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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)

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 A i assigned to the rows of M and B j assigned to the columns of M , of size k ˆ k, such that pi, jq-entry of M is the inner product of A i and B j. This is an example of a cone rank of a nonnegative matrix similar to… (More)

Parrilo (MIT) Equivariant semidefinite lifts and sum of squares hierarchies Cargese 2014 1 / 23

—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)

— 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… (More)

Semidefinite programming (SDP) is a nice class of convex optimization problems. Semidefinite programming (SDP) is a nice class of convex optimization problems. However, we don't yet really understand what SDP is... Existence and efficiency: When is a convex set representable by conic optimization? How to quantify the number of additional variables that are… (More)

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract The nonnegative rank of an entrywise nonnegative matrix A ∈ R m×n + is the smallest integer r such that A can be written as A = U V where U ∈ R m×r + and V ∈ R r×n + are both nonnegative. The nonnegative rank arises in different… (More)

There has been a lot of interest recently in proving lower bounds on the size of linear programs needed to represent a given polytope P. In a breakthrough paper Fiorini et al. [FMP + 12] showed that any linear programming formulation of maximum-cut must have exponential size. A natural question to ask is whether one can prove such strong lower bounds for… (More)