Resilient Interval Observer for Simultaneous Estimation of States, Modes and Attack Policies

This paper considers the problem of designing interval observers for hidden mode switched nonlinear systems with bounded noise signals that are compromised by false data injection and switching attacks. The proposed observer consists of three components: i) a bank of mode-matched observers, which simultaneously estimates the corresponding mode-matched continuous states and discrete states (modes), as well as learns a model of the unknown attack policy, ii) a mode observer that eliminates the incompatible modes based on a residual-based set-membership criterion, and iii) a global fusion observer that combines the outputs of i) and ii). Moreover, in addition to showing the correctness, stability and convergence of the mode-matched estimates, we provide sufficient conditions to guarantee that all false modes will be eliminated after sufficiently large finite time steps, i.e., the system is mode-detectable under the proposed observer.