Necessary conditions for asymptotic tracking in nonlinear systems

Author

Grizzle, J.W. ; Benedetto, M. D Di ; Lamnabhi-Lagarrigue, F.

Author_Institution

Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA

Volume

39

Issue

9

fYear

1994

fDate

9/1/1994 12:00:00 AM

Firstpage

1782

Lastpage

1794

Abstract

In the literature, it has been shown that if a single-input single-output analytic nonlinear plant 1) has a well-defined relative degree and 2) is minimum-phase, it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in C^N [0, ∞), the space of N-times continuously differentiable functions taking values in R. When either of these sufficient conditions is not met, various authors have investigated approximate analytic solutions, discontinuous solutions and solutions for restricted sets of trajectories. In this paper, it is shown that conditions 1) and 2) are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories. Analogous results are established for multi-input multi-output systems

Keywords

closed loop systems; compensation; multivariable control systems; nonlinear control systems; tracking; N-times continuously differentiable functions; analytic compensator; asymptotic tracking; minimum-phase systems; multi-input multi-output systems; necessary conditions; nonlinear systems; output trajectories; single-input single-output analytic nonlinear plant; sufficient conditions; well-defined relative degree; Computer science; Differential equations; Nonlinear systems; Open loop systems; Regulators; Robots; Servomechanisms; Signal generators; Sufficient conditions; Trajectory;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.317102

Filename

317102