Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-16T17:01:38.021Z Has data issue: false hasContentIssue false
  • English
  • Français

Necessary conditions of optimal impulse controls for distributed parameter systems

Published online by Cambridge University Press:  17 April 2009

Jiongmin Yong  and
Pingjian Zhang
Jiongmin Yong
Affiliation:
Department of MathematicsFudan UniversityShanghai 200433, China
Pingjian Zhang
Affiliation:
Department of MathematicsFudan UniversityShanghai 200433, China
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Optimal control problem of semilinear evolutionary distributed parameter systems with impulse controls is considered. Necessary conditions of optimal controls are derived. The result generalises the usual Pontryagin's maximum principle.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 305 - 326
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Barbu, V., Optimal control of variational inequalities (Pitman, Boston, 1984).Google Scholar
[2]Barles, G., ‘Deterministic impulse control problems’, SIAM J. Control Optim. 23 (1985), 419–432.CrossRefGoogle Scholar
[3]Belbas, S.A. and Lenhart, S.M., ‘Nonlinear PDE's for stochastic optimal control with switching and impulses’, Appl. Math. Optim. 14 (1986), 215–227.CrossRefGoogle Scholar
[4]Bensoussan, A. and Lions, J.L., Impulse control and quasi-variational inequalities (Bordes, Paris, 1984).Google Scholar
[5]Clarke, F.H., Optimization and nonsmooth analysis (Wiley, New York, 1983).Google Scholar
[6]Clarke, F.H. and Vinter, R.B., ‘Applications of optimal multiprocesses’, SIAM J. Control Optim. 27 (1989), 1048–1071.CrossRefGoogle Scholar
[7]Clarke, F.H. and Vinter, R.B., ‘Optimat multiprocesses’, SIAM J. Control Optim. 27 (1989), 1072–1091.CrossRefGoogle Scholar
[8]Curtain, R.F. and Pritchard, A.J., Infinite dimensional linear systems theory: Lecture Notes in Control and Information Sciences Vol 8 (Springer-Verlag, New York, 1981).Google Scholar
[9]Ekeland, I., ‘Nonconvex minimization problems’, Bull. Amer. Math. Soc. (new Series) 1 (1979), 443–474.CrossRefGoogle Scholar
[10]Fattorini, H.O., ‘A unified theory of necessary conditions for nonlinear nonconvex control systems’, Appl. Math. Optim. 15 (1987), 141–185.CrossRefGoogle Scholar
[11]Friedman, A., Huang, S. and Yong, J., ‘Bang-bang optimal control for the dam problem’, Appl. Math. Optim. 15 (1987), 65–85.CrossRefGoogle Scholar
[12]Friedman, A., Huang, S. and Yong, J., ‘Optimal periodic control for the two-phase Stefan problem’, SIAM J. Control Optim. 26 (1988), 23–41.CrossRefGoogle Scholar
[13]Hu, Y. and Yong, J., ‘Maximum principle for stochastic optimal impulse controls’, (in Chinese), Chinese Ann. Math. Ser. A. Suppl. 12 (1991), 109–114.Google Scholar
[14]Li, X. and Yao, Y., ‘Maximum principle of distributed parameter systems with time lags’, in Distributed Parameter Systems: Lecture Notes in Control and Information Sciences 75, pp. 410–427 (Springer-Verlag, Berlin, Heidelberg, New York, 1985).CrossRefGoogle Scholar
[15]Li, X. and Yong, J., ‘Necessary conditions of optimal control for distributed parameter systems’, SIAM J. Control Optim. 29 (1991), 895–908.CrossRefGoogle Scholar
[16]Rishel, R.W., ‘An extended Pontryagin principle for control systems whose control law contains measures’, SIAM J. Control Optim. 3 (1965), 191–205.Google Scholar
[17]Vinter, R.B. and Pereira, F.M.F.L., ‘A maximum principle for optimal processes with discontinuous trajectories’, SIAM J. Control Optim. 26 (1988), 205–229.CrossRefGoogle Scholar
[18]Yong, J., ‘Optimal switching and impulse controls for distributed parameter systems’, System Sci. and Math. Sci. 2 (1989), 137–160.Google Scholar
[19]Yong, J., ‘Systems governed by ordinary differential equations with continuous switching and impulse controls’, Appl. Math. Optim. 20 (1989), 223–236.CrossRefGoogle Scholar
[20]Yong, J., ‘A maximum principle for the optimal controls for a nonsmooth semilinear evolution system’, in Analysis and Optimization of Systems: Lecture Notes in Control and Inform. Sci. 144, Editors Bensoussan, A. and Lions, J.L., pp. 559–569 (Springer-Verlag, Berlin, Heidelberg, New York, 1990).CrossRefGoogle Scholar
[21]Yong, J., ‘Distributed parameter systems with measure controls’, in Control theory of distributed parameter systeme and applications: Lecture Notes in Control and Information Science 159, Editors Li, X. and Yong, J., pp. 176–185 (Springer-Verlag, Berlin, Heidelberg, New York, 1991).CrossRefGoogle Scholar
[22]Yong, J., ‘Infinite dimensional Volterra-Stieljes evolution equations and related optimal control problems’, SIAM J. Contol Optim. (to appear).Google Scholar