On the robust control of systems with respect to set valued objectives

This paper considers an extension of the Target Tube Reachability Problem (TTRP) for discrete-time, linear systems with set-constrained disturbance inputs and observation uncertainties to include set-bounded parametric uncertainty in the state transition matrix. A backwards recursive algorithm, similar in spirit to that developed by Bertsekas & Rohdes [1], is proposed for the determination of Robust Attainability Regions in state space. These guarantee the existence of admissible control actions that maintain possible state trajectories inside a pre-specified Target Tube defined over a finite planning horizon. The basic concepts for this extension are robust direct and inverse images of closed, convex, bounded (CCB) sets through linear maps with uncertain but bounded parameters. Formulae and simple examples are furnished in detail for the ellipsoidal case.