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The vast majority of today’s critical infrastructure is supported by numerous feedback control loops and an attack on these control loops can have disastrous consequences. This is a major concern since modern control systems are becoming large and decentralized and thus more vulnerable to attacks. This paper is concerned with the estimation and control of(More)
We consider the problem of state-estimation of a linear dynamical system when some of the sensor measurements are corrupted by an adversarial attacker. The errors injected by the attacker in the sensor measurements can be arbitrary and are not assumed to follow a specific model (in particular they can be of arbitrary magnitude). We first characterize the(More)
The positive semidefinite (psd) rank of a nonnegative real matrix M is the smallest integer k for which it is possible to find psd matrices Ai assigned to the rows of M and Bj assigned to the columns of M , of size k ˆ k, such that pi, jq-entry of M is the inner product of Ai and Bj . This is an example of a cone rank of a nonnegative matrix similar to(More)
We consider the problem of estimation and control of a linear system when some of the sensors or actuators are attacked by a malicious agent. In our previous work [1] we studied systems with no control inputs and we formulated the estimation problem as a dynamic error correction problem with sparse attack vectors. In this paper we extend our study and look(More)
The nonnegative rank of a matrix A is the smallest integer r such that A can be written as the sum of r rank-one nonnegative matrices. The nonnegative rank has received a lot of attention recently due to its application in optimization, probability and communication complexity. In this paper we study a class of atomic rank functions defined on a convex cone(More)
OBJECTIVES To document the pattern of recurrence of disease following large loop excision of the transformation zone (LLETZ) to identify a low risk group of women who might benefit from less intensive cytological surveillance. DESIGN Analysis of prospectively collected information with retrospective review of follow up smears. POPULATION Three thousand,(More)