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

Forecasting VARMA processes using VAR models and subspace-based state space models

VAR modelling is a frequent technique in econometrics for linear processes. VAR modelling offers some desirable features such as relatively simple procedures for model specification (order selection) and the possibility of obtaining quick non-iterative maximum likelihood estimates of the system parameters. However, if the process under study follows a finite-order VARMA structure, it cannot be equivalently represented by any finite-order VAR model. On the other hand, a finite-order state space model can represent a finite-order VARMA process exactly, and, for state-space modelling, subspace algorithms allow for quick and non-iterative estimates of the system parameters, as well as for simple specification procedures. Given the previous facts, we check in this paper whether subspace-based state space models provide better forecasts than VAR models when working with VARMA data generating processes. In a simulation study we generate samples from different VARMA data generating processes, obtain VAR-based and state-space-based models for each generating process and compare the predictive power of the obtained models. Different specification and estimation algorithms are considered; in particular, within the subspace family, the CCA (Canonical Correlation Analysis) algorithm is the selected option to obtain state-space models. Our results indicate that when the MA parameter of an ARMA process is close to 1, the CCA state space models are likely to provide better forecasts than the AR models. We also conduct a practical comparison (for two cointegrated economic time series) of the predictive power of Johansen restricted-VAR (VEC) models with the predictive power of state space models obtained by the CCA subspace algorithm, including a density forecasting analysis.subspace algorithms; VAR; forecasting; cointegration; Johansen; CCA

Robust Subspace System Identification via Weighted Nuclear Norm Optimization

Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework to handle outliers. The proposed framework takes the form of a convex optimization problem with an objective that trades off fit, rank and sparsity. As in robust PCA, it can be problematic to find a suitable regularization parameter. We show how the space in which a suitable parameter should be sought can be limited to a bounded open set of the two dimensional parameter space. In practice, this is very useful since it restricts the parameter space that is needed to be surveyed.Comment: Submitted to the IFAC World Congress 201