Optimal impulsive control theory

  • Alain Bensoussan
Part I: Survey Lectures
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 16)


We present in this survey some of the main ideas concerning impulse control theory. We have chosen the following framework. The process is a non degenerate diffusion stopped at the exit of a bounded regular domain of Rn. The control is excited by impulses, which modify the state of the system instantaneously. The cost involves an integral cost and a variable cost (depending on the size of the jump).

We mainly develop in this presentation the semi-group approach which is sufficient to prove the existence of an optimal impulse control. However, other analytic approaches of the characterization of the optimal cost are possible and in general are more convenient for the applications. We briefly mention them. Since the optimal stopping time problem is a necessary step to solve the impulse control problem, we present the main results of that theory also. The article ends with comments and remarks concerning other problems and extensions.


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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Alain Bensoussan
    • 1
  1. 1.Université Paris IX-Dauphine and IRIA/LABORIAFrance

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