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Economic MPC without terminal constraints : gradient-correcting end penalties enforce asymptotic stability
Publikationstyp
Journal Article
Date Issued
2018-03-01
Sprache
English
Author(s)
Zanon, Mario
Journal
Volume
63
Start Page
1
End Page
14
Citation
Journal of Process Control 63: 1-14 (2018)
Publisher DOI
Scopus ID
Publisher
Elsevier
ISSN
09591524
In recent years, economic MPC (EMPC) has gained popularity due to the promise of increasing performance by directly optimizing the performance index rather than tracking a given steady state. Moreover, EMPC formulations without terminal cost nor constraints are appealing for the simplicity of implementation. However, the stability and convergence analysis for such formulations is rather involved and so far only practical stability (in discrete time), respectively, practical convergence (in sampled-data continuous time) has been proven; i.e., convergence to a horizon-dependent neighborhood of the optimal steady state. In this paper, we prove that, whenever the cost has a non-zero gradient at the optimal steady-state and the MPC formulation satisfies a regularity assumption, nominal stability to the economic optimum cannot be achieved. Consequently, the average performance of EMPC is bound to be worse than that of tracking MPC. We propose to solve this problem by introducing a linear terminal penalty correcting the gradient at steady state. We prove that this simple correction enforces uniform exponential stability of the economically optimal steady state. We illustrate our findings in simulations using three examples.
Subjects
Cost rotation
Economic MPC
Optimal control
Strict dissipativity
DDC Class
330: Economics
004: Computer Sciences
510: Mathematics