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Control of Nonlinear Systems with Delays

Encyclopedia of Systems and Control

Abstract

The reader is introduced to the predictor feedback method for the control of general nonlinear systems with input delays of arbitrary length. The delays need not necessarily be constant but can be time-varying or state-dependent. The predictor feedback methodology employs a model-based construction of the (unmeasurable) future state of the system. The analysis methodology is based on the concept of infinite-dimensional backstepping transformation – a transformation that converts the overall feedback system to a new, cascade “target system” whose stability can be studied with the construction of a Lyapunov function.

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Notes

  1. 1.

    The main control design tool for general systems with input delays of arbitrary length is predictor feedback. The reader is referred to Artstein (1982) for the first systematic treatment of general linear systems with constant input delays. The applicability of predictor feedback was extended in Krstic (2009) to several classes of systems, such as nonlinear systems with constant input delays and linear systems with unknown input delays. Subsequently, predictor feedback was extended to general nonlinear systems with nonconstant input and state delays (Bekiaris-Liberis and Krstic 2013a). The main stability analysis tool for systems employing predictor feedback is backstepping. Backstepping was initially introduced for adaptive control of finite-dimensional nonlinear systems (Krstic et al 1995). The continuum version of backstepping was originally developed for the boundary control of several classes of PDEs in Krstic and Smyshlyaev (2008).

Bibliography

The main control design tool for general systems with input delays of arbitrary length is predictor feedback. The reader is referred to Artstein (1982) for the first systematic treatment of general linear systems with constant input delays. The applicability of predictor feedback was extended in Krstic (2009) to several classes of systems, such as nonlinear systems with constant input delays and linear systems with unknown input delays. Subsequently, predictor feedback was extended to general nonlinear systems with nonconstant input and state delays (Bekiaris-Liberis and Krstic 2013a). The main stability analysis tool for systems employing predictor feedback is backstepping. Backstepping was initially introduced for adaptive control of finite-dimensional nonlinear systems (Krstic et al 1995). The continuum version of backstepping was originally developed for the boundary control of several classes of PDEs in Krstic and Smyshlyaev (2008).

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Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, USA

    Nikolaos Bekiaris-Liberis & Miroslav Krstic

Authors
  1. Nikolaos Bekiaris-Liberis
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  2. Miroslav Krstic
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Correspondence to Nikolaos Bekiaris-Liberis .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, Massachusetts, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, Minnesota, USA

    Tariq Samad

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Bekiaris-Liberis, N., Krstic, M. (2014). Control of Nonlinear Systems with Delays. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_17-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_17-1

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  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Control of Nonlinear Systems with Delays
    Published:
    14 October 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_17-2

  2. Original

    Control of Nonlinear Systems with Delays
    Published:
    02 October 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_17-1

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