ABSTRACT
In this chapter, a novel security-enhanced filter (SEF) is proposed for the system state and malicious attack signal estimation of stochastic jump-diffusion systems with external disturbance, measurement noise, and malicious attack signal on the 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 state estimation of the SEF again. For optimal filtering robustness and security, the stochastic multi-objective H2 /H∞ SEF scheme is proposed to achieve optimal disturbance and noise filtering performance and optimal security enhancement under malicious attack. By using the suboptimal method, the stochastic MO H2 /H∞ SEF design could be equivalently transformed into a linear matrix inequality–constrained multi-objective optimization problem. In the case of a nonlinear stochastic system, the MO H2 /H∞ SEF design problem could be converted to a Hamilton-Jacobi inequality–constrained MOP. In order to overcome the difficulty in solving the HJI-constrained MOP, based on the global linearization technique, the HJI-constrained MOP for SEF design of nonlinear stochastic systems could be transformed into an LMI-constrained MOP. Further, a reverse-order LMI-constrained multi-objective evolution algorithm is proposed to efficiently solve the LMI-constrained MOP for the design of SEF. Two simulation examples, a missile trajectory estimation problem by ground radar system under malicious attack signals and estimation of a network-based mass spring system, are given to validate the effectiveness of the proposed method.
