This paper aims to present a state-of-the-art review of recent development within the areas of dynamic programming and optimal control for vector-valued functions.
Keywords: Dynamic programming, optimal control, calculus of variations, vector-valued functions, multiple objective optimization
@article{RO_2021__55_S1_S351_0,
author = {Ben Abdelaziz, Fouad and La Torre, Davide and Alaya, Houda},
title = {Dynamic programming and optimal control for vector-valued functions: {A} state-of-the-art review},
journal = {RAIRO. Operations Research},
pages = {S351--S364},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
doi = {10.1051/ro/2019085},
mrnumber = {4237375},
zbl = {1472.90148},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2019085/}
}
TY - JOUR AU - Ben Abdelaziz, Fouad AU - La Torre, Davide AU - Alaya, Houda TI - Dynamic programming and optimal control for vector-valued functions: A state-of-the-art review JO - RAIRO. Operations Research PY - 2021 SP - S351 EP - S364 VL - 55 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2019085/ DO - 10.1051/ro/2019085 LA - en ID - RO_2021__55_S1_S351_0 ER -
%0 Journal Article %A Ben Abdelaziz, Fouad %A La Torre, Davide %A Alaya, Houda %T Dynamic programming and optimal control for vector-valued functions: A state-of-the-art review %J RAIRO. Operations Research %D 2021 %P S351-S364 %V 55 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2019085/ %R 10.1051/ro/2019085 %G en %F RO_2021__55_S1_S351_0
Ben Abdelaziz, Fouad; La Torre, Davide; Alaya, Houda. Dynamic programming and optimal control for vector-valued functions: A state-of-the-art review. RAIRO. Operations Research, Tome 55 (2021), pp. S351-S364. doi: 10.1051/ro/2019085
[1] and , A compromise solution for the multiobjective stochastic linear programming under partial uncertainty. Eur. J. Oper. Res. 202 (2010) 55–59. | MR | Zbl | DOI
[2] and , Decomposition of multi-objective programming problems by hybrid fuzzy dynamic programming. Fuzzy Sets Syst. 60 (1993) 25–32. | MR | Zbl | DOI
[3] and , An algorithm for generating efficient solutions of multi-objective dynamic programming problems. Eur. J. Oper. Res. 80 (1995) 156–165. | Zbl | DOI
[4] , and , An Introduction to Optimal Control Problems in Life Sciences and Economics: From Mathematical Models to Numerical Simulation with MATLAB. Birkhauser (2011). | MR | Zbl
[5] , , Duality and weak efficiency in vector variational problems. J. Optim. Theory App. 159 (2013) 547–553. | MR | Zbl | DOI
[6] , Introduction to Stochastic Control Theory. Academic Press, Inc., London (1970). | MR | Zbl
[7] , Dynamic Programming. Republished 2003: Dover, ISBN 0-486-42809-5. Princeton University Press, Princeton, NJ (1957). | MR | Zbl
[8] , Solution approaches for the multiobjective stochastic programming. Eur. J. Oper. Res. 216 (2012) 1–16. | MR | Zbl | DOI
[9] , and , Dominance and efficiency in multiobjective decision under uncertainty. Theory Decis. 47 (1999) 191–211. | MR | Zbl | DOI
[10] and , Nonlinear Optimal Control Theory. Chapman & Hall, CRC Press (2012). | MR | Zbl | DOI
[11] and , MATLAB Optimization Toolbox User’s Guide, Version 1.5. The Mathworks (1996).
[12] , Optimal control – 1950 to 1985. IEEE Control Syst. Mag. 16 (1996) 26–33. | DOI
[13] and , Applied Optimal Control. Hemispheres (1975). | MR
[14] , and , A multiobjective dynamic programming method for capacity expansion. IEEE Trans. Autom. Control 26 (1981) 1195–1207. | MR | Zbl | DOI
[15] and , Chance constraints and normal deviates. J. Am. Stat. Assoc. 57 (1952) 134–148. | MR | Zbl | DOI
[16] , , and , Optimization and Optimal Control: Theory and Applications. In Vol. 39. Springer (2010). | Zbl
[17] , and , A dynamic programming approach to multi-objective time-dependent capacitated single vehicle routing problems with time windows. BETA Publicatie: working papers 313 (2010).
[18] and , On sufficient optimality conditions for multiobjective control problems. J. Global Optim. 64 (2016) 721–744. | MR | Zbl | DOI
[19] , Calculus of Variations. Courier Corporation (2012).
[20] and , Multi-objective optimal control: an introduction. In: 2011 8th Asian Control Conference (ASCC). IEEE (2011) 1084–1089.
[21] , and , A new approach to design multi-loop control systems with multiple controllers. In: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego (2006). | DOI
[22] and , The computational algorithm for the parametric objective function. Naval Res. Logistics Q. 2 (1955) 39–45. | MR | DOI
[23] , Optimal Control with Engineering Applications. Springer (2007). | Zbl
[24] and , Calculus of Variations. Dover Publications Inc., New York (2000). | Zbl
[25] , and , Optimality criteria for multiobjective dynamic optimization programs: the vector-valued ramsey model in Banach spaces, In: Nonlinear Analysis and Convex Analysis. Korea edited by , , , , and . (2012) 53–73. | Zbl
[26] , and , On a bicriterion formulation of the problems of integrated system identification and system optimization. IEEE Trans. Syst. Man Cybern. 1 (1971) 296–297. | MR | Zbl
[27] and , Directed multi-objective optimization for controller design. In: Proc. International Conference on Instrumentation, Communication and Information Technology (ICICI), Bandung, Indonesia. August 3–5 (2005) 751–756.
[28] , and , A multi-objective dynamic programming-based metaheuristic to solve a bi-objective unit commitment problem using a multi-objective decoder. Int. J. Metaheuristics 5 (2016) 3–30. | DOI
[29] and , Stochastic Programming. Wiley (1994). | MR | Zbl
[30] and , An optimal stopping problem with two decision makers. Sequential Anal. 26 (2007) 467–480. | MR | Zbl | DOI
[31] , Multiobjective dynamic programming. Math. Oper. Statist. Ser. Optim. 9 (1978) 423–426. | MR | Zbl
[32] and , Fuzzy Mathematical Programming, Methods and Applications. Springer-Verlag (1992). | MR | Zbl
[33] and , Optimal Control Applied to Biological Models, Mathematical and Computational Biology. Chapman & Hall, Boca Raton, FL, USA; CRC Press, London, UK (2007). | MR | Zbl
[34] , Switching in Systems and Control. Birkhauser, Boston (2003). | MR | Zbl | DOI
[35] , Calculus of Variations and Optimal Control Theory. A Concise Introduction. Princeton University Press, Princeton, NJ, USA (2012). | MR | Zbl
[36] , and , Multiobjective Optimisation and Control. Research Studies Press Ltd., Exeter (2003).
[37] , , and , Robust multi-objective optimal control of uncertain (bio) chemical processe. Chem. Eng. Sci. 66 (2011) 4670–4682. | DOI
[38] , , and (1964), The Mathematical Theory Of Optimal Processes (translated by . A Pergamon Press Book). The Macmillan Co., New York (2011).
[39] and , Optimal Control Theory with Economic Applications. North-Holland, Amsterdam (1987). | MR | Zbl
[40] , and , Multiobjective dynamic programming with application to a reservoir. Water Resour. Res. 15 (1979) 1403–1408. | DOI
[41] , , and , Strange: an interactive method for multi-objective linear programming under uncertainty. Eur. J. Oper. Res. 26 (1986) 65–82. | MR | Zbl | DOI
[42] , Optimal Control. Birkhauser (2010). | MR | Zbl
[43] and , Stochastic programs with recourse. SIAM J. Appl. Math. 15 (1967) 1299–1314. | MR | Zbl | DOI
[44] , and , Model-free multiobjective approximate dynamic programming for discrete-time nonlinear systems with general performance index functions. Neurocomputing 72 (2009) 1839–1848. | DOI
[45] and , Multiobjective optimal control of the linear wave equation. Ain Shams Eng. J. 5 (2014) 1299–1305. | DOI
[46] , and , Multiobjective dynamic cell formation problem: a stochastic programming approach. Comput. Ind. Eng. 98 (2016) 323–332. | DOI
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