Efficient Evaluation of Piecewise Control Laws Defined Over a Large Number of Polyhedra

Abstract

The on-line evaluation of a piecewise state feedback control law requires the determination of the state space region in which the measured state lies, in order to decide which ‘piece’ of the piecewise control law to apply. This procedure is called the point location problem, and the rate at which it can be solved determines the minimal sampling time of the system. In this chapter a novel and computationally efficient search tree algorithm is presented that significantly improves this point-location search for piecewise control laws defined over a large number of (possibly overlapping) polyhedra. Furthermore, the required off-line preprocessing is low and so the approach can be applied to very complex controllers.