Attack estimation of switched nonlinear control systems using invertibility

In this paper, we consider a class of nonlinear control systems subject to false data injection attacks and switching attacks. The problem of attack estimation is formulated as the simultaneous reconstruction of system states, attack vectors and system mode of a switched nonlinear system. In the proposed attack estimation algorithm, the inverse system of each mode aims to estimate system states and attack vectors when the corresponding mode has a finite relative order. A set-valued mode index inversion map correctly recovers the true mode when the switch-singular pair between any two modes does not exist. Two case studies including a consensus problem and a supervised learning problem are used to validate the performance of the developed algorithm.