Research Article
BibTex RIS Cite

On Signomial Constrained Optimal Control Problems

Year 2019, Volume: 2 Issue: 1, 55 - 59, 22.03.2019
https://doi.org/10.33434/cams.482470

Abstract

In this paper, using the notions of variational differential system, adjoint differential system and modified Legendrian duality, we formulate and prove necessary optimality conditions in signomial constrained optimal control problems.

References

  • [1] L.C. Evans, An Introduction to Mathematical Optimal Control Theory,Lecture Notes, University of California, Department of Mathematics,Berkeley, (2008).
  • [2] E.B. Lee, L. Markus, Foundations of Optimal Control Theory, Wiley,(1967).
  • [3] St. Mititelu, S. Treanta, Efficiency conditions in vector control problemsgoverned by multiple integrals, J. Appl. Math. Comput., 57, 1-2, 647-665,(2018).
  • [4] L. Pontriaguine, V. Boltianski, R. Gamkrelidze, E. Michtchenko,Theorie Mathematique des Processus Optimaux, Edition Mir Moscou,(1974).
  • [5] S. Treanta, C. Varsan, Weak small controls and approximations asso-ciated with controllable affine control systems, Journal of DifferentialEquations, 255, 7, 1867-1882, (2013).
  • [6] S. Treanta, C. Udriste, Optimal control problems with higher order ODEsconstraints, Balkan J. Geom. Appl., 18, 1, 71-86, (2013).
  • [7] S. Treanta, Optimal control problems on higher order jet bundles, BSGProceedings 21. The International Conference "Differential Geometry- Dynamical Systems" DGDS-2013, October 10-13, 2013, Bucharest-Romania. Balkan Society of Geometers, Geometry Balkan Press 2014,pp. 181-192.
  • [8] S. Treanta, Local uncontrollability for affine control systems with jumps,International Journal of Control, 90, 9, 1893-1902, (2017).
  • [9] S. Treanta, M. Arana-Jimenez, KT-pseudoinvex multidimensional con-trol problem, Optim. Control Appl. Meth., 39, 4, 1291-1300, (2018).
  • [10] C. Udriste, Simplified multitime maximum principle, Balkan J. Geom.Appl., 14, 1, 102-119, (2009).
  • [11] M. Wagner, Pontryagin's Maximum Principle for Dieudonne-RashevskyType Problems Involving Lipcshitz functions, Optimization, 46, 2, 165-184, (1999).
Year 2019, Volume: 2 Issue: 1, 55 - 59, 22.03.2019
https://doi.org/10.33434/cams.482470

Abstract

References

  • [1] L.C. Evans, An Introduction to Mathematical Optimal Control Theory,Lecture Notes, University of California, Department of Mathematics,Berkeley, (2008).
  • [2] E.B. Lee, L. Markus, Foundations of Optimal Control Theory, Wiley,(1967).
  • [3] St. Mititelu, S. Treanta, Efficiency conditions in vector control problemsgoverned by multiple integrals, J. Appl. Math. Comput., 57, 1-2, 647-665,(2018).
  • [4] L. Pontriaguine, V. Boltianski, R. Gamkrelidze, E. Michtchenko,Theorie Mathematique des Processus Optimaux, Edition Mir Moscou,(1974).
  • [5] S. Treanta, C. Varsan, Weak small controls and approximations asso-ciated with controllable affine control systems, Journal of DifferentialEquations, 255, 7, 1867-1882, (2013).
  • [6] S. Treanta, C. Udriste, Optimal control problems with higher order ODEsconstraints, Balkan J. Geom. Appl., 18, 1, 71-86, (2013).
  • [7] S. Treanta, Optimal control problems on higher order jet bundles, BSGProceedings 21. The International Conference "Differential Geometry- Dynamical Systems" DGDS-2013, October 10-13, 2013, Bucharest-Romania. Balkan Society of Geometers, Geometry Balkan Press 2014,pp. 181-192.
  • [8] S. Treanta, Local uncontrollability for affine control systems with jumps,International Journal of Control, 90, 9, 1893-1902, (2017).
  • [9] S. Treanta, M. Arana-Jimenez, KT-pseudoinvex multidimensional con-trol problem, Optim. Control Appl. Meth., 39, 4, 1291-1300, (2018).
  • [10] C. Udriste, Simplified multitime maximum principle, Balkan J. Geom.Appl., 14, 1, 102-119, (2009).
  • [11] M. Wagner, Pontryagin's Maximum Principle for Dieudonne-RashevskyType Problems Involving Lipcshitz functions, Optimization, 46, 2, 165-184, (1999).
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Savin Treanta 0000-0001-8209-3869

Publication Date March 22, 2019
Submission Date November 13, 2018
Acceptance Date January 14, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Treanta, S. (2019). On Signomial Constrained Optimal Control Problems. Communications in Advanced Mathematical Sciences, 2(1), 55-59. https://doi.org/10.33434/cams.482470
AMA Treanta S. On Signomial Constrained Optimal Control Problems. Communications in Advanced Mathematical Sciences. March 2019;2(1):55-59. doi:10.33434/cams.482470
Chicago Treanta, Savin. “On Signomial Constrained Optimal Control Problems”. Communications in Advanced Mathematical Sciences 2, no. 1 (March 2019): 55-59. https://doi.org/10.33434/cams.482470.
EndNote Treanta S (March 1, 2019) On Signomial Constrained Optimal Control Problems. Communications in Advanced Mathematical Sciences 2 1 55–59.
IEEE S. Treanta, “On Signomial Constrained Optimal Control Problems”, Communications in Advanced Mathematical Sciences, vol. 2, no. 1, pp. 55–59, 2019, doi: 10.33434/cams.482470.
ISNAD Treanta, Savin. “On Signomial Constrained Optimal Control Problems”. Communications in Advanced Mathematical Sciences 2/1 (March 2019), 55-59. https://doi.org/10.33434/cams.482470.
JAMA Treanta S. On Signomial Constrained Optimal Control Problems. Communications in Advanced Mathematical Sciences. 2019;2:55–59.
MLA Treanta, Savin. “On Signomial Constrained Optimal Control Problems”. Communications in Advanced Mathematical Sciences, vol. 2, no. 1, 2019, pp. 55-59, doi:10.33434/cams.482470.
Vancouver Treanta S. On Signomial Constrained Optimal Control Problems. Communications in Advanced Mathematical Sciences. 2019;2(1):55-9.

Creative Commons License   The published articles in CAMS are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License..