### Abstract

We propose a system theoretic approach to the identification and mitigation of vulnerabilities to cyber attacks, in networks of dynamical systems. Using the controllability and observability gramians, we define a network's vulnerability in terms of the impact of an attack input and the degree of difficulty with which this impact can be detected. In this framework, a network is deemed as vulnerable if it is easy for an attacker to steer it to a certain state and yet such a state is hard to observe through the network's sensing mechanisms. We propose strategies for finding the optimal location of a small number of sensors that minimize the network's vulnerability. Such strategies are obtained as the solution of convex optimization problems, formulated so as to strike a balance between maximal reduction of the system's vulnerability and employing a minimal number of sensors. The utility of the developed framework is demonstrated on a standard IEEE nine bus power system network model.

Original language | English (US) |
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Title of host publication | 2013 European Control Conference, ECC 2013 |

Pages | 3548-3553 |

Number of pages | 6 |

State | Published - Dec 1 2013 |

Event | 2013 12th European Control Conference, ECC 2013 - Zurich, Switzerland Duration: Jul 17 2013 → Jul 19 2013 |

### Publication series

Name | 2013 European Control Conference, ECC 2013 |
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### Other

Other | 2013 12th European Control Conference, ECC 2013 |
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Country | Switzerland |

City | Zurich |

Period | 7/17/13 → 7/19/13 |

### Keywords

- Convex optimization
- large-scale systems
- power networks
- relaxation
- semidefinite programming
- sensing strategy
- smart grid

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

*2013 European Control Conference, ECC 2013*(pp. 3548-3553). [6669723] (2013 European Control Conference, ECC 2013).