在本篇研究中，我們提出了一種新穎的安全性增強濾波器（SEF），用於隨機跳躍擴散系統和其感測器同時具有外部干擾、測量雜訊以及攻擊信號情況下的系統狀態和攻擊信號估計。為了使用傳統的 Luenberger-Type 濾波器來有效估計系統狀態和攻擊信號，我們將針對攻擊信號的平滑模型嵌入到系統模型之中。從實際的角度來看，工程師設計濾波器時不僅需要考量強健性，也要考慮最佳效能。因此，我們提出了一種對於隨機跳躍擴散系統的隨機多目標（MO）H_2/H_∞ SEF方案，用來降低攻擊信號和外部干擾對濾波能力的影響，進而提高系統的安全性。透過使用次優化方式，MO H_2/H_∞ SEF設計可以轉換成對於系統H_2以及H_∞性能各自的上限同時最小化問題。在非線性隨機系統的情況下，則可以將MO H_2/H_∞ SEF設計問題轉換為由 Hamilton-Jacobi 不等式（HJI）約束的多目標優化問題（MOP）。為了克服求解困難的HJI約束MOP，經由使用全局線性化技術，非線性隨機系統SEF設計的HJI約束MOP可以轉換為由線性矩陣不等式（LMI）約束的MOP。此外，我們提出了一種LMI約束多目標進化演算法（MOEA），以有效解決非線性隨機系統SEF設計中的LMI約束MOP。最後，使用一個非線性地面飛彈雷達系統在遭受惡意攻擊信號下的隨機飛彈彈道估計問題展示所提出的MO H_2/H_∞ SEF設計程序，並評估該設計方法的性能。

In this study, a novel security-enhanced filter (SEF) is proposed for the system state and attack signal estimation of the stochastic jump-diffusion systems with the external disturbance, measurement noise and attack signal on system and sensor. For the efficient estimation of system state and attack signal by conventional Luenberger-type filter, a novel smoothed model of attack signals is embedded in system model. From the practical perspective, the engineers consider the filter design to be not only robust but also optimal. Therefore, the stochastic multi-objective (MO) H_2/H_∞ SEF scheme for the stochastic jump-diffusion systems is proposed to attenuate the effect of the attack signal and external disturbance on the filtering ability for security enhancement. By using the suboptimal method, the stochastic MO H_2/H_∞ SEF design could be transformed to minimizing the upper bounds of the stochastic MO H_2/H_∞ filtering performance simultaneously. In the nonlinear stochastic system case, the MO H_2/H_∞ SEF design problem could be converted to a Hamilton-Jacobi inequalities (HJIs)-constrained multiobjective optimization problem (MOP). In order to overcome the difficulty in solving the HJIs-constrained MOP, based on the global linearization technique, the HJIs-constrainted MOP for SEF of nonlinear stochastic systems could be transformed to a linear matrix inequalities (LMIs)-constrained MOP. Further, an LMIs-constrained multiobjective evolution algorithm (MOEA) is proposed to efficiently solve the LMIs-constrained MOP for the design of SEF. Finally, a simulation example of the nonlinear stochastic missile trajectory estimation problem by ground missile radar system under the malicious attack signal is given to illustrate the design procedure and evaluate the performance of the proposed MO H_2/H_∞ SEF design method.

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