Set-membership state estimation for complex networks with chance constraints under multi-modal deception attacks

This paper focuses on the state estimation issue for a type of complex networks (CNs) subject to cyberattacks. A multi-modal deception attack (MMDA) model is introduced, in which different deception attack tactics target distinct sensor nodes randomly when signals are transported throughout the network to the filter. The objective is to propose design a proportional-integral observer (PIO), ensuring that estimation errors at each single nodes are contained, with a chance not lower than a predefined value, inside certain pre-specified ellipsoidal bounds. Sufficient conditions for the feasibility of the mentioned filtering technique are established using convex optimization techniques. The required observer parameters are subsequently determined by resolving the relevant matrix inequalities at each time step. Within the provided framework, two sub-optimization problems are formulated to identify locally optimal estimation performance. Finally, the effectiveness of the proposed paradigm is shown via a numerical simulation example.