Some results in nonlinear QFT

TLDR: In this paper, the problem of robust control of an uncertain nonlinear plant is reduced to a linear equivalent problem decoupled from the linear QFT formalism, and the problem is then reduced to linear equivalent control for the linear equivalent family of linear plants.

Abstract: SUMMARY Nonlinear QFT (quantitative feedback theory) is a technique for solving the problem of robust control of an uncertain nonlinear plant by replacing the uncertain nonlinear plant with an &equivalent’ family of linear plants. The problem is then "nding a linear QFT controller for this family of linear plants. While this approach is clearly limited, it follows in a long tradition of linearization approaches to nonlinear control (describing functions, extended linearization, etc.) which have been found to be quite e!ective in a wide range of applications. In recent work, the authors have developed an alternative function space method for the derivation and validation of nonlinear QFT that has clari"ed and simpli"ed several important features of this approach. In particular, single validation conditions are identi"ed for evaluating the linear equivalent family, and as a result, the nonlinear QFT problem is reduced to a linear equivalent problem decoupled from the linear QFT formalism. In this paper, we review this earlier work and use it in the development of (1) new results on the existence of nonlinear QFT solutions to robust control problems, and (2) new techniques for the circumvention of problems encountered in the application of this approach. Copyright ( 2001 John Wiley & Sons, Ltd.