NDLI: Computational Complexity Certification for Real-Time MPC With Input Constraints <newline/>Based on the Fast Gradient Method

Content Provider	IEEE Xplore Digital Library
Author	Richter, S. Jones, C.N. Morari, M.
Copyright Year	1963
Abstract	This paper proposes to use Nesterov's fast gradient method for the solution of linear quadratic model predictive control (MPC) problems with input constraints. The main focus is on the method's a priori computational complexity certification which consists of deriving lower iteration bounds such that a solution of pre-specified suboptimality is obtained for any possible state of the system. We investigate cold- and warm-starting strategies and provide an easily computable lower iteration bound for cold-starting and an asymptotic characterization of the bounds for warm-starting. Moreover, we characterize the set of MPC problems for which small iteration bounds and thus short solution times are expected. The theoretical findings and the practical relevance of the obtained lower iteration bounds are underpinned by various numerical examples and compared to certification results for a primal-dual interior point method.
Sponsorship	IEEE Control Systems Society
Starting Page	1391
Ending Page	1403
Page Count	13
File Size	906596
File Format	PDF
ISSN	00189286
Volume Number	57
Issue Number	6
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-06-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Gradient methods Convergence Upper bound Computational complexity Vectors Stability criteria predictive control Certification gradient methods optimization methods
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering Computer Science Applications

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