RRE as an order-preserving, strongly sublinear random dynamical system (RDS). Under a sufficient condition, stochastic boundedness, and using a limit-set dichotomy result for order-preserving, strongly sublinear RDS, we establish the asymptotic properties of the RRE: the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution, whose support exhibits fractal behavior. For stabilizable and detectable systems, stochastic boundedness (and hence weak convergence) holds for any nonzero observation packet arrival probability and, in particular, we can establish weak convergence at operating arrival rates well below the critical probability for mean stability (the resulting invariant measure in that situation does not possess a first moment). We apply the weak-Feller property of the Markov process governing the RRE to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points, which, in general, is not dense in the set of positive semi-definite matrices. We use the explicit characterization of the support of the invariant distribution and the almost sure (a.s.) ergodicity of the sample paths to easily compute statistics of the invariant distribution. A one-dimensional example illustrates that the support is a fractured subset of the non-negative reals with self-similarity properties.
We consider the problem of sensor selection for event detection in wireless sensor networks (WSNs). We want to choose a subset of p out of n sensors that yields the best detection performance. As the ...sensor selection optimality criteria, we propose the Kullback-Leibler and Chernoff distances between the distributions of the selected measurements under the two hypothesis. We formulate the maxmin robust sensor selection problem to cope with the uncertainties in distribution means. We prove that the sensor selection problem is NP hard, for both Kullback-Leibler and Chernoff criteria. To (sub)optimally solve the sensor selection problem, we propose an algorithm of affordable complexity. Extensive numerical simulations on moderate size problem instances (when the optimum by exhaustive search is feasible to compute) demonstrate the algorithm's near optimality in a very large portion of problem instances. For larger problems, extensive simulations demonstrate that our algorithm outperforms random searches, once an upper bound on computational time is set. We corroborate numerically the validity of the Kullback-Leibler and Chernoff sensor selection criteria, by showing that they lead to sensor selections nearly optimal both in the Neyman-Pearson and Bayes sense.
Wireless Sensor Networks (WSNs) enable a wealth of new applications where remote estimation is essential. Individual sensors simultaneously sense a dynamic process and transmit measured information ...over a shared channel to a central fusion center. The fusion center computes an estimate of the process state by means of a Kalman filter. In this technical note we assume that the WSN admits a tree topology with one fusion center at the root. At each time step only a subset of sensors can be selected to transmit observations to the fusion center due to a limited energy budget. We propose a stochastic sensor selection algorithm that randomly selects a subset of sensors according to a certain probability distribution, which is opportunely designed to minimize the asymptotic expected covariance matrix of the estimation error. We show that the optimal stochastic sensor selection problem can be relaxed into a convex optimization problem and thus efficiently solved. We also provide a possible implementation of our algorithm which does not introduce any communication overhead. The technical note ends with some numerical examples that show the effectiveness of the proposed approach.
PDF
