Yorie Nakahira and Yilin Mo
IEEE Conference on Decision and Control, 2015
Link to the paper
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In this article, we consider the state estimation problem of a linear time invariant system in adversarial environment. We assume that the process noise and measurement noise of the system are \(l_\infty\) functions. The adversary compromises at most \(\gamma\) sensors, the set of which is unknown to the estimation algorithm, and can change their measurements arbitrarily. We first prove that if after removing a set of \(2\gamma\) sensors, the system is undetectable, then there exists a destabilizing noise process and attacker's input to render the estimation error unbounded. For the case that the system remains detectable after removing an arbitrary set of \(2\gamma\) sensors, we construct a resilient estimator and provide an upper bound on the \(l_\infty\) norm of the estimation error. Finally, a numerical example is provided to illustrate the effectiveness of the proposed estimator design.