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Stability and Suboptimality Using Stabilizing Constraints

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Nonlinear Model Predictive Control

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

In this chapter we present a comprehensive stability and suboptimality analysis for NMPC schemes with stabilizing terminal constraints. Both endpoint constraints as well as regional constraints plus Lyapunov function terminal cost are covered. We show that viability of the state constraint set can be replaced by viability of the terminal constraint set in order to ensure feasibility of the NMPC optimal control problem along the closed loop trajectories. The “reversing of monotonicity” of the finite time optimal value functions is proved and used in order to apply the relaxed dynamic programming framework introduced in the previous chapter. Using this framework, stability, suboptimality (i.e., estimates about the infinite horizon performance of the NMPC closed loop system) and inverse optimality results are proved.

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Authors and Affiliations

    Authors
    1. Lars Grüne
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    2. Jürgen Pannek
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    Correspondence to Lars Grüne .

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    © 2011 Springer-Verlag London Limited

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    Grüne, L., Pannek, J. (2011). Stability and Suboptimality Using Stabilizing Constraints. In: Nonlinear Model Predictive Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-501-9_5

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    • DOI: https://doi.org/10.1007/978-0-85729-501-9_5

    • Publisher Name: Springer, London

    • Print ISBN: 978-0-85729-500-2

    • Online ISBN: 978-0-85729-501-9

    • eBook Packages: EngineeringEngineering (R0)

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