Open Access
Volume 27, 2021
Article Number 104
Number of page(s) 36
Published online 08 December 2021
  1. M. Bardi and I. Capuzzo-Dolcetta, Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser, Boston (1997). [Google Scholar]
  2. G. Barles, Quasi-variational inequalities and first-order Hamilton-Jacobi equations. Nonlinear Anal.: Theory, Methods Appl. 9 (1985) 131–148. [CrossRef] [Google Scholar]
  3. G. Barles, Deterministic impluse control problems. SIAM J. Control Optim. 23 (1985) 419–432. [CrossRef] [MathSciNet] [Google Scholar]
  4. C. Belak, S. Christensen and F.T. Seifried, A general verification result for stochastic impulse control problems. SIAM J. Control Optim. 55 (2019) 627–649. [Google Scholar]
  5. R. Bellma, Dynamic Programming. Princeton Univ. Press, Princeton (1957). [Google Scholar]
  6. A. Bensoussan and J.L. Lions, Nouvells formulation de problèmes de contrôle impulsonnel et applications. C. R. Acad. Sci. Paris 276 (1973) 1182–1192. [Google Scholar]
  7. A. Bensoussan and J.L. Lions, Impulse Control and Quasi-Variational Inequalities. Bordes, Paris (1984). [Google Scholar]
  8. A. Bensoussan and C.S. Tapiero, Impulsive control in management: prospects and applications. J. Optim. Theory Appl. 17 (1982) 419–442. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Chahim, R.F. Hartl and P.M. Kort, A tutorial on the deterministic impulse control maximum principle: necessary and sufficient optimality conditions. Eur. J. Oper. Res. 219 (2012) 18–26. [CrossRef] [Google Scholar]
  10. L. Chu, T. Kompas and Q. Grafton, Impulse controls and uncertainty in economics: method and application. Environ. Model. Softw. 65 (2015) 50–57. [CrossRef] [Google Scholar]
  11. M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. AMS 277 (1983) 1–42. [CrossRef] [Google Scholar]
  12. V. Dykhta and O. Samsonuk, Maximum principle for nonsmooth optimal impulse problems. Proc. IFAC Nonlinear Control Systems (2001) 1303–1307. [Google Scholar]
  13. B. El Asri, Deterministic minimax impulse control in finite horizon: the viscosity solution approach. ESAIM COCV 19 (2013) 63–77. [CrossRef] [EDP Sciences] [Google Scholar]
  14. N. El Farouq, Degenerate first-order quasi-variational inequalities: an approach to approximate the value function. SIAM J. Control Optim. 55 (2017) 2714–2733. [CrossRef] [MathSciNet] [Google Scholar]
  15. N. El Farouq, G. Barles and P. Bernhard, Deterministic minimax impulse control. Appl. Math. Optim. 61 (2010) 353–378. [CrossRef] [MathSciNet] [Google Scholar]
  16. X. Feng, Maximum principle for optimal control problems involving impulse controls with nonsmooth data. Stochastics 88 (2016) 1188–1206. [CrossRef] [MathSciNet] [Google Scholar]
  17. W.H. Fleming and H.M. Soner, Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York (1992). [Google Scholar]
  18. Y. Hu and J. Yong, Maximum principle for stochastic optimal impulse controls. Chin. Ann. Math. Ser. A, Suppl. 12 (1991) 109–114 (in Chinese). [Google Scholar]
  19. R. Korn, Some applications of impulse control in mathematical finance. Math. Methods Oper. Res. 50 (1999) 189–218. [CrossRef] [MathSciNet] [Google Scholar]
  20. R. Korn, Y. Melnyk and F.T. Seifried, Stochastic impulse control with regime-switching dynamics. Eur. J. Oper. Res. 260 (2017) 1024–1042. [CrossRef] [Google Scholar]
  21. R. Leander, S. Lenhart and V. Protopopescu, Optimal control of continuous systems with impusle controls. Optim. Control Appl. Meth. 36 (2015) 535–549. [CrossRef] [Google Scholar]
  22. S.M. Lenhart, Viscosity solutions associated with impulse control problems for piecewise-deterministic process. Internat. J. Math. Math. Sci. 12 (1989) 145–157. [CrossRef] [MathSciNet] [Google Scholar]
  23. X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems. Birkhäuser, Boston (1995). [CrossRef] [Google Scholar]
  24. J.L. Menaldi, Optimal impulse control problems for degenerate diffusion with jumps. Acta Math. Appl. 8 (1987) 165–198. [CrossRef] [MathSciNet] [Google Scholar]
  25. J.L. Mendaldi and M. Robin, On some impulse control problems with constraint. SIAM J. Control Optim. 55 (2017) 3204–3225. [CrossRef] [MathSciNet] [Google Scholar]
  26. A. Piunovskiy, A. Plakhov and M. Tumanov, Optimal impulse control os a SIR epidemic. Optim. Control Appl. Meth. 41 (2020) 448–468. [CrossRef] [Google Scholar]
  27. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Misjcjenko, The Mathematical Theory of Optimal Processes. Interscience, New York (1962). [Google Scholar]
  28. R. Rempala and J. Zabczyk, On the maximum principle for Deterministic impulse control problems. J. Optim. Theory Appl. 59 (1988) 281–288. [CrossRef] [MathSciNet] [Google Scholar]
  29. H.M. Soner and N. Touzi, Stochastic target problems, dynamic programming and viscosity solutions. SIAM J. Control Optim. 41 (2002) 404–424. [CrossRef] [MathSciNet] [Google Scholar]
  30. H.J. Sussmann, Small-time local controllability and continuity of the optimal time function for linear systems. J. Optim. Theory Appl. 53 (1987) 281–296. [CrossRef] [MathSciNet] [Google Scholar]
  31. S. Tang and J. Yong, Finite horizon stochastic optimal switching and impulse controls with a viscosity solution approach. Stochastics Stochastics Reports 45 (1993) 145–176. [CrossRef] [MathSciNet] [Google Scholar]
  32. N. Touzi, Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE. Fields Institute Monographs, 29, Springer, New York (2013). [Google Scholar]
  33. Z. Wu and F. Zhang, Maximum principle for stochastic recursive optimal control problems involving impusle controls. Abstr. Appl. Anal. (2012) Art. ID 709682. [Google Scholar]
  34. V. Yadav and S.N. Balakrishnan, Optimal impulse control of systems with control constraints and application to HIV treatment. Proc. Am. Control Conf . (2006) 4824–4829. [Google Scholar]
  35. J. Yong, Systems governed by ordinary differential equations with continuous, switching and impulse controls. Appl. Math. Optim. 20 (1989) 223–236. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Yong, Zero-sum differential games involving impulse controls. Appl. Math. Optim. 29 (1994) 243–261. [CrossRef] [MathSciNet] [Google Scholar]
  37. J. Yong, Differential Games: A Concise Introduction. World Scientific, Singapore (2015). [CrossRef] [Google Scholar]
  38. J. Yong and P. Zhang, Necessary conditions of optimal impulse controls for distributed parameter systems. Bull. Aust. Math. Soc. 45 (1992) 305–326. [CrossRef] [Google Scholar]
  39. J. Yong and X.Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations. Springer-Verlag, New York (1999). [Google Scholar]

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