Stabilization of nonlinear processes with input constraints

Abstract

This work deals with nonlinear processes which, in the absence of input constraints, can be locally stabilized by a linearizing static state feedback law. Such systems, under unconstrained linearizing control laws, possess a cascaded structure between a (asymptotically or exponentially) stable nonlinear subsystem and an exponentially stable linear subsystem, which allows for a straightforward stability analysis. In the presence of input constraints, however, this cascaded structure breaks down to an interconnection between two nonlinear subsystems; analyzing the stability of such interconnections is a rather cumbersome task, that typically results in conservative estimates of regions of stability. In this article, we present an analysis framework for the local stabilization of such processes and the estimation of regions of closed-loop stability in the presence of input constraints. The proposed approach entails: (i) specifying a region in state–space where the closed-loop system behaves effectively as a cascade and asymptotic stability can be guaranteed in the presence of constraints, provided that the states of the system remain in this region for all times; and (ii) constructing invariant sets within this region that qualify as regions of closed-loop stability. A detailed case study is carried out on a polymerization reactor example and the desirable features of the proposed methodology are aptly illustrated.