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.Comment: Submitted to Indian Control Conference, 2023 (6 pages