Robust Control of Distribution Networks with Uncertain Demand

The problem is considered of controlling a distribution network having reservoir and trnsport capacity constraints in the presence of unknown but bounded inputs representing the production and the demand uncertainty. The problem is approached via a worst case analysis in the sense that our goal is to detemine a control strategy that assures the constraints are fulfilled for all possible uncertain inputs. According with previous works we solve the problem by constructing off-line a sequence of polyhedral sets called the target tube. Such a target tube is then used on-line to produce the control. The main result of the paper is that in the class of systems we are considering, the number of delimiting planes of the sets forming the target tube is fixed and known a-priori. Moreover only the known terms of this plane have to be computed and they are the solution of a system of difference equations.