Explicit model predictive control via Delaunay tessellations
Abstract
Solutions to Model Predictive Control (MPC) problems can be given in an explicit form as piecewise affine (PWA) state feedback laws over a polyhedral partition of the feasible set, avoiding the online optimization. In this paper we propose a technique to compute an approximate PWA MPC law that is suboptimal only over the subregion of the feasible set where constraints are active. In this subregion, the problem of computing a suitable suboptimal PWA control law is related to an important problem in computer aided geometric design: surface reconstruction. The technique is based on a fundamental structure in computational geometry theory, Delaunay tessellation, which have been particularly successful in dealing with the surface reconstruction problem.