文章基本信息

标题：Asymptotic Stability of Economic NMPC: The Importance of Adjoints
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作者：Timm Faulwasser ; Mario Zanon
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2018
卷号：51
期号：20
页码：157-168
DOI：10.1016/j.ifacol.2018.11.009
语种：English
出版社：Elsevier
摘要：AbstractRecently, it has been shown in a sampled-data continuous-time setting that under certain regularity assumptions a simple linear end penalty enforces exponential stability of Economic (nonlinear) Model Predictive Control (EMPC) without terminal constraints. This paper investigates the same framework in the discrete-time case, i.e. we establish sufficient conditions for asymptotic stability of the optimal steady state under an EMPC scheme without terminal constraints. The key ingredient is a linear end penalty that can be understood as a gradient correction of the stage cost by means of the adjoint/dual variable of the underlying steady-state optimization problem. Although almost all stability proofs for EMPC focus on primal variables, our developments elucidate the importance of the adjoints for achieving asymptotic stability without terminal constraints. Moreover, we propose an adaptive gradient correction strategy which alleviates the need for solving explicitly the steady-state optimization. Finally, we draw upon two simulation examples to illustrate our results.
关键词：KeywordsEconomic MPCdissipativityasymptotic stability