Nicely Nonlinear Modelling and Control

Abstract

A system M tangent to a plant P at the nominal equilibrium is a nicely nonlinear model of P if it is (properly) linearizable by output feedback. For any nicely nonlinear model M, a composite controller can naturally be devised as the cascade connection of a (nonlinear) linearizing compensator C _L and a (possibly linear) controller R the design (or the tuning) of which can be carried out following standard paradigms of any peace of control theory where the plant is by assumption linear and time-invariant. Constructing parametrized families of nicely nonlinear models is therefore of obvious interest, inasmuch as it is also possible to provide, for each one of them, conceivably cheap algorithms able to identify one (at least) of the individual elements in the family, that best fit with (the known and significant behavior of) a given plant. Such a task is here referred to as nicely nonlinear modelling. The purpose of the present paper is to discuss, and to illustrate by examples, some aspects of its general (abstract) structure.