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arXiv · 2306.17606

Minimum-norm Sparse Perturbations for Opacity in Linear Systems

Varkey M John·Vaibhav Katewa
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Abstract

Opacity is a notion that describes an eavesdropper's inability to estimate a system's 'secret' states by observing the system's outputs. In this paper, we propose algorithms to compute the minimum sparse perturbation to be added to a system to make its initial states opaque. For these perturbations, we consider two sparsity constraints - structured and affine. We develop an algorithm to compute the global minimum-norm perturbation for the structured case. For the affine case, we use the global minimum solution of the structured case as initial point to compute a local minimum. Empirically, this local minimum is very close to the global minimum. We demonstrate our results via a running example.

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Varkey M John, Vaibhav Katewa. 2023-06-30. Minimum-norm Sparse Perturbations for Opacity in Linear Systems. https://arxiv.org/abs/2306.17606

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