DISCRETE APPROXIMATION AND CONTROL OF HIGH-ORDER NONLINEAR CONTINUOUS SYSTEMS

Abstract

Approximation-based approaches to hybrid control systems synthesis have been mostly limited to problems with low-order linear continuous dynamics. In this contribution, results from the theory of monotone dynamical systems are used to efficiently compute discrete approximations for a class of nonlinear models. Furthermore, a situation is investigated where the high-dimensional plant state converges to a low-dimensional manifold; in the proposed approach the computational effort is governed by the dimension of the low-order manifold without neglecting the high-order dynamics. Results are applied to synthesize a discrete event controller for the automatic start-up of a nonlinear distillation column model of 42nd order.