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Methods of Model Based Process Control pp 577–605Cite as

A Stability Analysis of Nonlinear Model Predictive Control

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Part of the book series: NATO ASI Series ((NSSE,volume 293))

Abstract

A methodology to analyze the closed-loop stability of nonlinear model predictive control is presented. The closed-loop system is described by a set of difference equations obtained by discretizing the continuous-time model. The method of discretization is shown to affect the input/output properties of the resulting discrete-time model. Some nominal closed-loop properties of linear model predictive control algorithms are shown to be valid for nonlinear systems. Lyapunov stability theory is used to prove the stabilizing nature of the model predictive control algorithm with properly chosen tuning parameters. The duality between iterative processes and the sampled-data representation of a continuous-time system is used to analyze closed-loop stability. The state and input sensitivity equations of the continuous-time model are used in computing the closed-loop stability criteria. The nominal stability analysis is extended to the important cases of unmeasured states and uncertain model parameters. A numerical Lyapunov function is used to estimate closed-loop regions of attraction. Simulation examples are presented to illustrate the analysis methods and closed-loop behavior.

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Author information

Authors and Affiliations

  1. The Howard P. Isermann Department of Chemical Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180-3590, USA

    P. B. Sistu & B. W. Bequette

Authors
  1. P. B. Sistu
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  2. B. W. Bequette
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Editor information

Editors and Affiliations

  1. Department of Chemical Engineering, Ankara University, Ankara, Turkey

    Ridvan Berber

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© 1995 Springer Science+Business Media Dordrecht

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Sistu, P.B., Bequette, B.W. (1995). A Stability Analysis of Nonlinear Model Predictive Control. In: Berber, R. (eds) Methods of Model Based Process Control. NATO ASI Series, vol 293. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0135-6_21

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  • DOI: https://doi.org/10.1007/978-94-011-0135-6_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4061-7

  • Online ISBN: 978-94-011-0135-6

  • eBook Packages: Springer Book Archive

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