Bode-Like Fundamental Performance Limitations in Control of Nonlinear Systems

Author

Yu, Sun ; Mehta, Prashant G.

Author_Institution

Dept. of Mech. Sci. & Eng., Univ. of Illinois at Urbana Champaign, Urbana, IL, USA

Volume

55

Issue

6

fYear

2010

fDate

6/1/2010 12:00:00 AM

Firstpage

1390

Lastpage

1405

Abstract

This paper is concerned with entropy based fundamental limitation results for the nonlinear disturbance rejection problem. We propose a hidden Markov model (HMM) framework for entropy calculations. We obtain explicit entropy bounds for both the classical Bode problem (with linear dynamics) as well as certain cases of nonlinear dynamics. An important message of this paper is that the limitations arise due to fundamental issues pertaining to estimation as opposed to the stabilization control problem.

Keywords

Bode diagrams; hidden Markov models; nonlinear control systems; stability; bode-like fundamental performance limitations; classical Bode problem; entropy based fundamental limitation results; hidden Markov model framework; linear dynamics; nonlinear disturbance rejection problem; nonlinear system control; stabilization control problem; Communication system control; Control systems; Entropy; Feedback; Hidden Markov models; Nonlinear control systems; Nonlinear dynamical systems; Nonlinear systems; Open loop systems; Transfer functions; Bode formula; nonlinear systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2010.2042227

Filename

5406123