American Institute of Mathematical Sciences

Advanced
January  2008, 4(1): 1-15. doi: 10.3934/jimo.2008.4.1

Optimal control of oscillatory systems by iterative dynamic programming

Rein Luus 1,

1. 

Department of Chemical Engineering, University of Toronto, Toronto, ON M5S 3E5, Canada

Received  March 2006 Revised  October 2006 Published  January 2008

Oscillatory inputs have been observed to increase the yield of chemical reactors beyond the level possible by steady inputs. To obtain the optimal inputs, iterative dynamic programming is well suited, because a very large number of time stages can be used without encountering computational problems. To observe the benefits of oscillatory inputs, the effects of the initial state and the final state can be eliminated by normalizing the average yields with respect to the yield from a shorter final time. Two examples show that optimal oscillatory control policy can improve the yield substantially. The third example shows that there are situations where oscillatory behaviour is optimal, but the benefits are negligible. The optimal control policies can be readily established with iterative dynamic programming with the use of a large number of time stages of flexible length.
Keywords: iterative dynamic programming., Oscillatory systems, global optimization, yield improvement.
Mathematics Subject Classification: Primary: 49N20, 49N90; Secondary: 49J15, 37N40, 90C3.
Citation: Rein Luus. Optimal control of oscillatory systems by iterative dynamic programming. Journal of Industrial & Management Optimization, 2008, 4 (1) : 1-15. doi: 10.3934/jimo.2008.4.1
[1]

Paul B. Hermanns, Nguyen Van Thoai. Global optimization algorithm for solving bilevel programming problems with quadratic lower levels. Journal of Industrial & Management Optimization, 2010, 6 (1) : 177-196. doi: 10.3934/jimo.2010.6.177
[2]

Roya Soltani, Seyed Jafar Sadjadi, Mona Rahnama. Artificial intelligence combined with nonlinear optimization techniques and their application for yield curve optimization. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1701-1721. doi: 10.3934/jimo.2017014
[3]

Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021013
[4]

Dung Le. Global existence and regularity results for strongly coupled nonregular parabolic systems via iterative methods. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 877-893. doi: 10.3934/dcdsb.2017044
[5]

Haibo Jin, Long Hai, Xiaoliang Tang. An optimal maintenance strategy for multi-state systems based on a system linear integral equation and dynamic programming. Journal of Industrial & Management Optimization, 2020, 16 (2) : 965-990. doi: 10.3934/jimo.2018188
[6]

Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473
[7]

Jérôme Renault. General limit value in dynamic programming. Journal of Dynamics & Games, 2014, 1 (3) : 471-484. doi: 10.3934/jdg.2014.1.471
[8]

Yahong Peng, Yaguang Wang. Reflection of highly oscillatory waves with continuous oscillatory spectra for semilinear hyperbolic systems. Discrete & Continuous Dynamical Systems, 2009, 24 (4) : 1293-1306. doi: 10.3934/dcds.2009.24.1293
[9]

Oliver Junge, Alex Schreiber. Dynamic programming using radial basis functions. Discrete & Continuous Dynamical Systems, 2015, 35 (9) : 4439-4453. doi: 10.3934/dcds.2015.35.4439
[10]

Eduardo Espinosa-Avila, Pablo Padilla Longoria, Francisco Hernández-Quiroz. Game theory and dynamic programming in alternate games. Journal of Dynamics & Games, 2017, 4 (3) : 205-216. doi: 10.3934/jdg.2017013
[11]

Qing Liu, Armin Schikorra. General existence of solutions to dynamic programming equations. Communications on Pure & Applied Analysis, 2015, 14 (1) : 167-184. doi: 10.3934/cpaa.2015.14.167
[12]

Claude Le Bris, Frédéric Legoll. Integrators for highly oscillatory Hamiltonian systems: An homogenization approach. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 347-373. doi: 10.3934/dcdsb.2010.13.347
[13]

Bin Cheng, Alex Mahalov. Time-averages of fast oscillatory systems. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1151-1162. doi: 10.3934/dcdss.2013.6.1151
[14]

Zhiang Zhou, Xinmin Yang, Kequan Zhao. $E$-super efficiency of set-valued optimization problems involving improvement sets. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1031-1039. doi: 10.3934/jimo.2016.12.1031
[15]

Morten Brøns. An iterative method for the canard explosion in general planar systems. Conference Publications, 2013, 2013 (special) : 77-83. doi: 10.3934/proc.2013.2013.77
[16]

Petr Kůrka. Minimality in iterative systems of Möbius transformations. Conference Publications, 2011, 2011 (Special) : 903-912. doi: 10.3934/proc.2011.2011.903
[17]

Petr Kůrka. Iterative systems of real Möbius transformations. Discrete & Continuous Dynamical Systems, 2009, 25 (2) : 567-574. doi: 10.3934/dcds.2009.25.567
[18]

Zecen He, Haihua Liang, Xiang Zhang. Limit cycles and global dynamic of planar cubic semi-quasi-homogeneous systems. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021049
[19]

Mohammed Abdelghany, Amr B. Eltawil, Zakaria Yahia, Kazuhide Nakata. A hybrid variable neighbourhood search and dynamic programming approach for the nurse rostering problem. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2051-2072. doi: 10.3934/jimo.2020058
[20]

Tengfei Yan, Qunying Liu, Bowen Dou, Qing Li, Bowen Li. An adaptive dynamic programming method for torque ripple minimization of PMSM. Journal of Industrial & Management Optimization, 2021, 17 (2) : 827-839. doi: 10.3934/jimo.2019136

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (51)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences