System recovery of MIMO nonlinear systems against false data injection attack

This article investigates the system recovery problem for a class of multi-input multi-output (MIMO) nonlinear systems under false data injection attack. Under the conditions that the attack is norm-bounded and the system has a vector relative degree and a trivial zero dynamics, the nonlinear system is transformed into a linear one by means of feedback-linearizing design. Then, a high-gain approximate differentiator is adopted to obtain the system states with any arbitrary accuracy. After that, by using a technique of replacing real-time with a small time delay, a recursive attack-compensation input signal is constructed and added into the system input to almost fully compensate for the impact of the attack on the system’s transient performance. At this time, the input of the nonlinear system includes two parts: desired input (or called reference input), which is designed according to the nominal model, and additional attack-compensation input. Theoretical analysis shows for the first time that the system can be almost fully recovered in the sense of the mapping relationship between the desired input and nonlinear system states, i.e ., the aforementioned mapping is almost the same as the one in the nominal system. Finally, a simulation on a near-space vehicle is provided for verifying the theoretical results.