Control of production-distribution systems under discrete disturbances and control actions

Abstract

Abstract-This paper deals with the robust control and optimization of production-distribution systems. The model used in our problem formulation is a general network flow model that describes production, logistics, and transportation applications. The novelty in our formulation is in the discrete nature of the control and disturbance inputs. We highlight three main contributions: First, we derive a necessary and sufficient condition for the existence of robustly control invariant hyperboxes. Second, we show that a stricter version of the same condition is sufficient for global convergence to an invariant set. Third, for the scalar case, we show that these results parallel existing results in the setting where the control actions and disturbances are analog. We conclude with two simple illustrative examples.

Bounding the smallest robustly control invariant sets in networks with discrete disturbances and controls

“…On the other hand, the study of systems under discrete controls and disturbances has sparked much interest in recent years as evidenced by the literature on finite alphabet and boolean control [2,14,16,[20][21][22], mixed integer model predictive control [1], and discrete team theory [23], to cite a few. Building on our recent results in which we derived necessary and sufficient conditions for the existence of robustly control invariant hyperboxes [4,18,19], we revisit the question of size of the smallest such invariant sets, when they do exist. In particular, we assess the existing bounds [17,19] on the size of the smallest robustly control invariant hyperbox set, when size is measured in an 'l∞' sense.…”