Partial-encryption-decryption-based secure state estimation of singularly perturbed complex networks: A Paillier encryption approach.

Abstract

This paper is concerned with the problem of secure and resilient state estimation for a class of discrete-time singularly perturbed complex networks subject to estimator gain perturbations, where measurement data are transmitted over open communication channels. To protect sensitive information against eavesdropping while avoiding excessive computational burden, a novel Paillier-based partial encryption-decryption (PED) mechanism is developed by integrating probabilistic measurement quantization with homomorphic encryption. Unlike conventional full-encryption schemes, the proposed PED strategy encrypts only a subset of measurements at each time instant according to a group-based round-robin protocol, thereby achieving an effective tradeoff between data security and computational efficiency. Under the proposed PED framework, a resilient state estimator is designed to explicitly accommodate quantization errors and gain perturbations. By employing Lyapunov stability theory, sufficient conditions are derived to guarantee that the resulting estimation error dynamics are exponentially ultimately bounded in the mean-square sense. Moreover, the estimator gains are systematically characterized via the solution of a set of matrix inequalities, leading to a computationally tractable design procedure. A numerical example is finally provided to demonstrate the effectiveness and robustness of the proposed secure state estimation scheme.