Secure Zonotopic Set-Membership State Estimation for Multi-Rate Complex Networks Under Encryption-Decryption Mechanism

In this paper, the zonotope-based distributed set-membership state estimation problem is considered for a class of nonlinear multi-rate complex networks (MRCNs) subjected to unknown-but-bounded (UBB) noises and eavesdropping attacks. The process and measurement noises and the errors generated by the linearization process are constrained within sets of zonotopes, respectively. To ensure the communication security between sensor and 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 paper is to design a distributed state estimation estimator where the state estimation errors are confined to a set of zonotopes in the presence of UBB noise, 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 zonotope constraint of state estimation error is analyzed. Firstly, the dynamic upper bound of the $F$ -radius of the zonotope constraint is calculated, and the conditions for upper bound convergence are discussed under the designed EDM. Then, the design rules of the dynamic encryption key are provided. Finally, an illustrative example is given to demonstrate the validity of the developed state estimation algorithm and the designed EDM.