在布朗連續雜訊及卜瓦松不連續雜訊下的飛彈導引多目標 控制

Multi-objective Missile Guidance Control with Stochastic Continuous Wiener and Discontinuous Poisson Noises

謝昭夷

哈密頓-雅可比不等式 ； 線性矩陣不等式 ； 多目標進化演算法 ； 多目標H2/H∞導引法 ； 帕雷托最優解 ； Hamilton-Jacobin inequality (HJI) ； Linear matrix inequality (LMI) ； Multi-objective evolutionary algorithm (MOEA) ； Multi-objective (MO) H_2/H_∞ guidance law ； Pareto optimal solution

清華大學電機工程學系所學位論文

2017年

碩士

陳博現

英文

本文提出的多目標導引法，可以同時最佳化 H_2 和 H_∞ 目標。第一個設計目標為 H_2 控制，飛彈內部要能夠容忍在布朗連續雜訊及卜瓦松不連續雜訊下對目標做攔截，其中，飛彈模型內部的不確定性及陀螺儀因飛彈位移造成的累積誤差視為維納連續雜訊；為了因應目標突發性側向閃躲，造成飛彈達偵測誤判作則視為卜瓦松不連續雜訊。第二個設計目標 H_∞ 控制，則是濾掉在飛彈導航過程中的外部干擾，在本文視為目標的加速度。 本文透過間接法來處理多目標 H_2/H_∞ 飛彈導引問題，為了避免處理 Hamilton-Jacobin 不等式，本文提出模糊內插法將其轉為現性矩陣不等式，並運用多目標演化演算法來求解多目標 H_2/H_∞ 飛彈導引問題。最後，會透過一個模擬範例來說明設計步驟並驗證本文所提出的多目標 H_2/H_∞ 導引法的效能。

This study proposes a Multi-objective (MO) guidance law simultaneously for optimal H_2 missile interception with stochastic continuous Wiener noise and discontinuous Poisson jump noise as well as optimal H_∞ external disturbance filtering of external disturbance on missile guidance. The first design objective of optimal H_2 missile interception is to minimize the effect of intrinsic stochastic Wiener noise due to modeling uncertainty of the missile and the accumulated angle error of the gyroscope as well as the intrinsic stochastic Poisson jump noise due to the inaccurate radar measurement of the missile because of the target suddenly side-step maneuver. The second design objective of H_∞ external disturbance filtering is to minimize the effect of external disturbance due to the target’s acceleration on the missile guidance. An indirect method is proposed to solve the MO H_2/H_∞ guidance problem of missiles. In order to avoid solving a Hamilton-Jacobin inequality (HJI)-constrained MO H_2/H_∞ missile guidance problem based on Pareto optimal solution, fuzzy interpolation method is proposed to transform the HJI-constrained MO missile guidance problem to a linear matrix inequalities (LMIs)-constrained MO missile guidance problem. An LMIs-based MO Evolutionary Algorithm (MOEA) is also proposed to solve the MO H_2/H_∞ missile guidance problem. Finally, a simulation example is conducted to illustrate the design procedure and to validate the performance of the proposed MO H_2/H_∞ guidance law.

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