### 博碩士論文 110323135 詳細資訊

 以作者查詢圖書館館藏 、以作者查詢臺灣博碩士 、以作者查詢全國書目 、勘誤回報 、線上人數：3 、訪客IP：44.220.62.183

(Fast Maneuvering-Target Interception at Pre-Specified Orientation Based on the State-Dependent Differential Riccati Equation Scheme)

 ★ 使用快速狀態相關微分Riccati方程方案的衝擊角導引 ★ 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

1. 本電子論文使用權限為同意立即開放。
2. 已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
3. 請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

targets. More specifically, regarding the two major computational burdens using SDDRE, we have replaced the burden in numerical applicability checking by a simple, equivalent, and closed-form condition for the entire state space, which is actually the dominant burden as supported by complexity analysis and extensive validations. Notably, the proposed analysis not only complements the early findings of applicability guarantee in literature, but also promotes the efficiency of the proposed philosophy as compared to the classic method, where the latter has caused concerns/reservations due to its feasibility and difficulty. On the other hand, we have largely mitigated the second major burden of SDDRE by – after exhaustive trials – selecting the most efficient Riccati-equation solver until the latest benchmarks.

★ 空間導程角導引
★ 撞擊角限制
★ 機動目標攔截
★ 計算效率

★ impact angle constraint
★ maneuvering-target interception
★ computational efficiency

Abstract ii

1.1 研究動機 1
1.2 本文結構 6

3.1 術語與常用縮寫 12
3.2 動態攔截 12
3.3 SDDRE 導引法則概要 16

5.1 [1, Fig. 10] 的模擬重建 22
5.2 更具挑戰性的延伸設定 28
5.3 更多的延伸設定 32
5.4 實驗之總結 37

[2] S. R. Kumar and D. Mukherjee, “Three-dimensional nonsingular impact time guidance with limited field-of-view,” IEEE Trans. Control Syst. Technol., vol. 30, no. 4, pp. 1448–1459, 2022.
[3] M.-G. Seo, C.-H. Lee, and M.-J. Tahk, “New design methodology for impact angle control guidance for various missile and target motions,” IEEE Trans. Control Syst. Technol., vol. 26, no. 6, pp. 2190–2197, 2018.
[4] X. Chen and J. Wang, “Two-stage guidance law with impact time and angle constraints,” Nonlinear Dyn., vol. 95, no. 3, pp. 2575–2590, 2019.
[5] 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.
[6] S. R. Nekoo, J. Á. Acosta, G. Heredia, and A. Ollero, “A PD-type statedependent Riccati equation with iterative learning augmentation for mechanical systems,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 8, pp. 1499–1511, 2022.
[7] R. V. Nanavati, S. R. Kumar, and A. Maity, “Lead-angle-based threedimensional guidance for angle-constrained interception,” AIAA J. Guid. Control Dyn., vol. 44, no. 1, pp. 190–199, 2021.
[8] W. Zhang, W. Chen, and W. Yu, “Impact-angle and terminal maneuvering-acceleration constrained guidance against maneuvering target,” Aerospace, vol. 9, no. 1, 2022.
[9] 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.
[10] 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.
[11] T. Çimen, “Survey of state-dependent Riccati equation in nonlinear optimal feedback control synthesis,” AIAA J. Guid. Control Dyn., vol. 35, no. 4, pp. 1025–1047, 2012.
[12] S. Mathavaraj and R. Padhi, Satellite Formation Flying: High Precision Guidance using Optimal and Adaptive Control Techniques. Springer Nature: Singapore, 2021.
[13] B. Qin, R. Zhang, H. Li, T. Ding, and W. Liu, “Disturbance attenuation control for LVRT capability enhancement of doubly fed wind generators,” IET Gener. Transm. Distrib., vol. 15, no. 18, pp. 2582–2592, 2021.
[14] B. Qin, H. Sun, J. Ma, W. Li, T. Ding, and A. Zomaya, “Robust H∞ control of doubly fed wind generator via state-dependent Riccati equation technique,” IEEE Trans. Power Syst., vol. 34, no. 3, pp. 2390–2400, 2019.
[15] 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.
[16] O. Saleem and K. Mahmood-ul-Hasan, “Hierarchical adaptive control of self-stabilizing electromechanical systems using artificial-immune selftuning mechanism for state weighting-factors,” J. Mech. Sci. Technol., vol. 35, no. 3, pp. 1235–1250, 2021.
[17] W. F. Arnold III and A. J. Laub, “Generalized eigenproblem algorithms and software for algebraic Riccati equations,” Proc. IEEE, vol. 72, no. 12, pp. 1746–1754, 1984.
[18] B. Sarsembayev, D. Zholtayev, and T. D. Do, “Maximum power tracking of variable-speed wind energy conversion systems based on a near-optimal servomechanism control system,” Optim. Control Appl. Methods, vol. 43, no. 4, pp. 904–924, 2022.
[19] Y. Huang and Y. Jia, “Nonlinear robust H∞ control for spacecraft body-fixed hovering around noncooperative target via modified θ –D method,” IEEE Trans. Aerosp. Electron. Syst., vol. 55, no. 5, pp. 2451–2463, 2019.
[20] L.-G. Lin and M. Xin, “Impact angle guidance using state-dependent (differential) Riccati equation: Unified applicability analysis,” AIAA J. Guid. Control Dyn., vol. 43, no. 11, pp. 2175–2182, 2020.
[21] 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 International Conf. on Nonlinear Problems in Aviation and Aerospace, (Daytona Beach, FL, USA), pp. 117–141, 1996.
[22] 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.
[23] B.-S. Chen and W. Zhang, “Stochastic H2/H∞ control with state-dependent noise,” IEEE Trans. Autom. Control, vol. 49, no. 1, pp. 45–57, 2004.
[24] W. Bużantowicz, “Tuning of a linear-quadratic stabilization system for an anti-aircraft missile,” Aerospace, vol. 8, no. 2, pp. 1–27, 2021.
[25] 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.
[26] L.-G. Lin and M. Xin, “Missile guidance law based on new analysis and design of SDRE scheme,” AIAA J. Guid. Control Dyn., vol. 42, no. 4, pp. 853–868, 2019.
[27] O. Halbe and M. Hajek, “Online waypoint trajectory generation using state-dependent Riccati equation,” AIAA J. Guid. Control Dyn., vol. 42, no. 12, pp. 2687–2693, 2019.
[28] C.-C. Chen, Y.-W. Liang, and W.-M. Jhu, “Global stability of a system with state-dependent Riccati equation controller,” AIAA J. Guid. Control Dyn., vol. 38, no. 10, pp. 2050–2054, 2015.
[29] A. Bracci, M. Innocenti, and L. Pollini, “Estimation of the region of attraction for state-dependent Riccati equation controllers,” AIAA J. Guid. Control Dyn., vol. 29, no. 6, pp. 1427–1430, 2006.
[30] K. D. Hammett, C. D. Hall, and D. B. Ridgely, “Controllability issues in nonlinear state-dependent Riccati equation control,” AIAA J. Guid. Control Dyn., vol. 21, no. 5, pp. 767–773, 1998.
[31] A. Heydari and S. N. Balakrishnan, “Path planning using a novel finite horizon suboptimal controller,” AIAA J. Guid. Control Dyn., vol. 36, no. 4, pp. 1210–1214, 2013.
[32] F. Topputo, M. Miani, and F. Bernelli-Zazzera, “Optimal selection of the coefficient matrix in state-dependent control methods,” AIAA J. Guid. Control Dyn., vol. 38, no. 5, pp. 861–873, 2015.
[33] M. Sznaier, J. Cloutier, R. Hull, D. Jacques, and C. Mracek, “Receding horizon control Lyapunov function approach to suboptimal regulation of nonlinear systems,” AIAA J. Guid. Control Dyn., vol. 23, no. 3, pp. 399– 405, 2000.
[34] L.-G. Lin and M. Xin, “Guaranteed continuity and computational improvement in SDRE controllers for cancer treatment analysis,” ASME J. Dyn. Sys., Meas., Control, vol. 142, no. 4, pp. 041005 (1–12), 2020.
[35] X. Wang, “Discrete time-coupled state-dependent Riccati equation control of nonlinear mechatronic systems,” ASME J. Dyn. Sys., Meas., Control, vol. 142, no. 8, pp. 081008 (1–8), 2020.
[36] X. Wang, E. E. Yaz, and S. C. Schneider, “Coupled state-dependent Riccati equation control for continuous time nonlinear mechatronics systems,” ASME J. Dyn. Sys., Meas., Control, vol. 140, no. 11, pp. 111013 (1–10), 2018.
[37] S. M. Ghadami, R. Amjadifard, and H. Khaloozadeh, “Optimizing a class of nonlinear singularly perturbed systems using SDRE technique,” J. Dyn. Sys., Meas., Control, vol. 136, no. 1, pp. 011003(1–13), 2014.
[38] B. Friedland, “New results in quasi-optimum control,” J. Dyn. Syst. Meas. Control-Trans. ASME, vol. 129, no. 1, pp. 96–99, 2007.
[39] W. Langson and A. Alleyne, “A stability result with application to nonlinear regulation,” J. Dyn. Syst. Meas. Control-Trans. ASME, vol. 124, no. 3, pp. 452–456, 2002.
[40] 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, 2015.
[41] Y.-W. Liang and L.-G. Lin, “Analysis of SDC matrices for successfully implementing the SDRE scheme,” Automatica, vol. 49, no. 10, pp. 3120– 3124, 2013.
[42] M. Jiménez-Lizárraga, M. Basin, V. Rodríguez, and P. Rodríguez, “Open-loop Nash equilibrium in polynomial differential games via statedependent Riccati equation,” Automatica, vol. 53, pp. 155–163, 2015.
[43] A. Wernli and G. Cook, “Suboptimal control for the nonlinear quadratic regulator problem,” Automatica, vol. 11, no. 1, pp. 75–84, 1975.
[44] T. Yoshida and K. A. Loparo, “Quadratic regulatory theory for analytic non-linear systems with additive controls,” Automatica, vol. 25, no. 4, pp. 531–544, 1989.
[45] J. Yu, A. Jadbabaie, J. Primbs, and Y. Huang, “Comparison of nonlinear control design techniques on a model of the Caltech ducted fan,” Automatica, vol. 37, no. 12, pp. 1971–1978, 2001.
[46] H. Dongfang and S. Ling, “Guaranteed cost control of affine nonlinear systems via partition of unity method,” Automatica, vol. 49, no. 2, pp. 660–666, 2013.
[47] V. N. Afanas’ev, “Control of nonlinear plants with state-dependent coefficients,” Autom. Remote Control, vol. 72, no. 4, pp. 713–726, 2011.
[48] V. N. Afanas’ev, “Control of nonlinear uncertain object in the problem of motion along the given trajectory,” Autom. Remote Control, vol. 76, no. 1, pp. 1–15, 2011.
[49] R. S. Lima and F. R. Chavarette, “Nonlinear dynamics, chaos and control of the Hindmarsh-Rose neuron model,” Bol. Soc. Paran. Mat., available online, doi: 10.5269/bspm.47770.
[50] L.-G. Lin and W.-W. Lin, “Computationally efficient SDRE control design for 3-DOF helicopter benchmark system,” IEEE Trans. Aerosp. Electron. Syst., vol. 57, pp. 3320–3336, 2021.
[51] R. Babazadeh and R. Selmic, “Distance-based multi-agent formation control with energy constraints using SDRE,” IEEE Trans. Aerosp. Electron. Syst., vol. 56, no. 1, pp. 41–56, 2020.
[52] J. Burghart, “A technique for suboptimal feedback control of nonlinear systems,” IEEE Trans. Autom. Control, vol. 14, no. 5, pp. 530–533, 1969.
[53] J. S. Shamma and J. R. Cloutier, “Existence of SDRE stabilizing feedback,” IEEE Trans. Autom. Control, vol. 48, no. 3, pp. 513–517, 2003.
[54] J. W. Curtis and R. W. Beard, “Satisficing: a new approach to constructivenonlinear control,” IEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1090– 1102, 2004.
[55] Y. Pan, K. D. Kumar, G. Liu, and K. Furuta, “Design of variable structure control system with nonlinear time-varying sliding sector,” IEEE Trans. Autom. Control, vol. 54, no. 8, pp. 1981–1986, 2009.
[56] Y. Sun, “Linear controllability versus global controllability,” IEEE Trans. Autom. Control, vol. 54, no. 7, pp. 1693–1697, 2009.
[57] A. P. Dani, S.-J. Chung, and S. Hutchinson, “Observer design for stochastic nonlinear systems via contraction-based incremental stability,” IEEE Trans. Autom. Control, vol. 60, no. 3, pp. 700–714, 2015.
[58] T. Mylvaganam, M. Sassano, and A. Astolfi, “Constructive ϵ-Nash equilibria for nonzero-sum differential games,” IEEE Trans. Autom. Control, vol. 60, no. 4, pp. 950–965, 2015.
[59] L.-G. Lin and M. Xin, “Alternative SDRE scheme for planar systems,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 66, no. 6, pp. 998–1002, 2019.
[60] L.-G. Lin, Y.-W. Liang, and W.-Y. Hsieh, “Convex quadratic equation,” J. Optim. Theory Appl., vol. 186, pp. 1006–1028, Sep. 2020.
[61] L.-G. Lin, Y.-W. Liang, and L.-J. Cheng, “Control for a class of secondorder systems via a state-dependent Riccati equation approach,” SIAM J. Control Optim., vol. 56, no. 1, pp. 1–18, 2018.
[62] D. McCaffrey and S. P. Banks, “Lagrangian manifolds and asymptotically optimal stabilizing feedback control,” Syst. Control Lett., vol. 43, no. 3, pp. 219–224, 2001.
[63] T. Çimen and S. P. Banks, “Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria,” Syst. Control Lett., vol. 53, no. 5, pp. 327–346, 2004.
[64] T. Kwon and J. K. Hodgins, “Momentum-mapped inverted pendulum models for controlling dynamic human motions,” ACM Trans. Graph, vol. 36, no. 1, pp. 10:1–10:14, 2017.
[65] S.-W. Kim, S.-Y. Park, and C. Park, “Spacecraft attitude control using neuro-fuzzy approximation of the optimal controllers,” Adv. Space Res, vol. 57, no. 1, pp. 137–152, 2016.
[66] H.-E. Park and Y.-R. Kim, “Relative navigation for autonomous formation flying satellites using the state-dependent Riccati equation filter,” Adv. Space Res., vol. 57, no. 1, pp. 166–182, 2016.
[67] Z. W. Tan, R. Fonod, and T. Shima, “Cooperative guidance law for target pair to lure two pursuers into Collision,” J. Guid. Control Dyn., vol. 41, no. 8, pp. 1687–1699, 2018.
[68] A. Bogdanov and E. Wan, “State-dependent Riccati equation control for small autonomous helicopters,” AIAA J. Guid. Control Dyn., vol. 30, no. 1, pp. 47–60, 2007.
[69] R. R. Harman and I. Y. Bar-Itzhack, “Pseudolinear and state-dependent Riccati equation filters for angular rate estimation,” J. Guid. Control Dyn., vol. 22, no. 5, pp. 723–725, 1999.
[70] M. He, “Data-driven approximated optimal control for chemical processes with state and input constraints,” Complexity, vol. 2019, pp. 1–11, 2019.
[71] P. Khalili and R. Vatankhah, “Derivation of an optimal trajectory and nonlinear adaptive controller design for drug delivery in cancerous tumor chemotherapy,” Comput. Biol. Med., vol. 109, pp. 195–206, 2019.
[72] M. Y. Arafat and S. Moh, “Localization and clustering based on swarm intelligence in UAV networks for emergency communications,” IEEE Internet Things J., vol. 6, no. 5, pp. 8958–8976, 2019.
[73] M. Sharifi, A. A. Jamshidi, and N. N. Sarvestani, “An adaptive robust control strategy in a cancer tumor-immune system under uncertainties,” IEEE/ACM Trans. Comput. Biol. Bioinf., vol. 16, no. 3, pp. 865–873, 2019.
[74] L.-G. Lin and M. Xin, “Nonlinear control of two-wheeled robot based on novel analysis and design of SDRE scheme,” IEEE Trans. Control Syst. Technol., vol. 28, no. 3, pp. 1140–1148, 2020.
[75] A. P. Dani, I. Salehi, G. Rotithor, D. Trombetta, and H. Ravichandar, “Human-in-the-loop robot control for human-robot collaboration: Human intention estimation and safe trajectory tracking control for collaborative tasks,” IEEE Control Syst. Mag., vol. 40, no. 6, pp. 29–56, 2020.
[76] Y. Batmani, M. Davoodi, and N. Meskin, “Nonlinear suboptimal tracking controller design using state-dependent Riccati equation technique,” IEEE Trans. Control Syst. Technol., vol. 25, no. 5, pp. 1833–1839, 2017.
[77] E. B. Erdem and A. G. Alleyne, “Design of a class of nonlinear controllers via state dependent Riccati equations,” IEEE Trans. Control Syst. Technol., vol. 12, no. 1, pp. 133–137, 2004.
[78] W. Ren and R. W. Beard, “Trajectory tracking for unmanned air vehicles with velocity and heading rate constraints,” IEEE Trans. Control Syst. Technol., vol. 12, no. 5, pp. 706–716, 2004.
[79] R. Padhi and S. N. Balakrishnan, “Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics,” IEEE Trans. Control Syst. Technol., vol. 14, no. 4, pp. 628–640, 2006.
[80] J. Villagra, B. d’Andréa Novel, H. Mounier, and M. Pengov, “Flatnessbased vehicle steering control strategy with SDRE feedback gains tuned via a sensitivity approach,” IEEE Trans. Control Syst. Technol., vol. 15, no. 3, pp. 554–565, 2007.
[81] Š. Janouš, J. Talla, V. Šmídl, and Z. Peroutka, “Constrained LQR control of dual induction motor single inverter drive,” IEEE Trans. Ind. Electron., vol. 68, no. 7, pp. 5548–5558, 2021.
[82] F. Ornelas-Tellez, J. J. Rico-Melgoza, R. Morfin-Magaña, and S. Ramos- Paz, “Optimal dynamic harmonic extraction and suppression in power conditioning applications,” IEEE Trans. Ind. Electron., vol. 67, no. 9, pp. 7909–7918, 2020.
[83] 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.
[84] Y. Batmani, M. Davoodi, and N. Meskin, “Event-triggered suboptimal tracking controller design for a class of nonlinear discrete-time systems,” IEEE Trans. Ind. Electron., vol. 64, no. 10, pp. 8079–8087, 2017.
[85] V. Šmídl, Š. Janouš, L. Adam, and Z. Peroutka, “Direct speed control of a PMSM drive using SDRE and convex constrained optimization,” IEEE Trans. Ind. Electron., vol. 65, no. 1, pp. 532–542, 2018.
[86] O. Špinka, O. Holub, and Z. Hanzálek, “Low-cost reconfigurable control system for small UAVs,” IEEE Trans. Ind. Electron., vol. 58, no. 3, pp. 880–889, 2011.
[87] H. T. Banks, S. C. Beeler, G. M. Kepler, and H. T. Tran, “Reduced order modeling and control of thin film growth in an HPCVD reactor,” SIAM J. Appl. Math., vol. 62, pp. 1251–1280, 2002.
[88] T. Do, H. Choi, and J. Jung, “SDRE-based near optimal control system design for PM synchronous motor,” IEEE Trans. Ind. Electron., vol. 59, no. 11, pp. 4063–4074, 2012.
[89] T. D. Do, S. Kwak, H. H. Choi, and J.-W. Jung, “Suboptimal control scheme design for interior permanent magnet synchronous motors: An SDRE-based approach,” IEEE Trans. Power Electron., vol. 29, no. 6, pp. 3020–3031, 2014.
[90] Y.-W. Liang, C.-C. Chen, D.-C. Liaw, and Y.-T. Wei, “Nonlinear reliable control with application to a vehicle antilock brake system,” IEEE Trans. Ind. Inform., vol. 9, no. 4, pp. 2114–2123, 2013.
[91] J. Pittner and M. A. Simaan, “Improving the availability of tandem hot metal strip rolling: The use of fault-tolerant techniques with virtual rolling,” IEEE Ind. Appl. Mag., vol. 25, no. 4, pp. 66–76, 2019.
[92] J. Pittner and M. A. Simaan, “Streamlining the tandem hot-metal-strip mill: Threading progress stems from the use of advanced control with virtual rolling,” IEEE Ind. Appl. Mag., vol. 24, no. 2, pp. 35–44, 2018.
[93] F. Kara and M. U. Salamci, “Model reference adaptive sliding surface design for nonlinear systems,” IEEE Trans. Ind Appl., vol. 54, no. 1, pp. 611–624, 2018.
[94] L.-G. Lin, “Computationally improved state-dependent Riccati equation scheme for nonlinear benchmark system,” IEEE/ASME Trans. Mechatronics, vol. 26, no. 2, pp. 1064–1075, 2021.
[95] S. Kim and S. J. Kwon, “Nonlinear optimal control design for underactuated two-wheeled inverted pendulum mobile platform,” IEEE/ASME Trans. Mechatronics, vol. 22, no. 6, pp. 2803–2808, 2017.
[96] L. Mellal, D. Folio, K. Belharet, and A. Ferreira, “Modeling of optimal targeted therapies using drug-loaded magnetic nanoparticles for liver cancer,” IEEE Trans. Nanobiosci., vol. 15, no. 3, pp. 265–274, 2016.
[97] L.-G. Lin and M. Xin, “Computational enhancement of the SDRE scheme: General theory and robotic control system,” IEEE Trans. Robot., vol. 36, no. 3, pp. 875–893, 2020.
[98] F. Ornelas-Tellez, J. J. Rico-Melgoza, E. Espinosa-Juarez, and E. N. Sanchez, “Optimal and robust control in DC microgrids,” IEEE Trans. Smart Grid, vol. 9, no. 6, pp. 5543–5553, 2018.
[99] M. Davoodi and J. M. Velni, “Heterogeneity-aware graph partitioning for distributed deployment of multiagent systems,” IEEE Trans. Cybern., vol. 52, no. 4, pp. 2578–2588, 2022.
[100] Y. Batmani and S. Najafi, “Event-triggeredH∞ depth control of remotely operated underwater vehicles,” IEEE Trans. Syst. Man Cybern. -Syst., vol. 51, no. 2, pp. 1224–1232, 2021.
[101] X. Wang, M. Reitz, and E. E. Yaz, “Field oriented sliding mode control of surface-mounted permanent magnet ac motors: Theory and applications to electrified vehicles,” IEEE Trans. Veh. Technol., vol. 67, no. 11, pp. 10343–10356, 2018.
[102] M. Kleindienst, M. Reichhartinger, M. Horn, and F. Staudegger, “Observer-based temperature control of an LED heated silicon wafer,” J. Process Control, vol. 70, pp. 96–108, 2018.
[103] R. Manikandan and N. Saha, “Dynamic modelling and non-linear control of TLP supported offshore wind turbine under environmental loads,” Mar. Struct., vol. 64, pp. 263–294, 2019.
[104] M. F. Hamza, H. J. Yap, I. A. Choudhury, A. I. Isa, A. Y. Zimit, and T. Kumbasar, “Current development on using Rotary Inverted Pendulum as a benchmark for testing linear and nonlinear control algorithms,” Mech. Syst. Signal Proc., vol. 116, pp. 347–369, 2019.
[105] A. M. Tusset, J. M. Balthazar, R. T. Rocha, M. A. Ribeiro, and W. B. Lenz, “On suppression of chaotic motion of a nonlinear MEMS oscillator,” Nonlinear Dyn., vol. 99, pp. 537–557, 2020.
[106] P. Razzaghi, E. Al Khatib, and Y. Hurmuzlu, “Nonlinear dynamics and control of an inertially actuated jumper robot,” Nonlinear Dyn., vol. 97, no. 1, pp. 161–176, 2019.
[107] J. M. Balthazar, A. M. Tusset, R. M. L. R. F. Brasil, J. L. P. Felix, R. T. Rocha, F. C. Janzen, A. Nabarrete, and C. Oliveira, “An overview on the appearance of the Sommerfeld effect and saturation phenomenon in nonideal vibrating systems (NIS) in macro and MEMS scales,” Nonlinear Dyn., vol. 93, no. 1, pp. 19–40, 2018.
[108] S. Kilicaslan, “Control of active suspension system considering nonlinear actuator dynamics,” Nonlinear Dyn., vol. 91, no. 2, pp. 1383–1394, 2018.
[109] A. Keymasi Khalaji and H. Tourajizadeh, “Nonlinear Lyapounov based control of an underwater vehicle in presence of uncertainties and obstacles,” Ocean Eng., vol. 198, pp. 106998 (1–9), 2020.
[110] A. K. D. Velayudhan, “Design of a supervisory fuzzy logic controller for monitoring the inflow and purging of gas through lift bags for a safe and viable salvaging operation,” Ocean Eng., vol. 171, pp. 193–201, 2019.
[111] H. Huang, S. Sharma, Y. Zhuang, and D. Xu, “Dynamic positioning of an uninhabited surface vehicle using state-dependent Riccati equation and pseudospectral method,” Ocean Eng., vol. 133, pp. 215–223, 2017. (Details of the Springer USV are available at plymouth.ac.uk/research/ autonomous-marine-systems/springer).
[112] L. M. Sanchez-Rodriguez, Y. Iturria-Medina, E. A. Baines, S. C. Mallo, M. Dousty, R. C. Sotero, and et al., “Design of optimal nonlinear network controllers for Alzheimer’s disease,” PLoS Comput. Biol., vol. 14, no. 5, p. e1006136, 2018.
[113] M. Y. Ovchinnikov and D. S. Roldugin, “A survey on active magnetic attitude control algorithms for small satellites,” Prog. Aerosp. Sci., vol. 109, p. 100546, 2019.
[114] A. S. Saeed, A. B. Younes, C. Cai, and G. Cai, “A survey of hybrid unmanned aerial vehicles,” Prog. Aero. Sci., vol. 98, pp. 91–105, Apr. 2018.
[115] M. Abolvafaei and S. Ganjefar, “Maximum power extraction from wind energy system using homotopy singular perturbation and fast terminal sliding mode method,” Renew. Energy, vol. 148, pp. 611–626, Apr. 2020.
[116] M. R. Arabshahi, H. Torkaman, M. Bagheri, and A. Keyhani, “On the modelling, analysis, and design of a suboptimal controller for a class of wind/PV/battery based DC microgrid,” IET Renew. Power Gener., vol. 16, no. 2, pp. 416–434, 2022.
[117] M. H. Korayem and S. R. Nekoo, “Controller design of cooperative manipulators using state-dependent Riccati equation,” Robotica, pp. 1–32, 2017.
[118] A. H. Korayem, M. Irani Rahagi, H. Babaee, and M. H. Korayem, “Maximum load of flexible joint manipulators using nonlinear controllers,” Robotica, vol. 35, no. 1, pp. 119–142, 2017.
[119] M. A. Simaan and J. Pittner, “Mill control system and method for control of metal strip rolling,” 2015.
[120] Q. M. Lam, M. Xin, and J. R. Cloutier, “SDRE control stability criteria and convergence issues: Where are we today addressing practitioners’ concerns?,” in AIAA Paper 2012-2475, 2012.
[121] T. Çimen, “Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method,” Annu. Rev. Control, vol. 34, no. 1, pp. 32–51, 2010.
[122] R. P. M. Chan, K. A. Stol, and C. R. Halkyard, “Review of modelling and control of two-wheeled robots,” Annu. Rev. Control, vol. 37, no. 1, pp. 89–103, 2013.
[123] E. B. Erdem and A. G. Alleyne, “Estimation of stability regions of SDRE controlled systems using vector norms,” in American Control Conf., pp. 80–85, IEEE, 2002.
[124] P. Seiler, “Stability region estimates for SDRE controlled systems using sum of squares optimization,” in American Control Conf., vol. 3, pp. 1867–1872, IEEE, 2003.
[125] I. Chang and S. J. Chung, “Exponential stability region estimates for the state-dependent Riccati equation controllers,” in Proc. of the 48th IEEE Conf. on Decision and Control, pp. 1974–1979, IEEE, 2009.
[126] Y. Danik and M. Dmitriev, “The construction of stabilizing regulators sets for nonlinear control systems with the help of Padé approximations,” in Nonlinear Dynamics of Discrete and Continuous Systems (A. K. Abramian, I. V. Andrianov, and V. A. Gaiko, eds.), ch. 4, Springer, Cham, 2021.
[127] Y.-W. Liang and L.-G. Lin, “On factorization of the nonlinear drift term for SDRE approach,” in Proc. of the 18th IFAC Triennial World Congress, vol. 44, pp. 9607–9612, 2011.
[128] K. D. Hammett, Control of Nonlinear Systems via State Feedback State- Dependent Riccati Equation Techniques. PhD thesis, 1997.
[129] S. P. Banks and K. J. Mhana, “Optimal control and stabilization for nonlinear systems,” IMA J. Math. Control Inf., vol. 9, no. 2, pp. 179–196, 1992.
[130] Q. M. Lam and M. W. Oppenheimer, “Investigation of adaptive SDRE control reconfiguration subject to control surface failures,” in AIAA Infotech@ Aerospace, (Atlanta, Georgia), April 2010.
[131] Q. M. Lam, M. Xin, and J. R. Cloutier, “A view of SDRE control methods as one branch of indirect adaptive control,” in AIAA Infotech@Aerospace, Garden Grove, California, June 2012.
[132] Q. Lam, P. Krishnamurthy, and F. Khorrami, “Enhancing flight control system performance using SDRE based controller as an augmentation layer,” in AIAA Guidance, Navigation, and Control Conf., (Chicago, Illinois), August 2009.
[133] A. Jones and A. Astolfi, “On the solution of optimal control problems using parameterized state-dependent Riccati equations,” in 59th IEEE Conf. on Decis. and Control, pp. 1098–1103, 2020.
[134] X. Liu, X. Xin, Z. Li, and Z. Chen, “Near optimal control based on the tensor-product technique,” IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 64, no. 5, pp. 560–564, 2017.
[135] Z. Qu and J. R. Cloutier, “A new suboptimal control design for cascaded non-linear systems,” Optim. Control Appl. Methods, vol. 23, no. 6, pp. 303–328, 2002.
[136] C. P. Mracek and J. R. Cloutier, “Control designs for the nonlinear benchmark problem via the state-dependent Riccati equation method,” Int. J. Robust Nonlinear Control, vol. 8, no. 4-5, pp. 401–433, 1998.
[137] J. W. Curtis and R. W. Beard, “Ensuring stability of state-dependent Riccati equation controllers via satisficing,” in Proc. of the 41st IEEE Conf. on Decision and Control, vol. 3, pp. 2645–2650, IEEE, 2002.
[138] J. W. Curtis and R. W. Beard, “A complete parameterization of clf-based input-to-state stabilizing control laws,” Int. J. Robust Nonlinear Control, vol. 14, no. 17, pp. 1393–1420, 2004.
[139] M. S. Naik and S. N. Singh, “State-dependent Riccati equation-based robust dive plane control of AUV with control constraints,” Ocean Eng., vol. 34, no. 11, pp. 1711–1723, 2007.
[140] P. Jantapremjit and P. A. Wilson, “Control and guidance for homing and docking tasks using an autonomous underwater vehicle,” in Intelligent Robots and Systems (IROS), IEEE/RSJ International Conference on, pp. 3672–3677, 2007.
[141] H. Pan and M. Xin, “Depth control of autonomous underwater vehicles using indirect robust control method,” in American Control Conf., pp. 6216–6221, 2012.
[142] H. Pan and M. Xin, “Depth control of autonomous underwater vehicles using indirect robust control method,” Int. J. Control, vol. 85, no. 1, pp. 98–113, 2012.
[143] M. Xin and H. Pan, “Integrated nonlinear optimal control of spacecraft in proximity operations,” Int. J. Control, vol. 83, no. 2, pp. 347–363, 2010.
[144] R. Padmanabhan, N. Meskin, and A.-E. Al Moustafa, Mathematical Models of Cancer and Different Therapies: Unified Framework. Springer, 2021.
[145] L. Mellal, D. Folio, K. Belharet, and A. Ferreira, “Modeling approach of transcatheter arterial delivery of drug-loaded magnetic nanoparticles,” in The Encyclopedia of Medical Robotics (J. P. Desai, R. Patel, A. Ferreira, and S. Agrawal, eds.), vol. 2: Micro and Nano Robotics in Medicine, ch. 10, pp. 207–229, Singapore: World Scientific, 2018.
[146] A. M. Tusset, V. Piccirillo, and J. M. Balthazar, “A note on SDRE control applied in predator-prey model: Biological control of spider mite panonychus ulmi,” J. Biol. Syst., vol. 24, no. 2, pp. 333–344, 2016.
[147] S. Nansai, M. R. Elara, and M. Iwase, “Dynamic hybrid position force control using virtual internal model to realize a cutting task by a snakelike robot,” in IEEE International Conference on 6th Biomedical Robotics and Biomechatronics (BioRob), pp. 151–156, 2016.
[148] H. T. Banks, S. C. Beeler, H. D. Kwon, B. M. Lewis, J. A. Toivanen, and H. T. Tran, “An SDRE-based approach for HIV feedback control and control of thin film growth in a CVD reactor,” in Proc. of the 18th IFAC Triennial World Congress, vol. 18, pp. 9601–9606, 2011.
[149] M. Itik, M. U. Salamci, and S. P. Banks, “SDRE optimal control of drug administration in cancer treatment,” Turk. J. Electr. Eng. Comput. Sci., vol. 18, no. 5, pp. 715–729, 2010.
[150] V. Polito, “Nonlinear business cycle and optimal policy: A VSTAR perspective,” CESifo Working Paper Series, no. 8060, pp. 1–54, 2020.
[151] V. Manousiouthakis and D. J. Chmielewski, “On constrained infinite-time nonlinear optimal control,” Chem. Eng. Sci., vol. 57, no. 1, pp. 105—114, 2002.
[152] Y. Chen, V. Manousiouthakis, and T. Edgar, “Globally optimal nonlinear feedback: Application to nonisothermal CSTR control,” Chem. Eng. Commun., vol. 193, no. 2, pp. 233–245, 2006.
[153] S. Kanarachos, M. Alirezaei, S. Jansen, and J. P. Maurice, “Control allocation for regenerative braking of electric vehicles with an electric motor at the front axle using the state-dependent Riccati equation control technique,” P. I. Mech. Eng. D-J. Aut., vol. 228, no. 2, pp. 129–143, 2014.
[154] M. Alirezaei, S. Kanarachos, B. Scheepers, and J. P. Maurice, “Experimental evaluation of optimal vehicle dynamic control based on the state dependent Riccati equation technique,” in American Control Conf., pp. 408–412, IEEE, 2013.
[155] Y.-W. Liang, Y.-T. Wei, D.-C. Liaw, C.-C. Cheng, and L.-G. Lin, “A study of SDRE and ISMC combined scheme with application to vehicle brake control,” in SICE Annual Conference, Proceedings of, pp. 497–502, IEEE, 2010.
[156] 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.
[157] A. Al-Tamimi, M. Abu-Khalaf, and F. Lewis, “Heuristic dynamic programming nonlinear optimal controller,” Mach. Learn., pp. 361–380, 2009.
[158] M. H. Korayem and S. R. Nekoo, “The SDRE control of mobile base cooperative manipulators: Collision free path planning and moving obstacle avoidance,” Robot. Auton. Syst., vol. 86, pp. 86–105, 2016.
[159] M. H. Korayem, A. Zehfroosh, H. Tourajizadeh, and S. Manteghi, “Optimal motion planning of non-linear dynamic systems in the presence of obstacles and moving boundaries using SDRE: Application on cablesuspended robot,” Nonlinear Dyn., vol. 76, no. 2, pp. 1423–1441, 2014.
[160] M. H. Korayem and S. R. Nekoo, “State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities,” ISA Transactions, vol. 57, pp. 117–135, 2015.
[161] S. Stępień and P. Superczyńska, “Modified infinite-time state-dependent Riccati equation method for nonlinear affine systems: Quadrotor control,” Appl. Sci., vol. 11, no. 22, p. 10714, 2021.
[162] A. Nemra and N. Aouf, “Robust INS/GPS sensor fusion for UAV localization using SDRE nonlinear filtering,” IEEE Sens. J., vol. 10, no. 4, pp. 789–798, 2010.
[163] R. Guo, A. Wu, Z. Lang, and X. Zhang, “A nonlinear attitude control method for an unmanned helicopter,” in Informatics in Control, Automation and Robotics (CAR), 2nd International Asia Conference on, vol. 1, pp. 166–169, IEEE, 2010.
[164] C.-D. Yang, C.-W. Chaung, and C.-H. Kuo, “Evaluating qubit control performance by indices of quantum entanglement,” J. Phys. Sci., vol. 7, no. 5, pp. 1–18, 2017.
[165] Y.-L. Kuo, “Glucose concentration regulation using the SDRE-based sliding mode control,” J. Chin. Inst. Eng., vol. 41, no. 1, pp. 26–31, 2018.
[166] F. Tyan and J.-F. Shen, “SDRE missile guidance law,” in Control and Automation (ICCA), 8th IEEE International Conf. on, pp. 866–870, IEEE, 2010.
[167] D. Folio and A. Ferreira, “Modeling and estimation of self-phoretic magnetic Janus microrobot with uncontrollable inputs,” IEEE Trans. Control Syst. Technol., vol. 30, no. 6, pp. 2681–2688, 2022.
[168] D. Bhattacharjee and K. Subbarao, “Set-membership filter for discretetime nonlinear systems using state dependent coefficient parameterization,” IEEE Trans. Autom. Control, vol. 67, no. 2, pp. 894–901, 2022.
[169] P. Parvathy and J. Jacob, “Inverse optimal control via diagonal stabilization applied to attitude tracking of a reusable launch vehicle,” J. Optim. Theory Appl., vol. 191, no. 2, pp. 794–822, 2021.
[170] P. Razzaghi, E. Al Khatib, S. Bakhtiari, and Y. Hurmuzlu, “Real time control of tethered satellite systems to de-orbit space debris,” Aerosp. Sci. Technol., vol. 109, p. 106379, 2021.
[171] L.-G. Lin, R.-S. Wu, P.-K. Huang, M. Xin, C.-T. Wu, and W.-W. Lin, “Fast SDDRE-based maneuvering-target interception at pre-specified orientation,” IEEE Trans. Control Syst. Technol., available online, doi: 10.1109/TCST.2023.3261463.
[172] B. D. O. Anderson, “Second-order convergent algorithms for the steadystate Riccati equation,” Int. J. Control, vol. 28, no. 2, pp. 295–306, 1978.
[173] 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.
[174] P. Van Dooren, “The generalized eigenstructure problem in linear system theory,” IEEE Trans. Autom. Control, vol. 26, no. 1, pp. 111–129, 1981.
[175] N. L. Tan and C.-T. Pham, “Optimal tracking control for PMSM with partially-unknown dynamics, saturation voltages, torque and voltage disturbances,” IEEE Trans. Ind. Electron., vol. 69, no. 4, pp. 3481–3491, 2022.
[176] B.-S. Chen, Y.-Y. Chen, and C.-L. Lin, “Nonlinear fuzzy H∞ guidance law with saturation of actuators against maneuvering targets,” IEEE Trans. Control Syst. Technol., vol. 10, no. 6, pp. 769–779, 2002.
[177] L.-G. Lin, R.-S. Wu, C.-T. Yeh, and M. Xin, “Impact angle guidance using computationally enhanced state-dependent differential Riccati equation scheme,” AIAA J. Spacecr. Rockets, available online, doi: 10.2514/1.A35624.