Objective function design for robust optimality of linear control under state-constraints and uncertainty

¹ Dipartimento di Matematica, Università di Trento, Via Sommarive 14, 38050 Povo-Trento, Italy. bagagiol@science.unitn.it
² DINFO, Università di Palermo, 90128 Palermo, Italy. dario.bauso@unipa.it

Received: 12 March 2009
Revised: 27 July 2009

Abstract

We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.