Free Access
Volume 54, Number 1, January-February 2020
Page(s) 79 - 103
Published online 14 January 2020
  1. H. Amann and J. Escher, Analysis. I. Translated from the 1998 German original by Gary Brookfield. Birkhäuser Verlag, Basel (2005). [Google Scholar]
  2. L. Bonifacius, Numerical analysis of parabolic time-optimal control problems. Ph.D. thesis, Technische Universität München (2018). [Google Scholar]
  3. L. Bonifacius and K. Pieper, Strong stability of linear parabolic time-optimal control problems. ESAIM: COCV 25 (2019) 35. [CrossRef] [EDP Sciences] [Google Scholar]
  4. L. Bonifacius, K. Pieper and B. Vexler, Error estimates for space-time discretization of parabolic time-optimal control problems with bang-bang controls. SIAM J. Control Optim. 57 (2019) 1730–1756. [Google Scholar]
  5. E. Casas, D. Wachsmuth and G. Wachsmuth, Sufficient second-order conditions for bang-bang control problems. SIAM J. Control Optim. 55 (2017) 3066–3090. [Google Scholar]
  6. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology. Evolution problems. I, With the collaboration of Michel Artola, Michel Cessenat and Hélène Lanchon, Translated from the French by Alan Craig . Springer-Verlag, Berlin (1992). [Google Scholar]
  7. J.C. Dunn, Convergence rates for conditional gradient sequences generated by implicit step length rules. SIAM J. Control Optim. 18 (1980) 473–487. [Google Scholar]
  8. H.O. Fattorini, Infinite dimensional linear control systems. The time optimal and norm optimal problems. In: Vol. 201 of North-Holland Mathematics Studies. Elsevier Science B.V., Amsterdam (2005). [Google Scholar]
  9. R. Glowinski, J.-L. Lions and J. He, Exact and approximate controllability for distributed parameter systems. A numerical approach. In: Vol. of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2008). [Google Scholar]
  10. F. Gozzi and P. Loreti, Regularity of the minimum time function and minimum energy problems: the linear case. SIAM J. Control Optim. 37 (1999) 1195–1221. [Google Scholar]
  11. M. Gugat, A Newton method for the computation of time-optimal boundary controls of one-dimensional vibrating systems. Control of partial differential equations (Jacksonville, FL, 1998). J. Comput. Appl. Math. 114 (2000) 103–119. [Google Scholar]
  12. Q. Han and F.-H. Lin, Nodal sets of solutions of parabolic equations. II. Comm. Pure Appl. Math. 47 (1994) 1219–1238. [CrossRef] [Google Scholar]
  13. H. Hermes and J.P. LaSalle, Functional analysis and time optimal control. In: Vol. 56 of Mathematics in Science and Engineering. Academic Press, New York-London (1969). [Google Scholar]
  14. M. Hintermüller and K. Kunisch, Path-following methods for a class of constrained minimization problems in function space. SIAM J. Optim. 17 (2006) 159–187. [Google Scholar]
  15. K. Ito and K. Kunisch, Semismooth Newton methods for time-optimal control for a class of ODEs, SIAM J. Control Optim. 48 (2010) 3997–4013. [Google Scholar]
  16. C.Y. Kaya and J.L. Noakes, Computational method for time-optimal switching control. J. Optim. Theory Appl. 117 (2003) 69–92. [Google Scholar]
  17. W. Krabs, Optimal control of processes governed by partial differential equations. I. Heating processes. Z. Oper. Res. Ser. A-B 26 (1982) A21–A48. [Google Scholar]
  18. K. Kunisch and D. Wachsmuth, On time optimal control of the wave equation, its regularization and optimality system. ESAIM: COCV 19 (2013) 317–336. [CrossRef] [EDP Sciences] [Google Scholar]
  19. K. Kunisch, K. Pieper and A. Rund, Time optimal control for a reaction diffusion system arising in cardiac electrophysiology – a monolithic approach. ESAIM: M2AN 50 (2016) 381–414. [CrossRef] [EDP Sciences] [Google Scholar]
  20. X.J. Li and J.M. Yong, Optimal control theory for infinite-dimensional systems. Systems & Control: Foundations & Applications. Birkhäuser Boston Inc, Boston, MA (1995). [Google Scholar]
  21. X. Lu, L. Wang and Q. Yan, Computation of time optimal control problems governed by linear ordinary differential equations. J. Sci. Comput. 73 (2017) 1–25. [Google Scholar]
  22. J.W. Macki and A. Strauss, Introduction to optimal control theory. Undergraduate Texts in Mathematics. Springer-Verlag, New York-Berlin (1982). [CrossRef] [Google Scholar]
  23. E.-B. Meier and A.E. Bryson Jr, Efficient algorithm for time-optimal control of a two-link manipulator. J. Guidance Control Dynam. 13 (1990) 859–866. [CrossRef] [Google Scholar]
  24. A. Münch and F. Periago, Numerical approximation of bang-bang controls for the heat equation: an optimal design approach. Syst. Control Lett. 62 (2013) 643–655. [Google Scholar]
  25. A. Münch and E. Zuazua. Numerical approximation of null controls for the heat equation: ill-posedness and remedies. Inverse Prob. 26 (2010) 085018, 39. [Google Scholar]
  26. J. Nocedal and S.J. Wright, Numerical optimization, 2nd edition. In: Springer Series in Operations Research and Financial Engineering. Springer, New York, NY (2006). [Google Scholar]
  27. E.M. Ouhabaz, Analysis of heat equations on domains. In: Vol. 31 of London Mathematical Society Monographs Series. Princeton University Press, Princeton, NJ (2005). [Google Scholar]
  28. A. Pazy, Semigroups of linear operators and applications to partial differential equations. In: Vol. 44 of Applied Mathematical Sciences. Springer-Verlag, New York (1983). [CrossRef] [Google Scholar]
  29. K. Pieper, Finite element discretization and efficient numerical solution of elliptic and parabolic sparse control problems. Ph.D. thesis, Technische Universität München (2015). [Google Scholar]
  30. S. Qin and G. Wang, Equivalence between minimal time and minimal norm control problems for the heat equation. SIAM J. Control Optim. 56 (2018) 981–1010. [Google Scholar]
  31. S.M. Robinson, Normal maps induced by linear transformations. Math. Oper. Res. 17 (1992) 691–714. [CrossRef] [MathSciNet] [Google Scholar]
  32. F. Trltzsch, Optimal control of partial differential equations. Theory, methods and applications, Translated from the 2005 German original by Jürgen Sprekels. In: Vol. 112 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2010). [CrossRef] [Google Scholar]
  33. M. Tucsnak and G. Weiss, Observation and Control for Operator Semigroups. Birkhäuser Advanced Texts: Basler Lehrbücher [Birkhäuser Advanced Texts: Basel Textbooks]. Birkhäuser Verlag, Basel (2009). [Google Scholar]
  34. W. Wang and M.Á. Carreira-Perpiñán, Projection onto the probability simplex: an efficient algorithm with a simple proof, and an application. Preprint arXiv:1309.1541 (2013). [Google Scholar]
  35. G. Wang and Y. Xu, Equivalence of three different kinds of optimal control problems for heat equations and its applications. SIAM J. Control Optim. 51 (2013) 848–880. [Google Scholar]
  36. G. Wang and E. Zuazua, On the equivalence of minimal time and minimal norm controls for internally controlled heat equations. SIAM J. Control Optim. 50 (2012) 2938–2958. [Google Scholar]
  37. G. Wang, L. Wang, Y. Xu and Y. Zhang, Time optimal control of evolution equations. Progress in Nonlinear Differential Equations and Their Applications, Springer International Publishing (2018). [CrossRef] [Google Scholar]
  38. C. Zhang, The time optimal control with constraints of the rectangular type for linear time-varying ODEs. SIAM J. Control Optim. 51 (2013) 1528–1542. [Google Scholar]
  39. Y. Zhang, Two equivalence theorems of different kinds of optimal control problems for Schrödinger equations. SIAM J. Control Optim. 53 (2015) 926–947. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you