High-order fully actuated system approaches: Part VIII. Optimal control with application in spacecraft attitude stabilisation

References

• Abo-Sinna, M. A. (2004). Multiple objective (fuzzy) dynamic programming problems: A survey and some applications. Applied Mathematics and Computation, 157(3), 861–888. https://doi.org/https://doi.org/10.1016/j.amc.2003.08.083
   Web of Science ®Google Scholar
• Agrawal, O. P. (2006). A formulation and a numerical scheme for fractional optimal control problems. IFAC Proceedings Volumes, 39(11), 68–72. https://doi.org/https://doi.org/10.3182/20060719-3-PT-4902.00011
   Google Scholar
• Anderson, B. D. O., & Moore, J. B. (1990). Optimal control: Linear quadratic methods. Prentice Hall.
   Google Scholar
• Arutyunov, A. V., Karamzin, D. Y., & Pereira, F. (2012). Pontryagin's maximum principle for constrained impulsive control problems. Nonlinear Analysis: Theory, Methods and Applications, 75(3), 1045–1057. https://doi.org/https://doi.org/10.1016/j.na.2011.04.047
   Web of Science ®Google Scholar
• Ball, J. A., & Helton, J. W. (1990). Nonlinear H ∞ control theory: A literature survey. In Robust Control of Linear Systems and Nonlinear Control (pp. 1–12). Birkhäuser.
   Google Scholar
• Bellman, R. (1952). On the theory of dynamic programming. Proceedings of the National Academy of Sciences of the United States of America, 38(8), 716–719. https://doi.org/https://doi.org/10.1073/pnas.38.8.716
   PubMed Web of Science ®Google Scholar
• Bellman, R., & Kalaba, R. (1957). On the role of dynamic programming in statistical communication theory. IRE Transactions on Information Theory, 3(3), 197–203. https://doi.org/https://doi.org/10.1109/TIT.1957.1057416
   Web of Science ®Google Scholar
• Bellman, R., & Kalaba, R. (1960). Dynamic programming and adaptive processes: Mathematical foundation. IRE Transactions on Automatic Control, 5(1), 5–10. https://doi.org/https://doi.org/10.1109/TAC.1960.6429288
   Google Scholar
• Bender, D. J., & Laub, A. J. (1987a). The linear-quadratic optimal regulator for descriptor systems. IEEE Transactions on Automatic Control, 32(8), 672–688. https://doi.org/https://doi.org/10.1109/TAC.1987.1104694
   Web of Science ®Google Scholar
• Bender, D. J., & Laub, A. J. (1987b). The linear-quadratic optimal regulator for descriptor systems: Discrete-time case. Automatica, 23(1), 71–85. https://doi.org/https://doi.org/10.1016/0005-1098(87)90119-1
   Web of Science ®Google Scholar
• Bertsekas, D. P., & Tsitsiklis, J. N. (1995, December). Neuro-dynamic programming: An overview. Proceedings of 1995 34th IEEE Conference on Decision and Control (pp. 560–564). IEEE.
   Google Scholar
• Bokov, G. V. (2011). Pontryagin's maximum principle of optimal control problems with time-delay. Journal of Mathematical Sciences, 172(5), 623–634. https://doi.org/https://doi.org/10.1007/s10958-011-0208-y
   Google Scholar
• Chen, S., Li, X., & Zhou, X. Y. (1998). Stochastic linear quadratic regulators with indefinite control weight costs. SIAM Journal on Control and Optimization, 36(5), 1685–1702. https://doi.org/https://doi.org/10.1137/S0363012996310478
   Web of Science ®Google Scholar
• Chmielewski, D., & Manousiouthakis, V. (1996). On constrained infinite-time linear quadratic optimal control. Systems & Control Letters, 29(3), 121–129. https://doi.org/https://doi.org/10.1016/S0167-6911(96)00057-6
   Web of Science ®Google Scholar
• Çimen, T. (2008). State-dependent Riccati equation (SDRE) control: A survey. IFAC Proceedings Volumes, 41(2), 3761–3775. https://doi.org/https://doi.org/10.3182/20080706-5-KR-1001.00635
   Google Scholar
• Çimen, T. (2012). Survey of state-dependent Riccati equation in nonlinear optimal feedback control synthesis. Journal of Guidance, Control, and Dynamics, 35(4), 1025–1047. https://doi.org/https://doi.org/10.2514/1.55821
   Web of Science ®Google Scholar
• Dmitruk, A. V., & Kaganovich, A. M. (2008). The hybrid maximum principle is a consequence of pontryagin maximum principle. Systems & Control Letters, 57(11), 964–970. https://doi.org/https://doi.org/10.1016/j.sysconle.2008.05.006
   Web of Science ®Google Scholar
• Doyle, J., Glove, K., Khargonekar, P., & Francis, B. A. (1988). State-space solutions to standard H 2 and H ∞ control problems. In 1988 American control conference (pp. 1691–1696).
   Google Scholar
• Duan, G. R. (2014, July). Satellite attitude control–a direct parametric approach. Proceeding of the 11th World Congress on intelligent control and automation (pp. 3989–3996). IEEE.
   Google Scholar
• Duan, G. R. (2016). Linear system theory (Volume II) (3rd ed). The Science Press.
   Google Scholar
• Duan, G. R. (2020a). High-order system approaches: I. Full-actuation and parametric design. Acta Automatica Sinica, 46(7), 1333–1345. https://doi.org/https://doi.org/10.16383/j.aas.c200234 (in Chinese)
   Google Scholar
• Duan, G. R. (2020b). High-order system approaches: II. Controllability and fully-actuation. Acta Automatica Sinica, 46(8), 1571–1581. https://doi.org/https://doi.org/10.16383/j.aas.c200369 (in Chinese)
   Google Scholar
• Duan, G. R. (2020c). High-order system approaches: III. Observability and observer design. Acta Automatica Sinica, 46(9), 1885–1895. https://doi.org/https://doi.org/10.16383/j.aas.c200370 (in Chinese)
   Google Scholar
• Duan, G. R. (2020d). High-order fully actuated system approaches: Part I. Models and basic procedure. International Journal of System Sciences, 52(2), 422–435. https://doi.org/https://doi.org/10.1080/00207721.2020.1829167
   Web of Science ®Google Scholar
• Duan, G. R. (2020e). High-order fully actuated system approaches: Part II. Generalized strict-feedback systems. International Journal of System Sciences, 52(3), 437–454. https://doi.org/https://doi.org/10.1080/00207721.2020.1829168
   Web of Science ®Google Scholar
• Duan, G. R. (2020f). High-order fully actuated system approaches: Part III. Robust control and high-order backstepping. International Journal of System Sciences, 52(5), 952–971. https://doi.org/https://doi.org/10.1080/00207721.2020.1849863
   Web of Science ®Google Scholar
• Duan, G. R. (2020g). High-order fully actuated system approaches: Part IV. Adaptive control and high-order backstepping. International Journal of System Sciences, 52(5), 972–989. https://doi.org/https://doi.org/10.1080/00207721.2020.1849864
   Web of Science ®Google Scholar
• Duan, G. R. (2020h). High-order fully actuated system approaches: Part V. Robust adaptive control. International Journal of System Sciences. https://doi.org/https://doi.org/10.1080/00207721.2021.1879964
   Web of Science ®Google Scholar
• Duan, G. R. (2020i). High-order fully actuated system approaches: Part VI. Disturbance attenuation and decoupling. International Journal of System Sciences. https://doi.org/https://doi.org/10.1080/00207721.2021.1879966
   Web of Science ®Google Scholar
• Duan, G. R. (2020j). High-order fully actuated system approaches: Part VII. Controllability, stabilizability and parametric designs. International Journal of System Sciences. https://doi.org/https://doi.org/10.1080/00207721.2021.1921307
   Web of Science ®Google Scholar
• Findeisen, R., Imsland, L., Allgower, F., & Foss, B. A. (2003). State and output feedback nonlinear model predictive control: an overview. European Journal of Control, 9(2–3), 190–206. https://doi.org/https://doi.org/10.3166/ejc.9.190-206
   Web of Science ®Google Scholar
• Gao, C. Y., Zhao, Q., & Duan, G. R. (2013). Robust actuator fault diagnosis scheme for satellite attitude control systems. Journal of Franklin Institute, 350(9), 2560–2580. https://doi.org/https://doi.org/10.1016/j.jfranklin.2013.02.021
   Web of Science ®Google Scholar
• Garcia, C. E., Prett, D. M., & Morari, M. (1989). Model predictive control: theory and practice – A survey. Automatica, 25(3), 335–348. https://doi.org/https://doi.org/10.1016/0005-1098(89)90002-2
   Web of Science ®Google Scholar
• Hwang, C. L., & Fan, L. T. (1967). A discrete version of Pontryagin's maximum principle. Operations Research, 15(1), 139–146. https://doi.org/https://doi.org/10.1287/opre.15.1.139
   Web of Science ®Google Scholar
• Kalman, R. E. (1960). Contributions to the theory of optimal control. Boletín De La Sociedad Matemática Mexicana, 5(2), 102–119. https://doi.org/https://doi.org/10.1109/9780470544334.ch8
   Google Scholar
• Laschov, D., & Margaliot, M. (2011a). A maximum principle for single-input Boolean control networks. IEEE Transactions on Automatic Control, 56(4), 913–917. https://doi.org/https://doi.org/10.1109/TAC.2010.2101430
   Web of Science ®Google Scholar
• Laschov, D., & Margaliot, M. (2011b). A Pontryagin maximum principle for multi-input Boolean control networks. In Recent advances in dynamics and control of neural networks. Cambridge Scientific Publishers.
   Google Scholar
• Lee, J. H. (2011). Model predictive control: review of the three decades of development. International Journal of Control, Automation and Systems, 9(3), 415–424. https://doi.org/https://doi.org/10.1007/s12555-011-0300-6
   Web of Science ®Google Scholar
• Lewis, F. L., & Vrabie, D. (2009). Reinforcement learning and adaptive dynamic programming for feedback control. IEEE Circuits and Systems Magazine, 9(3), 32–50. https://doi.org/https://doi.org/10.1109/MCAS.7384
   Web of Science ®Google Scholar
• Li, Y., & Chen, Y. Q. (2008, October). Fractional order linear quadratic regulator. 2008 IEEE/ASME international conference on mechtronic and embedded systems and applications (pp. 363–368). IEEE. https://doi.org/https://doi.org/10.1109/MESA.2008.4735696
   Google Scholar
• Li, W., & Todorov, E. (2004, August). Iterative linear quadratic regulator design for nonlinear biological movement systems. ICINCO 2004 Proceedings of the first international conference on informatics in control, automation and robotics, Setúbal, Portugal (pp. 222–229). Springer.
   Google Scholar
• Mayne, D. Q. (2014). Model predictive control: recent developments and future promise. Automatica, 50(12), 2967–2986. https://doi.org/https://doi.org/10.1016/j.automatica.2014.10.128
   Web of Science ®Google Scholar
• Nekoo, S. R. (2019). Tutorial and review on the state-dependent Riccati equation. Journal of Applied Nonlinear Dynamics, 8(2), 109–166. https://doi.org/https://doi.org/10.5890/JAND.2019.06.001
   Google Scholar
• Pontiyagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mjshchenko, E. F. (1962). The mathematical theory of optimal processes. John Wiley and Sons.
   Google Scholar
• Rami, M. A., Chen, X., & Zhou, X. Y. (2002). Discrete-time indefinite LQ control with state and control dependent noises. Journal of Global Optimization, 23(3-4), 245–265. https://doi.org/https://doi.org/10.1023/A:1016578629272
   Web of Science ®Google Scholar
• Rozonoer, L. I. (1959). The maximum principle of LS Pontryagin in optimal system theory. Automation and Remote Control, 20(10), 11.
   Google Scholar
• Scokaert, P. O. M., & Rawlings, J. B. (1998). Constrained linear quadratic regulation. IEEE Transactions on Automatic Control, 43(8), 1163–1169. https://doi.org/https://doi.org/10.1109/9.704994
   Web of Science ®Google Scholar
• Seierstad, A. (1975). An extension to Banach space of Pontryagin's maximum principle. Journal of Optimization Theory and Applications, 17(3-4), 293–335. https://doi.org/https://doi.org/10.1007/BF00933882
   Web of Science ®Google Scholar
• Sussmann, H. J. (1999, December). A maximum principle for hybrid optimal control problems. Proceedings of the 38th IEEE conference on decision and control (pp. 425–430). IEEE. https://doi.org/https://doi.org/10.1109/CDC.1999.832814
   Google Scholar
• Terra, M. H., Cerri, J. P., & Ishihara, J. Y. (2014). Optimal robust linear quadratic regulator for systems subject to uncertainties. IEEE Transactions on Automatic Control, 59(9), 2586–2591. https://doi.org/https://doi.org/10.1109/TAC.2014.2309282
   Web of Science ®Google Scholar
• Tsitsiklis, J. N., & Roy, B. V. (1997). An analysis of temporal-difference learning with function approximation. IEEE Transactions on Automatic Control, 42(5), 674–690. https://doi.org/https://doi.org/10.1109/9.580874
   Web of Science ®Google Scholar
• Wang, L., Peng, H., Zhu, H., & Shen, L. (2009, August). A survey of approximate dynamic programming. 2009 international conference on intelligent human-machine systems and cybernetics, Hangzhou, China  (pp. 396–399). IEEE.
   Google Scholar
• Werbos, P. J. (1977). Advanced forecasting methods for global crisis warning and models of intelligence. General System Yearbook, 22, 25–38.
   Google Scholar
• Werbos, P. J. (1989, August). Neural networks for control and system identification. Proceedings of the 28th IEEE conference on decision and control, Tampa, FL, USA (pp. 260–265). IEEE.
   Google Scholar
• Xie, L., & C. E. de Souza (1990). Robust H ∞ control for linear time-invariant systems with norm-bounded uncertainty in the input matrix. Systems & Control Letters, 14(5), 389–396. https://doi.org/https://doi.org/10.1016/0167-6911(90)90088-C
   Web of Science ®Google Scholar
• Xu, S. Y., & Chen, T. W. (2002). Robust H-infinity control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control, 47(12), 2089–2094. https://doi.org/https://doi.org/10.1109/TAC.2002.805670
   Web of Science ®Google Scholar
• Xu, S., Yang, C., & Zhou, S. (2000). Robust H ∞ control for uncertain discrete-time systems with circular pole constraints. Systems & Control Letters, 39(1), 13–18. https://doi.org/https://doi.org/10.1016/S0167-6911(99)00066-3
   Web of Science ®Google Scholar
• Zhang, W., Hu, J., & Abate, A. (2009). On the value functions of the discrete-time switched LQR problem. IEEE Transactions on Automatic Control, 54(11), 2669–2674. https://doi.org/https://doi.org/10.1109/TAC.2009.2031574
   Web of Science ®Google Scholar
• Zhang, W., Hu, J., & Abate, A. (2012). Infinite-horizon switched LQR problems in discrete time: A suboptimal algorithm with performance analysis. IEEE Transactions on Automatic Control, 57(7), 1815–1821. https://doi.org/https://doi.org/10.1109/TAC.2011.2178649
   Web of Science ®Google Scholar