Abstract
This chapter is the overview of the book. We first briefly reivew the development of optimal control theory. Then the pseudospectral methods and the property of symplectic conservation are introduced. Finally, the motivation and the arrangement of the book are given.
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References
Aschepkov LT, Dolgy DV, Kim T, Agarwal RP (2016) Optimal control. Springer, Cham
Bowon Kim (2017) Optimal control applications for operations strategy. Springer, Cham
Pontryagin LS (1962) The mathematical theory of optimal processes (Trirogoff KN, trans). Interscience, New York
Bellman RE, Deryfus SE (1962) Applied dynamic programming. Princeton University Press, New Jersey
Moiseev NN, Lebedev VN (1966) Review paper on the research completed at the Computing Center of the Academy of Sciences of the USSR on the theory of optimal control functions of spacecraft. In: Aseltine JA (ed) Peaceful uses of automation in outer space. Springer, Boston
Kalman RE, Bucy RS (1961) New results in linear filtering and prediction theory. Trans ASME J Basic Eng 83:95–108
Mufti IH (1970) Computational methods in optimal control problems. Springer, Berlin
Bulirsch R, Kraft D (1994) Computational optimal control. Birkhäuser, Basel
Seywald H, Kumar RR (1997) Some recent developments in computational optimal control. In: Biegler LT, Coleman TF, Conn AR, Santosa FN (eds) Large-scale optimization with applications. The IMA volumes in mathematics and its applications, vol 93. Springer, New York
Ross IM, Karpenko M (2012) A review of pseudospectral optimal control: From theory to flight. Ann Rev Control 36(2):182–197
Kang W, Bedrossian N (2008) Pseudospectral optimal control theory makes debut flight, Saves NASA $1 M in Under Three Hours. SIAM News 40(7)
Arnold VI (1978) Mathematical methods of classical mechanics. Springer, New York
Zhong W (2004) Duality system in applied mechanics and optimal control. Springer, Boston
Junge O, Marsden JE, Ober-Blöbaum S (2005) Discrete mechanics and optimal control. IFAC Proc Volumes 38(1):538–543
Leyendecker S, Ober-Blöbaum S, Marsden JE et al (2010) Discrete mechanics and optimal control for constrained systems. Opt Control Appl Methods 31(6):505–528
Peng H, Gao Q, Wu Z et al (2013) Efficient sparse approach for solving receding-horizon control problems. J Guid Control Dyn 36(6):1864–1872
Peng H, Gao Q, Zhang H et al (2014) Parametric variational solution of linear-quadratic optimal control problems with control inequality constraints. Appl Math Mech (English Ed) 35(9):1079–1098
Peng H, Gao Q, Wu Z et al (2015) Symplectic algorithms with mesh refinement for a hypersensitive optimal control problem. Int J Comput Math 92(11):2273–2289
Peng H, Tan S, Gao Q et al (2017) Symplectic method based on generating function for receding horizon control of linear time-varying systems. Eur J Control 33:24–34
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Wang, X., Liu, J., Peng, H. (2021). Overview of This Book. In: Symplectic Pseudospectral Methods for Optimal Control. Intelligent Systems, Control and Automation: Science and Engineering, vol 97. Springer, Singapore. https://doi.org/10.1007/978-981-15-3438-6_1
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DOI: https://doi.org/10.1007/978-981-15-3438-6_1
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Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-3437-9
Online ISBN: 978-981-15-3438-6
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