On the genericity properties in networked estimation: Topology design and sensor placement

In this paper, we consider networked estimation of linear, discrete-time dynamical systems monitored by a network of agents. In order to minimize the power requirement at the (possibly, battery-operated) agents, we require that the agents can exchange information with their neighbors only \emph{once per dynamical system time-step}; in contrast to consensus-based estimation where the agents exchange information until they reach a consensus. It can be verified that with this restriction on information exchange, measurement fusion alone results in an unbounded estimation error at every such agent that does not have an observable set of measurements in its neighborhood. To over come this challenge, state-estimate fusion has been proposed to recover the system observability. However, we show that adding state-estimate fusion may not recover observability when the system matrix is structured-rank ($S$-rank) deficient. In this context, we characterize the state-estimate fusion and measurement fusion under both full $S$-rank and $S$-rank deficient system matrices.Comment: submitted for IEEE journal publicatio

Subspace Methods for Data Attack on State Estimation: A Data Driven Approach

Data attacks on state estimation modify part of system measurements such that the tempered measurements cause incorrect system state estimates. Attack techniques proposed in the literature often require detailed knowledge of system parameters. Such information is difficult to acquire in practice. The subspace methods presented in this paper, on the other hand, learn the system operating subspace from measurements and launch attacks accordingly. Conditions for the existence of an unobservable subspace attack are obtained under the full and partial measurement models. Using the estimated system subspace, two attack strategies are presented. The first strategy aims to affect the system state directly by hiding the attack vector in the system subspace. The second strategy misleads the bad data detection mechanism so that data not under attack are removed. Performance of these attacks are evaluated using the IEEE 14-bus network and the IEEE 118-bus network.Comment: 12 page

Consensus for quantum networks: from symmetry to gossip iterations

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consensus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutation-invariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed

Partial Observability and its Consistency for PDEs

In this paper, a quantitative measure of partial observability is defined for PDEs. The quantity is proved to be consistent if the PDE is approximated using well-posed approximation schemes. A first order approximation of an unobservability index using an empirical Gramian is introduced. Several examples are presented to illustrate the concept of partial observability, including Burgers' equation and a one-dimensional nonlinear shallow water equation.Comment: 5 figures, 25 pages. arXiv admin note: substantial text overlap with arXiv:1111.584