Data-Driven Koopman Operator Based Cyber-Attacks for Nonlinear Control Affine Cyber-Physical Systems

This paper studies the data-driven implementation of stealthy cyber-attacks for a class of nonlinear cyber-physical systems (CPS). In particular, we consider and study zero dynamics and covert cyber-attacks. By utilizing the Koopman operator theory, a given control affine CPS is transformed into the Koopman canonical form, and its relative degree is defined in terms of the Koopman modes, Koopman eigenvalues, and Koopman eigenfunctions. Consequently, the relative degree of the CPS is utilized to determine zero dynamics cyber-attacks. In contrast to the linear case, adversaries need to compromise both input and output communication channels of the CPS to maintain their attacks undetected. Moreover, the Koopman canonical form of the CPS is used to define and implement covert cyber-attacks in nonlinear CPS. The extended dynamic mode decomposition (EDMD) provides a linear finite-dimensional approximation of the CPS. Consequently, approximated dynamics of the CPS are utilized to introduce data-driven zero dynamics and covert cyber-attacks. Finally, a numerical example is provided to illustrate the effectiveness of our proposed methods.