This paper focuses on securely estimating the state of a nonlinear dynamicalsystem from a set of corrupted measurements. In particular, we consider twobroad classes of nonlinear systems, and propose a technique which enables us toperform secure state estimation for such nonlinear systems. We then provideguarantees on the achievable state estimation error against arbitrarycorruptions, and analytically characterize the number of errors that can beperfectly corrected by a decoder. To illustrate how the proposed nonlinearestimation approach can be applied to practical systems, we focus on secureestimation for the wide area control of an interconnected power system undercyber-physical attacks and communication failures, and propose a secureestimator for the power system. Finally, we numerically show that the proposedsecure estimation algorithm enables us to reconstruct the attack signalsaccurately.
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