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.

摘要---------------------------------------------------------(i)
Abstract----------------------------------------------------(ii)
誌謝--------------------------------------------------------(iii)
Contents----------------------------------------------------(iv)
List of Figures----------------------------------------------(v)
List of Tables----------------------------------------------(vi)
Notations--------------------------------------------------(vii)
I. Introduction-------------------------------------------(1)
II. The 3-D Spherical Coordinates Stochastic
Missile Guidance System--------------------------------------(5)
III. MO H_2/H_∞ Guidance Control Design for
Nonlinear Stochastic Missile Systems------------------------(11)
IV. MO H_2/H_∞ Guidance Control Design via
Fuzzy Interpolation ----------------------------------------(15)
V. MO H_2/H_∞ Guidance Control of Nonlinear
Stochastic Missile System Design via LMIs-Constrained MOEA--(23)
VI. Simulation Example and Result------------------------(28)
VII. Conclusion------------------------------------------(38)
Appendix----------------------------------------------------(40)
Bibliography------------------------------------------------(61)

[1] G. M. Siouris, Mis1guidance and control systems. Springer Science & Business
Media, 2004.
[2] C.-F. Lin, Modern navigation, guidance, and control processing. Prentice Hall
Englewood Cliff s, 1991, vol. 2.
[3] A. S. Locke, Guidance. D. Van Nostrand Company, 1955, vol. 1.
[4] N. F. Palumbo, R. A. Blauwkamp, and J. M. Lloyd, “Basic principles of homing
guidance,” Johns Hopkins APL Technical Digest, vol. 29, no. 1, pp. 25–41, 2010.
[5] I. Rusnak, H. Weiss, R. Eliav, and T. Shima, “Missile guidance with constrained
intercept body angle,” IEEE Transactions on Aerospace and Electronic Systems,
vol. 50, no. 2, pp. 1445–1453, 2014.
[6] N. Dhananjay, K.-Y. Lum, and J.-X. Xu, “Proportional navigation with delayed line-
of-sight rate,” IEEE Transactions on Control Systems Technology, vol. 21, no. 1, pp.
247–253, 2013.
[7] K. D. S. Raj and I. S. S. Ganesh, “Estimation of line-of-sight rate in a homing mis-
sile guidance loop using optimal fi lters,” in Communications and Signal Processing
(ICCSP), 2015 International Conference on. IEEE, 2015, pp. 0398–0402.
62[8] C.-M. Lin and Y.-J. Mon, “Fuzzy-logic-based clos guidance law design,” IEEE Trans-
actions on Aerospace and Electronic Systems, vol. 37, no. 2, pp. 719–727, 2001.
[9] D. Dawson, Z. Qu, and F. Lewis, “Hybrid adaptive-robust control for a robot ma-
nipulator,” International journal of adaptive control and signal processing, vol. 6,
no. 6, pp. 537–545, 1992.
[10] Z. Koruba and L. Nocon, “Programmed control of the fl at track anti-tank guided
missile,” in Control Conference (ICCC), 2014 15th International Carpathian. IEEE,
2014, pp. 237–242.
[11] T.-H. Kim, C.-H. Lee, and M.-J. Tahk, “Time-to-go polynomial guidance with trajec-
tory modulation for observability enhancement,” IEEE Transactions on Aerospace
and Electronic Systems, vol. 49, no. 1, pp. 55–73, 2013.
[12] R. H. Venkatesan and N. K. Sinha, “A new guidance law for the defense missile
of nonmaneuverable aircraft,” IEEE Transactions on Control Systems Technology,
vol. 23, no. 6, pp. 2424–2431, 2015.
[13] C.-H. Lee, T.-H. Kim, and M.-J. Tahk, “Biased png for target observability en-
hancement against nonmaneuvering targets,” IEEE Transactions on Aerospace and
Electronic Systems, vol. 51, no. 1, pp. 2–17, 2015.
[14] C. Heller and I. Yaesh, “Proportional navigation with integral action,” in MELECON
2010-2010 15th IEEE Mediterranean Electrotechnical Conference. IEEE, 2010, pp.
1546–1550.
[15] M. Guelman, “Proportional navigation with a maneuvering target,” IEEE Transac-
tions on Aerospace and Electronic Systems, no. 3, pp. 364–371, 1972.
63[16] P.-J. Yuan and J.-S. Chern, “Ideal proportional navigation,” Journal of Guidance,
Control, and Dynamics, vol. 15, no. 5, pp. 1161–1165, 1992.
[17] C.-M. Lin, C.-F. Hsu, S.-K. Chang, and R.-J. Wai, “Guidance law evaluation for
missile guidance systems,” Asian Journal of Control, vol. 2, no. 4, pp. 243–250,
2000.
[18] C.-D. Yang and C.-C. Yang, “Analytical solution of generalized 3d proportional nav-
igation,” in Decision and Control, 1995., Proceedings of the 34th IEEE Conference
on, vol. 4. IEEE, 1995, pp. 3974–3979.
[19] Z. Xiong, J. Chen, Q. Li, and Z. Ren, “Time-varying lqr on hypersonic vehicle profi le-
following,” in Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on.
IEEE, 2014, pp. 994–998.
[20] G. Hexner, T. Shima, and H. Weiss, “An lqg guidance law with bounded acceleration
command,” in Decision and Control, 2003. Proceedings. 42nd IEEE Conference on,
vol. 1. IEEE, 2003, pp. 715–720.
[21] G. Hexner and H. Weiss, “Stochastic approach to optimal guidance with uncertain
intercept time,” IEEE Transactions on Aerospace and Electronic Systems, vol. 46,
no. 4, pp. 1804–1820, 2010.
[22] N. Harl and S. Balakrishnan, “Impact time and angle guidance with sliding mode
control,” IEEE Transactions on Control Systems Technology, vol. 20, no. 6, pp.
1436–1449, 2012.
[23] F.-K. Yeh, “Adaptive-sliding-mode guidance law design for missiles with thrust vec-
64tor control and divert control system,” IET control theory & applications, vol. 6,
no. 4, pp. 552–559, 2012.
[24] A. Zhurbal and M. Idan, “Eff ect of estimation on the performance of an integrated
missile guidance and control system,” IEEE Transactions on Aerospace and Elec-
tronic systems, vol. 47, no. 4, pp. 2690–2708, 2011.
[25] C. Hu, X. Hu, and S. Fang, “Fuzzy switched h∞ control for fl exible air-breathing
hypersonic vehicles,” in Guidance, Navigation and Control Conference (CGNCC),
2014 IEEE Chinese. IEEE, 2014, pp. 1895–1899.
[26] H.-J. Uang and B.-S. Chen, “Robust adaptive optimal tracking design for uncertain
missile systems: a fuzzy approach,” Fuzzy Sets and Systems, vol. 126, no. 1, pp.
63–87, 2002.
[27] B.-S. Chen, Y.-Y. Chen, and C.-L. Lin, “Nonlinear fuzzy h∞ guidance law with
saturation of actuators against maneuvering targets,” IEEE Transactions on Control
Systems Technology, vol. 10, no. 6, pp. 769–779, 2002.
[28] C.-L. Lin, H.-Z. Hung, Y.-Y. Chen, and B.-S. Chen, “Development of an integrated
fuzzy-logic-based missile guidance law against high speed target,” IEEE Transactions
on Fuzzy Systems, vol. 12, no. 2, pp. 157–169, 2004.
[29] H. O. Wang, K. Tanaka, and M. F. Griffi n, “An approach to fuzzy control of nonlinear
systems: Stability and design issues,” IEEE transactions on fuzzy systems, vol. 4,
no. 1, pp. 14–23, 1996.
[30] C.-L. Lin and T.-L. Wang, “Fuzzy side force control for missile against hypersonic
target,” IET Control Theory & Applications, vol. 1, no. 1, pp. 33–43, 2007.
65[31] C.-L. Lin and C.-L. Hwang, “A dynamically fuzzy gain–scheduled design for missile
autopilot,” The Aeronautical Journal (1968), vol. 107, no. 1076, pp. 599–606, 2003.
[32] J. A. Ball, J. W. Helton, and M. L. Walker, “h 2 /h∞ control for nonlinear systems
with output feedback,” IEEE Transactions on Automatic Control, vol. 38, no. 4, pp.
546–559, 1993.
[33] B.-S. Chen and C.-F. Wu, “Robust scheduling fi lter design for a class of nonlinear
stochastic poisson signal systems,” IEEE Transactions on Signal Processing, vol. 63,
no. 23, pp. 6245–6257, 2015.
[34] B.-S. Chen, W.-H. Chen, and H.-L. Wu, “Robust h 2 /h∞ global linearization fi lter
design for nonlinear stochastic systems,” IEEE Transactions on Circuits and Systems
I: Regular Papers, vol. 56, no. 7, pp. 1441–1454, 2009.
[35] S. Sivasundaram, Advances in dynamics and control. CRC Press, 2004, vol. 2.
[36] F. B. Hanson, Applied stochastic processes and control for Jump-diff usions: modeling,
analysis, and computation. Siam, 2007, vol. 13.
[37] P.-L. Chow, Stochastic partial diff erential equations. CRC Press, 2014.
[38] B.-S. Chen, H.-C. Lee, and C.-F. Wu, “Pareto optimal fi lter design for nonlinear
stochastic fuzzy systems via multiobjective h 2 /h∞ optimization,” IEEE Transactions
on Fuzzy Systems, vol. 23, no. 2, pp. 387–399, 2015.
[39] K. Tanaka and H. O. Wang, Fuzzy control systems design and analysis: a linear
matrix inequality approach. John Wiley & Sons, 2004.
66[40] B.-S. Chen, C.-S. Tseng, and H.-J. Uang, “Robustness design of nonlinear dynamic
systems via fuzzy linear control,” IEEE Transactions on fuzzy systems, vol. 7, no. 5,
pp. 571–585, 1999.
[41] A. Asrari, S. Lotfi fard, and M. S. Payam, “Pareto dominance-based multiobjective
optimization method for distribution network reconfi guration,” IEEE Transactions
on Smart Grid, vol. 7, no. 3, pp. 1401–1410, 2016.
[42] W.-Y. Chiu, H. Sun, and H. V. Poor, “A multiobjective approach to multimicrogrid
system design,” IEEE Transactions on Smart Grid, vol. 6, no. 5, pp. 2263–2272,
2015.
[43] W.-Y. Chiu, B.-S. Chen, and H. V. Poor, “A multiobjective approach for source
estimation in fuzzy networked systems,” IEEE Transactions on Circuits and Systems
I: Regular Papers, vol. 60, no. 7, pp. 1890–1900, 2013.
[44] Z. He, G. G. Yen, and J. Zhang, “Fuzzy-based pareto optimality for many-objective
evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, vol. 18,