### 博碩士論文 108323110 詳細資訊

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(Impact Angle Guidance Using Fast State-Dependent Differential Riccati Equation Scheme)

 ★ 使用快速觀測器的SDRE控制方案應用在電動車的馬達驅動系統 ★ 使用狀態相關Riccati方程式控制器設計實現雙輪機器人 ★ 基於快速狀態相關微分形式黎卡迪方程式導控策略對於機動目標的攔截於預先規畫之方向

based on the state-dependent differential Riccati equation (SDDRE) scheme,
and proposes a new theory that is effective and guarantees the applicability of
SDDRE and can greatly reduce the burden of online calculation by using prior
proofs. However, the applicability analysis is a complete classification and discussion
of the state space based on simple equivalence conditions. All inapplicable
situations, or it can be said that the situations encountered in the simulation
of failure points are newly discovered and effectively solved. Conditions almost
eliminate tedious online inspection procedures, which are equivalent conditions
recognized by complexity analysis and actual certification. On the other hand,
we analyzed the computational complexity of this SDDRE controller, first using
the library under the MATLAB® framework that most people use, and then using
the most advanced functions for comparison. The latter comes from extensive experimentation and comparison, and it is found to be sufficient to achieve the
best performance. Finally, the simulation enhances the confidence in the analysis
results, and at the same time enriches the value of robustness and versatility,
which is beneficial to the development of other guidance and control systems in
the field.

★ 導航
★ 控制系統

★ Control Systems

Abstract iv

2.1 攔截器的動力方程式................................................... 8
2.2 SDDRE 導引法概述..................................................... 11

3.1 等價適用性保證......................................................... 16

3.2 SDDRE 的一般複雜性.................................................. 31

4.1 具有故障點的快速適用性保證之展示.............................. 42
4.2 Riccati 方程的有效求解................................................ 48

A.1 攔截器攔截靜止的目標物............................................. 64
A.2 仿真攔截器攔截等速前進之目標物................................. 69

[1] R. V. Nanavati, S. R. Kumar, and A. Maity, “Lead-angle-based threedimensional
guidance for angle-constrained interception,” J. Guid. Control
Dyn., vol. 44, no. 1, pp. 190–199, 2021.
[2] S. R. Kumar and A. Maity, “Finite-horizon robust suboptimal control based
impact angle guidance,” IEEE Trans. Aerosp. Electron. Syst., vol. 56, no. 3,
pp. 1955–1965, 2020.
[3] R. V. Nanavati, S. R. Kumar, and A. Maity, “Spatial nonlinear guidance
strategies for target interception at pre-specified orientation,” Aerosp. Sci.
Technol., vol. 114, p. 106735, 2021.
[4] H. Li, J. Wang, S. He, and C. Lee, “Nonlinear optimal impact-angleconstrained
guidance with large initial heading error,” Journal of Guidance,
Control, and Dynamics, vol. 44, no. 9, pp. 1–14, 2021.
[5] Z. Wang, Q. Hu, T. Han, and M. Xin, “Two-stage guidance law with constrained
impact via circle involute,” IEEE Trans. Aerosp. Electron. Syst.,vol. 57, no. 2, pp. 1301–1316, 2021.
[6] C. Wang, W. Dong, J. Wang, and J. Shan, “Nonlinear suboptimal guidance
law with impact angle constraint: An SDRE-based approach,” IEEE Trans.
Aerosp. Electron. Syst., vol. 56, no. 6, pp. 4831–4840, 2020.
[7] B. Wang, Y. Sun, N. Zhao, and G. Gui, “Learn to coloring: Fast response to
perturbation in uav-assisted disaster relief networks,” IEEE Transactions
on Vehicular Technology, vol. 69, no. 3, pp. 3505–3509, 2020.
[8] S. He, C. Lee, H. Shin, and A. Tsourdos, “Minimum-effort waypointfollowing
guidance,” J. Guid. Control Dyn., vol. 42, no. 7, pp. 1551–1561,
2019.
[9] T. Çimen, “Survey of state-dependent Riccati equation in nonlinear optimal
feedback control synthesis,” J. Guid. Control Dyn., vol. 35, no. 4,
pp. 1025–1047, 2012.
[10] S. H. Song and I. J. Ha, “A Lyapunov-like approach to performance analysis
of 3-dimensional pure PNG laws,” IEEE Trans. Aerosp. Electron. Syst.,
vol. 30, no. 1, pp. 238–248, 1994.
[11] W. Bużantowicz, “Tuning of a linear-quadratic stabilization system for an
anti-aircraft missile,” Aerospace, vol. 8, no. 2, pp. 1–27, 2021.
[12] J. R. Cloutier, C. N. D’Souza, and C. P. Mracek, “Nonlinear regulation
and nonlinear H∞ control via the state-dependent Riccati equation technique:
Part 1, theory; part 2, examples,” in Proc. of the Internat. Conf. on
Nonlinear Probl. in Aviation and Aerosp., pp. 117–141, 1996.
[13] D. Haessig and B. Friedland, “State dependent differential Riccati equation
for nonlinear estimation and control,” in Proc. of the 15th IFAC Triennial
World Congress, vol. 35, pp. 405–410, 2002.
[14] A. Heydari, R. G. Landers, and S. N. Balakrishnan, “Optimal control approach
for turning process planning optimization,” IEEE Trans. Control
Syst. Technol., vol. 22, no. 4, pp. 1337–1349, 2014.
[15] A. Bavarsad, A. Fakharian, and M. B. Menhaj, “Nonlinear observer-based
optimal control of an active transfemoral prosthesis,” J. Cent. South Univ.,
vol. 28, no. 1, pp. 140–152, 2021.
[16] A. Ebrahimi, A. Mohammadi, and A. Kashaninia, “Suboptimal midcourse
guidance design using generalized model predictive spread control,”
Trans. Inst. Meas. Control, available online.
[17] Q. Mao, L. Dou, Z. Yang, B. Tian, and Q. Zong, “Fuzzy disturbance
observer-based adaptive sliding mode control for reusable launch vehicles with aeroservoelastic characteristic,” IEEE Trans. Ind. Informat., vol. 16,no. 2, pp. 1214–1223, 2020.
[18] S. Ozcan, M. U. Salamci, and V. Nalbantoglu, “Nonlinear sliding sector
design for multi-input systems with application to helicopter control,” Int.
J. Robust Nonlinear Control, vol. 30, no. 6, pp. 2248–2291, 2020.
[19] B. Qin, H. Sun, J. Ma, W. Li, T. Ding, and A. Zomaya, “RobustH∞ control
of doubly fed wind generator via state-dependent Riccati equation technique,”
IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2390–2400, 2019.
[20] P. Benner, Z. Bujanović, P. Kürschner, and J. Saak, “A numerical comparison
of different solvers for large-scale, continuous-time algebraic Riccati
equations and LQR problems,” SIAM J. Sci. Comput., vol. 42, no. 2,
pp. A957–A996, 2020.
[21] P. Khalili, S. Zolatash, R. Vatankhah, and S. Taghvaei, “Optimal control
methods for drug delivery in cancerous tumour by anti-angiogenic therapy
and chemotherapy,” IET Syst. Biol., vol. 15, no. 1, pp. 14–25, 2021.
[22] S. R. Nekoo, “Digital implementation of a continuous-time nonlinear optimal
controller: An experimental study with real-time computations,” ISA
T., vol. 101, pp. 346–357, Jun. 2020.
[23] L.-G. Lin, J. Vandewalle, and Y.-W. Liang, “Analytical representation of
the state-dependent coefficients in the SDRE/SDDRE scheme for multivariable
systems,” Automatica, vol. 59, pp. 106–111, Sep. 2015.
[24] Y. Huang and Y. Jia, “Nonlinear robust H∞ control for spacecraft bodyfixed
hovering around noncooperative target via modified θ – D method,”
IEEE Trans. Aerosp. Electron. Syst., vol. 55, no. 5, pp. 2451–2463, 2019.
[25] L.-G. Lin and M. Xin, “Impact angle guidance using state-dependent (differential)
Riccati equation: Unified applicability analysis,” J. Guid. Control
Dyn., vol. 43, no. 11, pp. 2175–2182, 2020.
[26] S. Kang, J. Wang, G. Li, J. Shan, and I. R. Petersen, “Optimal cooperative
guidance law for salvo attack: An MPC-based consensus perspective,”
IEEE Trans. Aerosp. Electron. Syst., vol. 54, no. 5, pp. 2397–2410, 2018.
[27] H. Tsukamoto, S.-J. Chung, and J.-J. E. Slotine, “Neural stochastic contraction
metrics for learning-based control and estimation,” IEEE Control
Syst. Lett., vol. 5, no. 5, pp. 1825–1830, 2021.
[28] M. Masoumnezhad, M. Saeedi, H. Yu, and H. Saberi Nik, “A Laguerre
spectral method for quadratic optimal control of nonlinear systems in a
semi-infinite interval,” Automatika, vol. 61, no. 3, pp. 461–474, 2020.
[29] T.-M. Huang, R.-C. Li, and W.-W. Lin in Structure-Preserving Doubling
Algorithms for Nonlinear Matrix Equations, vol. 14 of Fundamentals of
Algorithms, SIAM, Philadelphia, 2018.
[30] H. Rouzegar, A. Khosravi, and P. Sarhadi, “Spacecraft formation flying
control around L2 sun-earth libration point using on–off SDRE approach,”
Adv. Space Res., vol. 67, no. 7, pp. 2172–2184, 2021.
[31] K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. NJ,
USA: Prentice Hall, 1996.
[32] P. Benner and S. W. R. Werner, “MORLAB – A model order reduction
framework in MATLAB and Octave,” in Mathematical Software –
ICMS 2020 (A. M. Bigatti, J. Carette, J. H. Davenport, M. Joswig, and
T. de Wolff, eds.), vol. 12097 of Lecture Notes in Computer Science,
pp. 432–441, Cham, Switzerland:Springer International Publishing, 2020.
(“ml care nwt fac” and “ml lyap sgn” routines).
[33] G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD,
USA: Johns Hopkins University Press, 4th ed., 2013.
[34] R. H. Bartels and G. W. Stewart, “Solution of the matrix equation AX +
XB = C,” Commun. ACM, vol. 15, no. 9, pp. 820–826, 1972.
[35] G. H. Golub, S. Nash, and C. Van Loan, “A Hessenberg-Schur method for
the problem AX + XB = C,” IEEE Trans. Autom. Control, vol. 24, no. 6,
pp. 909–913, 1979.
[36] S. J. Hammarling, “Numerical solution of the stable, non-negative definite
Lyapunov equation,” IMA J. Numer. Anal., vol. 2, no. 3, pp. 303–323,
1982.
[37] N. J. Higham, “The scaling and squaring method for the matrix exponential
revisited,” SIAM J. Matrix Anal. Appl., vol. 26, no. 4, pp. 1179–1193, 2005.
[38] A. H. Al-Mohy and N. J. Higham, “A new scaling and squaring algorithm
for the matrix exponential,” SIAM J. Matrix Anal. A., vol. 31, no. 3,
pp. 970–989, 2010.
[39] C. Moler and C. Van Loan, “Nineteen dubious ways to compute the exponential
of a matrix, twenty-five years later,” SIAM Rev., vol. 45, no. 1,
pp. 3–49, 2003.
[40] M.-J. Yu and D. S. Bernstein, “Retrospective cost subsystem estimation
and smoothing for linear systems with structured uncertainty,” J. Aerosp.
Inf. Syst., vol. 15, no. 10, pp. 566–584, 2018.
[41] P. Van Dooren, “The generalized eigenstructure problem in linear system
theory,” IEEE Trans. Autom. Control, vol. 26, no. 1, pp. 111–129, 1981.
[42] C. Annam, A. Ratnoo, and D. Ghose, “Singular-perturbation-based guidance
of pulse motor interceptors with look angle constraints,” J. Guid. Control
Dyn., vol. 44, no. 7, pp. 1–15, 2021.
[43] P. Kee, L. Dong, and C. Siong, “Near optimal midcourse guidance law
for flight vehicle,” in 36th AIAA Aerospace Sciences Meeting and Exhibit,
p. 583, 1998.
[44] F. Imado, T. Kuroda, and M.-J. Tahk, “A new missile guidance algorithm
against a maneuvering target,” in Guidance, navigation, and control conference
and exhibit, p. 4114, 1998.