Advertisement

Impulse Controls and Double Constraints

Chapter
  • 911 Downloads
Part of the Systems & Control: Foundations & Applications book series (SCFA, volume 85)

Abstract

In the first section of this chapter we deal with the problem of feedback impulse control in the class of generalized inputs that may involve delta functions and discontinuous trajectories in the state space. Such feedback controls are not physically realizable. The second section thus treats the problem of feedback control under double constraints: both hard bounds and integral bounds. Such solutions are then used for approximating impulse controls by bounded “ordinary” functions.

Keywords

Bounded variation Impulsive inputs δ-Function Closed-loop control Value function Variational inequality Double constraints 

References

  1. 16.
    Bardi, M., Capuzzo Dolcetta, I.: Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations. SCFA. Birkhäuser, Boston (1997)CrossRefzbMATHGoogle Scholar
  2. 23.
    Bensoussan, A., Lions, J.-L.: Contrôle impulsionnel et inéquations quasi-variationnelles. Dunod, Paris (1982)zbMATHGoogle Scholar
  3. 33.
    Bolza, O.: Lectures on Calculus of Variations. Hafer Pub. Co, New York (1946). Dover reprintGoogle Scholar
  4. 42.
    Carter, T.E.: Optimal impulsive space trajectories based on linear equations. J. Optim. Theory Appl. 70(2), 277–297 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 43.
    Carter, T.E., Brient, J.: Linearized impulsive rendezvous problem. J. Optim. Theory Appl. 86(3), 553–584 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 55.
    Daryin, A.N., Kurzhanski, A.B., Seleznev, A.V.: A dynamic programming approach to the impulse control synthesis problem. In: Proceedings of Joint 44th IEEE Conference on Decision and Control and European Control Conference ECC 2005, Seville, Spain, pp. 8215–8220 (2005)Google Scholar
  7. 70.
    Fan, K.: Minimax theorems. Proc. Natl. Acad. Sci. USA 39(1), 42–47 (1953)CrossRefzbMATHGoogle Scholar
  8. 75.
    Filippov, A.F.: On certain questions in the theory of optimal control. SIAM J. Control. 1, 76–84 (1962)zbMATHGoogle Scholar
  9. 120.
    Krasovski, N.N.: Motion Control Theory. Nauka, Moscow (1968) [in Russian]Google Scholar
  10. 152.
    Kurzhanski, A.B.: On synthesizing impulse controls and the theory of fast controls. Proc. Steklov Math. Inst. 268(1), 207–221 (2010)CrossRefzbMATHGoogle Scholar
  11. 154.
    Kurzhanski, A.B., Daryin, A.N.: Dynamic programming for impulse controls. Ann. Rev. Control 32(2), 213–227 (2008)CrossRefGoogle Scholar
  12. 219.
    Neustadt, L.W.: Optimization, a moment problem and nonlinear programming. SIAM J. Control Optim. 2(1), 33–53 (1964)MathSciNetzbMATHGoogle Scholar
  13. 234.
    Riesz, F., Sz-.Nagy, B.: Leçons d’analyse fonctionnelle. Akadémiai Kiadó, Budapest (1972)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State (Lomonosov) UniversityMoscowRussia
  2. 2.Electrical Engineering and Computer SciencesUniversity of California, BerkeleyBerkeleyUSA

Personalised recommendations