Reachability under uncertainty and measurement noise

This paper deals with the problem of reachability under unknown but bounded disturbances and piecewise open-loop controls which may be feedback-corrected at isolated ‘points of correction’. It is presumed that there are hard bounds on the controls and the unknown but bounded items. The open-loop controls are reassigned at prespecified points of correction on the basis of additional information on the state space variable which arrives at these points. Such information typically comes through a given noisy instantaneous measurement of the state space variable which sometimes may or may not be complemented by information on the forthcoming disturbance. Thus the process is ‘piecewise feedback’ with feedback introduced at points of correction. The described situation is intermediate relative to purely open-loop control and continuous measurement feedback control under uncertainty. The novelty of this paper lies in considering incomplete noisy measurements of the state space variable at points of correction rather than exact complete measurements of these. The paper also describes some numerical algorithms relevant for computer modelling. It is emphasized that effective computational results may be obtained if one relies on ellipsoidal techniques as given by Kurzhanski et al.