Robust control of uncertain multi-inventory systems via linear matrix inequality

Abstract

We consider a continuous time linear multi-inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes. We address the problem of ε-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which ε-stabilizability is possible through a saturated linear state feedback control. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.

Game-Theoretic Learning and Allocations in Robust Dynamic Coalitional Games

“…The results we provide collocate within the learning, control and optimisation research areas. This research direction finds applications in various problems such as wind energy (Opathella and Venkatesh , 2013;Bayens et al , 2013), and the inventory control problem Bauso et al (2008); Bauso et al (2010).…”

“…Such a game was first formulated by (Bauso andTimmer, 2009, 2012). The evolution of the excesses is also captured by a fluid flow system of the type discussed in (Bauso et al, 2010).…”

Experiments in Iterative Feedback tuning for level control of three-tank system

“…, (6) where the subscript 2 outlines the experiment index and 1  q is the backward shift operator.  Step 3.…”

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

“…One practical way to deal with robustly controlled invariant set is to apriori impose some structure and restrict the search to polytopic or ellipsoidal sets (cfg. [4], [5], [6], [7]). The simplicity with which these sets can be formulated translates into computational tractability for the optimization problems involved in the study (linear or quadratic mathematical programs).…”

“…Questions of existence of robustly control invariant sets, as well as their properties when they do exist, are thus of interest. Of course, this problem has been previously considered in the literature, for instance in [6] [7] where polytopic invariant sets as considered and in [5] where ellipsoidal sets are considered. Restricting the discussion to polytopic sets has the advantage of reducing the problem to linear programs, with the relative computational benefits: The problem turns into a robust quadratic programming problem involving linear matrix inequalities when the sets are ellipsoidal.…”