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

This paper addresses the problem of resilient state estimation and attack reconstruction for bounded-error nonlinear discrete-time systems with nonlinear observations/ constraints, where both sensors and actuators can be compromised by false data injection attack signals/unknown inputs. By leveraging mixed-monotone decomposition of nonlinear functions, as well as affine parallel outer-approximation of the observation functions, along with introducing auxiliary states to cancel out the effect of the attacks/unknown inputs, our proposed observer recursively computes interval estimates that by construction, contain the true states and unknown inputs of the system. Moreover, we provide several semi-definite programs to synthesize observer gains to ensure input-to-state stability of the proposed observer and optimality of the design in the sense of minimum $\mathcal{H}_{\infty}$ gain.