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- Hamza Fawzi, Paulo Tabuada, Suhas N. Diggavi
- IEEE Trans. Automat. Contr.
- 2014

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)

- Hamza Fawzi, Paulo Tabuada, Suhas N. Diggavi
- 2011 49th Annual Allerton Conference on…
- 2011

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)

- Hamza Fawzi, João Gouveia, Pablo A. Parrilo, Richard Z. Robinson, Rekha R. Thomas
- Math. Program.
- 2015

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)

- Hamza Fawzi, Paulo Tabuada, Suhas N. Diggavi
- CDC
- 2012

— 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)

- Hamza Fawzi, James Saunderson, Pablo A. Parrilo
- SIAM Journal on Optimization
- 2015

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

- Hamza Fawzi, João Gouveia, Richard Z. Robinson
- Oper. Res. Lett.
- 2016

- Hamza Fawzi, Pablo A. Parrilo
- Math. Program.
- 2015

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)

- Hamza Fawzi, James Saunderson, Pablo A. Parrilo
- CDC
- 2015

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)

- Hamza Fawzi, Pablo A. Parrilo
- Math. Program.
- 2016

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract 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… (More)

- Hamza Fawzi, James Saunderson, Pablo A. Parrilo
- Math. Program.
- 2016