Bode-like fundamental performance limitations in control of nonlinear systems

Sun Yu; Prashant G. Mehta

doi:10.1109/TAC.2010.2042227

Bode-like fundamental performance limitations in control of nonlinear systems

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	5406123
Pages (from-to)	1390-1405
Number of pages	16
Journal	IEEE Transactions on Automatic Control
Volume	55
Issue number	6
DOIs	https://doi.org/10.1109/TAC.2010.2042227
State	Published - Jun 2010

Keywords

Bode formula
Nonlinear systems

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

Online availability

10.1109/TAC.2010.2042227

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title = "Bode-like fundamental performance limitations in control of nonlinear systems",

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 formula, Nonlinear systems",

author = "Sun Yu and Mehta, {Prashant G.}",

note = "Manuscript received January 13, 2009; revised August 17, 2009. First published February 05, 2010; current version published June 09, 2010. This work was supported by the National Science Foundation under Grant CMS 05-56352. Recommended by Associate Editor Z. Wang.",

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N2 - 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.

AB - 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.

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Bode-like fundamental performance limitations in control of nonlinear systems

Abstract

Keywords

ASJC Scopus subject areas

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