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2017 | OriginalPaper | Chapter

5. Stability and Suboptimality Using Stabilizing Terminal Conditions

Authors : Lars Grüne, Jürgen Pannek

Published in: Nonlinear Model Predictive Control

Publisher: Springer International Publishing

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Abstract

In this chapter, we present a comprehensive stability and suboptimality analysis for NMPC schemes with stabilizing terminal conditions. 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 admissibility of the resulting NMPC-feedback law. 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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previous chapter Infinite Horizon Optimal Control
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Appendix
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Metadata
Title
Stability and Suboptimality Using Stabilizing Terminal Conditions
Authors
Lars Grüne
Jürgen Pannek
Copyright Year
2017
Book
Nonlinear Model Predictive Control

Print ISBN: 978-3-319-46023-9

Electronic ISBN: 978-3-319-46024-6

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-46024-6_5