Secure Zonotopic Set-Membership State Estimation for Multirate Complex Networks Under Encryption–Decryption Mechanism

In this article, the zonotope-based distributed set-membership state estimation problem is considered for a class of nonlinear multirate complex networks (MRCN) subjected to unknown but bounded (UBB) noises and eavesdropping attacks. Both the process and measurement noises and the system linearization errors are constrained within known zonotopes. To ensure the communication security between the sensor and the estimator, an encryption–decryption mechanism (EDM) is proposed to prevent data from being eavesdropped by illegal intruders during transmission. The encryption errors generated by the signal encryption process are also constrained within a set of zonotopes. One purpose of this article is to design a distributed state estimation approach where the state estimation errors are confined to a set of zonotopes in the presence of UBB noises, linearization errors, and encryption errors. By minimizing the
$F$
-radius, which characterizes the size of zonotope, the desired estimator gains are recursively obtained. Subsequently, the influence of the designed EDM on the zonotope constraints of state estimation error is analyzed. Firstly, the dynamic upper bounds of the
$F$
-radius of the zonotope constraints are calculated, and the conditions for upper bound convergence are discussed under the designed EDM. Then, the design rule of the dynamic encryption keys is provided. Finally, an illustrative example is given to demonstrate the validity of the developed state estimation algorithm and the designed EDM.