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Journal articles on the topic 'Optimal control theory'

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Published: 4 June 2021

Last updated: 6 September 2023

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1

James, M. R. "Optimal Quantum Control Theory." Annual Review of Control, Robotics, and Autonomous Systems 4, no. 1 (May 3, 2021): 343–67. http://dx.doi.org/10.1146/annurev-control-061520-010444.

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This article explains some fundamental ideas concerning the optimal control of quantum systems through the study of a relatively simple two-level system coupled to optical fields. The model for this system includes both continuous and impulsive dynamics. Topics covered include open- and closed-loop control, impulsive control, open-loop optimal control, quantum filtering, and measurement feedback optimal control.

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2

Werschnik, J., and E. K. U. Gross. "Quantum optimal control theory." Journal of Physics B: Atomic, Molecular and Optical Physics 40, no. 18 (September 4, 2007): R175—R211. http://dx.doi.org/10.1088/0953-4075/40/18/r01.

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3

Daund, Arvind, Shrihari Mahishi, and Nirnay Berde. "Synchronization of Parallel Dual Inverted Pendulums using Optimal Control Theory." SIJ Transactions on Advances in Space Research & Earth Exploration 2, no. 2 (April 11, 2014): 7–11. http://dx.doi.org/10.9756/sijasree/v2i2/0202520301.

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4

CHERRUAULT, Y., and J. GALLEGO. "INTRODUCTION TO OPTIMAL CONTROL THEORY." Kybernetes 14, no. 3 (March 1985): 151–56. http://dx.doi.org/10.1108/eb005712.

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5

Zelikin, M. I., D. D. Kiselev, and L. V. Lokutsievskiy. "Optimal control and Galois theory." Sbornik: Mathematics 204, no. 11 (November 30, 2013): 1624–38. http://dx.doi.org/10.1070/sm2013v204n11abeh004352.

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6

Martínez, Eduardo. "Reduction in optimal control theory." Reports on Mathematical Physics 53, no. 1 (February 2004): 79–90. http://dx.doi.org/10.1016/s0034-4877(04)90005-5.

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7

Yong, Jiongmin. "Infinite dimensional optimal control theory." IFAC Proceedings Volumes 32, no. 2 (July 1999): 2778–89. http://dx.doi.org/10.1016/s1474-6670(17)56473-3.

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8

FUKUSHIMA, Naoto, Syo OTA, Mehmet Selcuk ARSLAN, and Ichiro HAGIWARA. "B10 Energy Optimal Control Theory : An Optimal Control Theory Based on a New Framework of Control Problem." Proceedings of the Symposium on the Motion and Vibration Control 2009.11 (2009): 109–13. http://dx.doi.org/10.1299/jsmemovic.2009.11.109.

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9

Pant, D. K., R. D. Coalson, M. I. Hernandez, and J. Campos-Martinez. "Optimal control theory for the design of optical waveguides." Journal of Lightwave Technology 16, no. 2 (1998): 292–300. http://dx.doi.org/10.1109/50.661023.

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10

Herrmann, Avriel A., and Joseph Z. Ben-Asher. "Flight Control Law Clearance Using Optimal Control Theory." Journal of Aircraft 53, no. 2 (March 2016): 515–29. http://dx.doi.org/10.2514/1.c033517.

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11

Slavík, Michal. "Contemporary macroeconomics and optimal control theory." Politická ekonomie 52, no. 4 (August 1, 2004): 551–61. http://dx.doi.org/10.18267/j.polek.475.

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12

Shah, A. "Optimal control theory and fishery model." Journal of Development and Agricultural Economics 5, no. 12 (December 31, 2013): 476–81. http://dx.doi.org/10.5897/jdae2013.0487.

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13

Renee Fister, K., and Jennifer Hughes Donnelly. "Immunotherapy: An Optimal Control Theory Approach." Mathematical Biosciences and Engineering 2, no. 3 (2005): 499–510. http://dx.doi.org/10.3934/mbe.2005.2.499.

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14

KONDORSKIY, ALEXEY, and HIROKI NAKAMURA. "SEMICLASSICAL FORMULATION OF OPTIMAL CONTROL THEORY." Journal of Theoretical and Computational Chemistry 04, no. 01 (March 2005): 75–87. http://dx.doi.org/10.1142/s0219633605001416.

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In the present paper, semiclassical formulation of optimal control theory is made by combining the conjugate gradient search method with new approximate semiclassical expressions for correlation function. Two expressions for correlation function are derived. The simpler one requires calculations of coordinates and momenta of classical trajectories only. The second one requires extra calculation of common semiclassical quantities; as a result additional quantum effects can be taken into account. The efficiency of the method is demonstrated by controlling nuclear wave packet motion in a two-dimensional model system.

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15

Becker, Robert A., Atle Sierstad, Knut Sydsæter, and Knut Sydsaeter. "Optimal Control Theory with Economic Applications." Scandinavian Journal of Economics 91, no. 1 (March 1989): 175. http://dx.doi.org/10.2307/3440172.

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16

Žampa, Pavel, Jiří Mošna, and Pavel Prautsch. "New Approach to Optimal Control Theory." IFAC Proceedings Volumes 30, no. 21 (September 1997): 133–38. http://dx.doi.org/10.1016/s1474-6670(17)41428-5.

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17

Buttazzo, G., and E. Cavazzuti. "Limit Problems in Optimal Control Theory." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 6 (November 1989): 151–60. http://dx.doi.org/10.1016/s0294-1449(17)30019-7.

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18

De la Salle, S. "Stochastic optimal control theory and application." Automatica 24, no. 3 (May 1988): 425–26. http://dx.doi.org/10.1016/0005-1098(88)90086-6.

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19

Zeidan, V., and P. Zezza. "Coupled points in optimal control theory." IEEE Transactions on Automatic Control 36, no. 11 (1991): 1276–81. http://dx.doi.org/10.1109/9.100937.

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20

Fernández, Antonio, and Pedro L. García. "Regular discretizations in optimal control theory." Journal of Geometric Mechanics 5, no. 4 (2013): 415–32. http://dx.doi.org/10.3934/jgm.2013.5.415.

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21

Yiu, K. F. C., K. L. Mak, and K. L. Teo. "Airfoil design via optimal control theory." Journal of Industrial & Management Optimization 1, no. 1 (2005): 133–48. http://dx.doi.org/10.3934/jimo.2005.1.133.

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22

Zhifeng, Kuang, Yang Mingzhu, and Zhu Guangtian. "Optimal control applications in transport theory." Transport Theory and Statistical Physics 27, no. 5-7 (August 1998): 691–700. http://dx.doi.org/10.1080/00411459808205651.

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23

Handa, V. K., and R. M. Barcia. "Linear Scheduling Using Optimal Control Theory." Journal of Construction Engineering and Management 112, no. 3 (September 1986): 387–93. http://dx.doi.org/10.1061/(asce)0733-9364(1986)112:3(387).

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24

Arantes, Santina de F., and Jaime E. Muñoz Rivera. "Optimal control theory for ambient pollution." International Journal of Control 83, no. 11 (November 2010): 2261–75. http://dx.doi.org/10.1080/00207179.2010.513716.

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25

Pukhlikov, A. V. "Hamiltonian structures in optimal control theory." Journal of Dynamical and Control Systems 1, no. 3 (July 1995): 379–401. http://dx.doi.org/10.1007/bf02269376.

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26

Hartl, Richard F. "Optimal control theory with economic applications." European Journal of Operational Research 35, no. 2 (May 1988): 292–93. http://dx.doi.org/10.1016/0377-2217(88)90044-6.

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27

Mathis, Mackenzie W., and Steffen Schneider. "Motor control: Neural correlates of optimal feedback control theory." Current Biology 31, no. 7 (April 2021): R356—R358. http://dx.doi.org/10.1016/j.cub.2021.01.087.

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28

Ahmed, ABOULFTOUH, EL-BAYOUMI Gamal, and MADBOULI Mohamed. "Hover flight control of helicopter using optimal control theory." INCAS BULLETIN 7, no. 3 (September 10, 2015): 113–24. http://dx.doi.org/10.13111/2066-8201.2015.7.3.2.

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29

Yang, J. N., Z. Li, and S. Vongchavalitkul. "Generalization of Optimal Control Theory: Linear and Nonlinear Control." Journal of Engineering Mechanics 120, no. 2 (February 1994): 266–83. http://dx.doi.org/10.1061/(asce)0733-9399(1994)120:2(266).

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30

Peskir, Goran. "Maximum process problems in optimal control theory." Journal of Applied Mathematics and Stochastic Analysis 2005, no. 1 (January 1, 2005): 77–88. http://dx.doi.org/10.1155/jamsa.2005.77.

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Given a standard Brownian motion (Bt)t≥0 and the equation of motion dXt=vtdt+2dBt, we set St=max0≤s≤tXs and consider the optimal control problem supvE(Sτ−Cτ), where c>0 and the supremum is taken over all admissible controls v satisfying vt∈[μ0,μ1] for all t up to τ=inf{t>0|Xt∉(ℓ0,ℓ1)} with μ0<0<μ1 and ℓ0<0<ℓ1 given and fixed. The following control v∗ is proved to be optimal: “pull as hard as possible,” that is, vt∗=μ0 if Xt<g∗(St), and “push as hard as possible,” that is, vt∗=μ1 if Xt>g∗(St), where s↦g∗(s) is a switching curve that is determined explicitly (as the unique solution to a nonlinear differential equation). The solution found demonstrates that the problem formulations based on a maximum functional can be successfully included in optimal control theory (calculus of variations) in addition to the classic problem formulations due to Lagrange, Mayer, and Bolza.

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31

Gurman, V. I. "On Certain Problems in Optimal Control Theory." Bulletin of Irkutsk State University 19 (2017): 26–43. http://dx.doi.org/10.26516/1997-7670.2017.19.26.

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32

Pei, Xiaoxuan, Kewen Li, and Yongming Li. "A survey of adaptive optimal control theory." Mathematical Biosciences and Engineering 19, no. 12 (2022): 12058–72. http://dx.doi.org/10.3934/mbe.2022561.

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<abstract><p>This paper makes a survey about the recent development of optimal control based on adaptive dynamic programming (ADP). First of all, based on DP algorithm and reinforcement learning (RL) algorithm, the origin and development of the optimization idea and its application in the control field are introduced. The second part introduces achievements in the optimal control direction, then we classify and summarize the research results of optimization method, constraint problem, structure design in control algorithm and practical engineering process based on optimal control. Finally, the possible future research topics are discussed. Through a comprehensive and complete investigation of its application in many existing fields, this survey fully demonstrates that the optimal control algorithms via ADP with critic-actor neural network (NN) structure, which also have a broad application prospect, and some developed optimal control design algorithms have been applied to practical engineering fields.</p></abstract>

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33

Emms, Paul, and Steven Haberman. "Pricing General Insurance Using Optimal Control Theory." ASTIN Bulletin 35, no. 02 (November 2005): 427–53. http://dx.doi.org/10.2143/ast.35.2.2003461.

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Insurance premiums are calculated using optimal control theory by maximising the terminal wealth of an insurer under a demand law. If the insurer sets a low premium to generate exposure then profits are reduced, whereas a high premium leads to reduced demand. A continuous stochastic model is developed, which generalises the deterministic discrete model of Taylor (1986). An attractive simplification of this model is that existing policyholders should pay the premium rate currently set by the insurer. It is shown that this assumption leads to a bang-bang optimal premium strategy, which cannot be optimal for the insurer in realistic applications. The model is then modified by introducing an accrued premium rate representing the accumulated premium rates received from existing and new customers. Policyholders pay the premium rate in force at the start of their contract and pay this rate for the duration of the policy. It is shown that, for two demand functions, an optimal premium strategy is well-defined and smooth for certain parameter choices. It is shown for a linear demand function that these strategies yield the optimal dynamic premium if the market average premium is lognormally distributed.

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34

Lewis, Debra. "Modeling student engagement using optimal control theory." Journal of Geometric Mechanics 14, no. 1 (2022): 131. http://dx.doi.org/10.3934/jgm.2021032.

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<p style='text-indent:20px;'>Student engagement in learning a prescribed body of knowledge can be modeled using optimal control theory, with a scalar state variable representing mastery, or self-perceived mastery, of the material and control representing the instantaneous cognitive effort devoted to the learning task. The relevant costs include emotional and external penalties for incomplete mastery, reduced availability of cognitive resources for other activities, and psychological stresses related to engagement with the learning task. Application of Pontryagin's maximum principle to some simple models of engagement yields solutions of the synthesis problem mimicking familiar behaviors including avoidance, procrastination, and increasing commitment in response to increasing mastery.</p>

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35

Prussing, John E. "Review of Optimal Control Theory for Applications." Journal of Guidance, Control, and Dynamics 28, no. 1 (January 2005): 191. http://dx.doi.org/10.2514/1.15003.

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36

Ashokkumar, C. R., and Singiresu S. Rao. "Structural Control Using Inverse H Optimal Theory." AIAA Journal 41, no. 12 (December 2003): 2478–85. http://dx.doi.org/10.2514/2.6848.

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37

Sharp, R. S., and Huei Peng. "Vehicle dynamics applications of optimal control theory." Vehicle System Dynamics 49, no. 7 (July 2011): 1073–111. http://dx.doi.org/10.1080/00423114.2011.586707.

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38

Rosa, Marta, Gabriel Gil, Stefano Corni, and Roberto Cammi. "Quantum optimal control theory for solvated systems." Journal of Chemical Physics 151, no. 19 (November 21, 2019): 194109. http://dx.doi.org/10.1063/1.5125184.

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39

Chawla, Sanjay, and Suzanne M. Lenhart. "Application of optimal control theory to bioremediation." Journal of Computational and Applied Mathematics 114, no. 1 (January 2000): 81–102. http://dx.doi.org/10.1016/s0377-0427(99)00290-3.

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40

Xu, Ruixue, Jixin Cheng, and Yan. "A Simple Theory of Optimal Coherent Control." Journal of Physical Chemistry A 103, no. 49 (December 1999): 10611–18. http://dx.doi.org/10.1021/jp991965b.

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41

Shastri, Yogendra, Urmila Diwekar, and Heriberto Cabezas. "Optimal Control Theory for Sustainable Environmental Management." Environmental Science & Technology 42, no. 14 (July 2008): 5322–28. http://dx.doi.org/10.1021/es8000807.

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42

Emms, Paul, and Steven Haberman. "Pricing General Insurance Using Optimal Control Theory." ASTIN Bulletin 35, no. 2 (November 2005): 427–53. http://dx.doi.org/10.1017/s051503610001432x.

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Insurance premiums are calculated using optimal control theory by maximising the terminal wealth of an insurer under a demand law. If the insurer sets a low premium to generate exposure then profits are reduced, whereas a high premium leads to reduced demand. A continuous stochastic model is developed, which generalises the deterministic discrete model of Taylor (1986). An attractive simplification of this model is that existing policyholders should pay the premium rate currently set by the insurer. It is shown that this assumption leads to a bang-bang optimal premium strategy, which cannot be optimal for the insurer in realistic applications.The model is then modified by introducing an accrued premium rate representing the accumulated premium rates received from existing and new customers. Policyholders pay the premium rate in force at the start of their contract and pay this rate for the duration of the policy. It is shown that, for two demand functions, an optimal premium strategy is well-defined and smooth for certain parameter choices. It is shown for a linear demand function that these strategies yield the optimal dynamic premium if the market average premium is lognormally distributed.

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43

Curtain, Ruth F. "Optimal control theory for infinite dimensional systems." Automatica 33, no. 4 (April 1997): 750–51. http://dx.doi.org/10.1016/s0005-1098(97)85780-9.

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44

Bisiacco, Mauro. "New results in 2D optimal control theory." Multidimensional Systems and Signal Processing 6, no. 3 (July 1995): 189–222. http://dx.doi.org/10.1007/bf00981083.

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45

Karamzin, Dmitry Yu, Valeriano A. de Oliveira, Fernando L. Pereira, and Geraldo N. Silva. "On some extension of optimal control theory." European Journal of Control 20, no. 6 (November 2014): 284–91. http://dx.doi.org/10.1016/j.ejcon.2014.09.003.

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46

Jones, R. W. "Application of optimal control theory in biomedicine." Automatica 23, no. 1 (January 1987): 130–31. http://dx.doi.org/10.1016/0005-1098(87)90126-9.

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47

Loring, Stephen H. "Applications of optimal control theory in biomedicine." Mathematical Modelling 7, no. 9-12 (1986): 1659–60. http://dx.doi.org/10.1016/0270-0255(86)90105-3.

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48

Frederico, Gastão S. F., and Delfim F. M. Torres. "Fractional conservation laws in optimal control theory." Nonlinear Dynamics 53, no. 3 (November 30, 2007): 215–22. http://dx.doi.org/10.1007/s11071-007-9309-z.

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49

de León, Manuel, David Martín de Diego, and Aitor Santamaría-Merino. "Discrete variational integrators and optimal control theory." Advances in Computational Mathematics 26, no. 1-3 (August 9, 2006): 251–68. http://dx.doi.org/10.1007/s10444-004-4093-5.

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50

Veliov, Vladimir M. "Optimal control of heterogeneous systems: Basic theory." Journal of Mathematical Analysis and Applications 346, no. 1 (October 2008): 227–42. http://dx.doi.org/10.1016/j.jmaa.2008.05.012.

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