Have a personal or library account? Click to login
A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint Cover

A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint

Open Access
|Aug 2022

References

  1. Aubin, J.-P. and Frankowska, H. (1990) Set-valued Analysis. Birkhäuser, Boston.
  2. Bonnans, J.F. and Hermant, A. (2009) Second-order analysis for optimal control problems with pure state constraints and mixed control-state constraints. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, 561-–598.
  3. Bonnans, J.F. and Osmolovskii, N.P. (2010) Second-order analysis of optimal control problems with control and initial-final state constraints. J. Convex Anal. 17, 885-–913.
  4. Bonnans, J. F. and Osmolovskii, N. P. (2012) Characterization of a local quadratic growth of the Hamiltonian for control constrained optimal control problems. Dynamics of Continuous, Discrete and Impulsive Systems, Series B (DCDIS-B), University of Waterloo, Canada, 19, 1-2, 1–16.
  5. Bonnans, J.F. and Shapiro, A. (2000) Perturbation Analysis of Optimal Control Problems. Springer, New York.10.1007/978-1-4612-1394-9
  6. Cominetti, R. (1990) Metric regularity, tangent sets, and second-order optimality conditions. Applied Mathematics and Optimization 21, 265-–287.10.1007/BF01445166
  7. Levitin, E.S., Milyutin, A.A. and Osmolovskii, N.P. (1978) Higher-order local minimum conditions in problems with constraints. Uspekhi Mat. Nauk 33 (1978) 85–148; English translation in Russian Math. Surveys 33, 97-–168.
  8. Malanowski, K. (1994) Stability and sensitivity of solutions to nonlinear optimal control problems. Appl. Math. Optim. 32, 111-–141.
  9. Malanowski, K. (2001) Sensitivity analysis for parametric control problems with control–state constraints. Dissertationes Mathematicae CCCXCIV. Polska Akademia Nauk, Instytut Matematyczny, Warszawa, 1-–51.
  10. Malanowski, K. and Maurer, H. (1996) Sensitivity analysis for parametric control problems with control–state constraints. Computational Optimization and Applications 5, 253–283.10.1007/BF00248267
  11. Maurer, H. (1981) First and second order sufficient optimality conditions in mathematical programming and optimal control. Mathematical Programming Study 14, 163—177.10.1007/BFb0120927
  12. Maurer, H. and Pickenhain, S. (1995)Second order sufficient conditions for optimal control problems with mixed control-state constraints. J. Optim. Theory Appl. 86, 649—667.
  13. Milyutin, A.A. and Osmolovskii, N.P. (1998) Calculus of Variations and Optimal Control, Translations of Mathematical Monographs 180. American Mathematical Society, Providence.
  14. Osmolovskii, N.P. (2011) Sufficient quadratic conditions of extremum for discontinuous controls in optimal control problems with mixed constraints. J. Math. Science 173, 1–106.
  15. Osmolovskii, Nikolai P. (2012) Second-order optimality conditions for control problems with linearly independent gradients of control constraints. ESAIM: Control, Optimisation and Calculus of Variations, 18, 2, 02, April 2012, 452–482.10.1051/cocv/2011101
  16. Osmolovskii, N.P. and Maurer, H. (2012) Applications to regular and bang-bang control: Second-Order Necessary and Sufficient Optimality Conditions in Calculus of Variations and Optimal Control. SIAM, Philadelphia.10.1137/1.9781611972368
  17. Zeidan, V. (1984) Extended Jacobi sufficiency criterion for optimal control. SIAM J. Control. Optim. 22, 294—301.
  18. Zeidan, V. (1994) The Riccati equation for optimal control problems with mixed state-control constraints: necessity and sufficiency. SIAM J. Control Optim. 32, 1297—1321.10.1137/S0363012992233640
DOI: https://doi.org/10.2478/candc-2022-0012 | Journal eISSN: 2720-4278 | Journal ISSN: 0324-8569
Language: English
Page range: 151 - 169
Submitted on: Feb 1, 2022
|
Accepted on: Apr 1, 2022
|
Published on: Aug 12, 2022
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2022 Nikolai P. Osmolovskii, published by Systems Research Institute Polish Academy of Sciences
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.