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 Hββ gain.Comment: 7 page