Security-Enhanced Filter Design for Stochastic Systems under Malicious Attack via Smoothed Signal Model and Multiobjective Estimation Method

Abstract

In this study, a novel security-enhanced filter (SEF) is proposed for the system state and malicious attack signal estimation of the stochastic jump-diffusion systems with the external disturbance, measurement noise and malicious attack signal on system and sensor. To efficiently estimate the system state and malicious attack signal by the traditional Luenberger-type filter, a novel smoothed signal model of malicious attack signals is embedded in the system model so that the attack signals in the augmented system do not corrupt the augmented states estimation of SEF again. For the optimal filtering robustness and security, the stochastic multi-objective (MO) $H_{2}/H_{\infty }$ SEF scheme is proposed to achieve optimal disturbance and noise filtering performance and the optimal security enhancement under malicious attack. By using the suboptimal method, the stochastic MO $H_{2}/H_{\infty }$ SEF design could be equivalently transformed to linear matrix inequalities (LMIs)-constrained multi-objective optimization problem (MOP). In the case of nonlinear stochastic system, the MO $H_{2}/H_{\infty }$ SEF design problem could be converted to a Hamilton-Jacobi inequalities (HJIs)-constrained MOP. In order to overcome the difficulty in solving the HJIs-constrained MOP, based on the global linearization technique, the HJIs-constrained MOP for SEF design of nonlinear stochastic systems could be transformed to an LMIs-constrained MOP. Further, an LMIs-constrained multi-objective evolution algorithm (MOEA) is proposed to efficiently solve the LMIs-constrained MOP for the design of SEF. Two simulation examples including the missile trajectory estimation problem by ground radar system under the malicious attack signals and estimation of netwoked-based mass spring system are given to validate the effectiveness of the proposed method.