  In this paper, we study the problem of designing a simultaneous mode, input,
and state set-valued observer for a class of hidden mode switched nonlinear
systems with bounded-norm noise and unknown input signals, where the hidden
mode and unknown inputs can represent fault or attack models and exogenous
fault/disturbance or adversarial signals, respectively. The proposed
multiple-model design has three constituents: (i) a bank of mode-matched
set-valued observers, (ii) a mode observer, and (iii) a global fusion observer.
The mode-matched observers recursively find the sets of compatible states and
unknown inputs conditioned on the mode being the true mode, while the mode
observer eliminates incompatible modes by leveraging a residual-based
criterion. Then, the global fusion observer outputs the estimated sets of
states and unknown inputs by taking the union of the mode-matched set-valued
estimates over all compatible modes. Moreover, sufficient conditions to
guarantee the elimination of all false modes (i.e., mode-detectability) are
provided and the effectiveness of our approach is demonstrated and compared
with existing approaches using an illustrative example.
