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This paper addresses the problem of resilient state estimation and attackreconstruction for bounded-error nonlinear discrete-time systems with nonlinearobservations/ constraints, where both sensors and actuators can be compromisedby false data injection attack signals/unknown inputs. By leveragingmixed-monotone decomposition of nonlinear functions, as well as affine parallelouter-approximation of the observation functions, along with introducingauxiliary states to cancel out the effect of the attacks/unknown inputs, ourproposed observer recursively computes interval estimates that by construction,contain the true states and unknown inputs of the system. Moreover, we provideseveral semi-definite programs to synthesize observer gains to ensureinput-to-state stability of the proposed observer and optimality of the designin the sense of minimum $\mathcal{H}_{\infty}$ gain.

Resilient State Estimation for Nonlinear Discrete-Time Systems via Input and State Interval Observer Synthesis