Guaranteed cost control for multi-inventory systems with uncertain demand

  • Authors:

  • Franco Blanchini;Stefano Miani;Franca Rinaldi

  • Affiliations:

  • Dipartimento di Matematica ed Informatica, Universití degli Studi di Udine, Via delle Scienze 206, Udine 33100, Italy;Dipartimento di Ingegneria Gestionale, Elettrica e Meccanica, Universití degli Studi di Udine, Via delle Scienze 206, Udine 33100, Italy;Dipartimento di Matematica ed Informatica, Universití degli Studi di Udine, Via delle Scienze 206, Udine 33100, Italy

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2004

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Abstract

In this paper we consider the problem of controlling a multi-inventory system in the presence of uncertain demand. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be also constrained in a compact set. We consider an integral cost function of the buffer levels and we face the problem of minimizing the worst-case cost. We show that the optimal cost of a suitable auxiliary problem with no uncertainties is always an upper bound for the original problem. In the special case of minimum-time control, this upper bound is tight, namely its optimal cost is equal to the worst-case cost for the original system. Furthermore, the result is constructive, since the optimal control law can be explicitly computed.