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.

中文翻译：

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基于平滑信号模型和多目标估计方法的恶意攻击下随机系统的安全增强滤波器设计

在这项研究中，提出了一种新的安全增强滤波器（SEF），用于在系统和传感器上具有外部干扰、测量噪声和恶意攻击信号的随机跳跃扩散系统的系统状态和恶意攻击信号估计。为了通过传统的 Luenberger 型滤波器有效地估计系统状态和恶意攻击信号，在系统模型中嵌入了一种新颖的恶意攻击信号平滑信号模型，使得增强系统中的攻击信号不会破坏增强状态估计又是海基会。为了获得最佳过滤鲁棒性和安全性，随机多目标 (MO)$H_{2}/H_{\infty }$提出了SEF方案，以实现最佳的干扰和噪声过滤性能以及恶意攻击下的最佳安全增强。通过使用次优方法，随机 MO$H_{2}/H_{\infty }$SEF 设计可以等效地转换为线性矩阵不等式 (LMI) 约束的多目标优化问题 (MOP)。在非线性随机系统的情况下，MO$H_{2}/H_{\infty }$SEF 设计问题可以转换为受 Hamilton-Jacobi 不等式 (HJI) 约束的 MOP。为了克服HJIs约束MOP求解的困难，基于全局线性化技术，可以将用于非线性随机系统SEF设计的HJIs约束MOP转化为LMIs约束MOP。此外，提出了一种 LMIs 约束的多目标进化算法（MOEA）来有效地解决 LMIs 约束的 MOP，用于 SEF 的设计。给出了两个仿真实例，包括恶意攻击信号下地面雷达系统的导弹弹道估计问题和基于网络的质量弹簧系统估计问题，以验证所提出方法的有效性。