ISSUES IN THE CONTROL OF HALFSPACE SYSTEMS

By the name HALFSPACE SYSTEMS, this dissertation refers to systems whose dynamics are modeled by linear constraints of the form Exk+1 \u3c= Fxk + Buk (where E, F 2 andlt;mn, B 2 andlt;mp). This dissertation explores the concepts of BOUNDEDNESS, STABILITY, IRREDUNDANCY, and MAINTAINABILITY (which is the same as REACHABILITY OF A TARGET TUBE) that are related to the control of halfspace systems. Given that a halfspace system is bounded, and that a given static target tube is reachable for this system, this dissertation presents algorithms to MAINTAIN the system in this target tube. A DIFFERENCE INCLUSION has the form xk+1 = Axk + Buuk, where xk, xk+1 2 andlt;n, uk 2 andlt;p, A 2 andlt;nn, Bu 2 andlt;np, Ai 2 andlt;nn, Bj 2 andlt;np, and A and Bu belong to the convex hulls of (A1,A2, . . . ,Aq) and (B1, B2, . . . , Br) respectively. This dissertation investigates the possibility that halfspace systems have equivalent difference inclusion representation for the case of uk = 0. An affirmitive result in this direction may make it possible to apply to halfspace systems the control theory that exists for difference inclusions