NDLI: Certification of fixed computation time first-order optimization-based controllers for a class of nonlinear dynamical systems

Content Provider	IEEE Xplore Digital Library
Author	Korda, M. Jones, C.N.
Copyright Year	2014
Description	Author affiliation: Lab. d'Autom., Ecole Polytech. Fed. de Lausanne, Lausanne, Switzerland (Korda, M.; Jones, C.N.)
Abstract	This paper proposes a stability verification method for systems controlled by an early terminated first-order method (e.g., an MPC problem approximately solved by a fixed number of iterations of the fast gradient method). The method is based on the observation that each step of the vast majority of first-order methods is characterized by a Karush-Kuhn-Tucker (KKT) system which (provided that all data are polynomial) is a basic semialgebraic set; M steps of a first-order method is then characterized by a basic semialgebraic set given by the intersection of M coupled KKT systems. Using sum-of-squares techniques, one can then search for a polynomial Lyapunov function that decreases between two consecutive time instances for all control inputs belonging to this coupled KKT system. The proposed method applies to nonlinear dynamical systems described by polynomial (or trigonometric) data affected by a (possibly state-dependent) disturbance; in particular the method is not restricted to linear systems and/or convex cost functions. To the best of the authors' knowledge, this is the first verification approach for early terminated optimization schemes with this level of generality.
Starting Page	3602
Ending Page	3608
File Size	385315
Page Count	7
File Format	PDF
ISBN	9781479932726
ISSN	07431619
e-ISBN	9781479932740
DOI	10.1109/ACC.2014.6858719
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-04
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	American Automatic Control Council(AACC)
Subject Keyword	Polynomials Lyapunov methods Stability analysis Gradient methods Closed loop systems Approximation methods certification First-order methods model predictive control early termination
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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