NDLI: The double description method for the approximation of explicit MPC control laws

Content Provider	IEEE Xplore Digital Library
Author	Jones, C.N. Morari, M.
Copyright Year	2008
Description	Author affiliation: Dept. of Electr. Eng., Swiss Fed. Inst. of Technol. Zurich, Zurich, Switzerland (Jones, C.N.; Morari, M.)
Abstract	A standard model predictive controller (MPC) can be written as a parametric optimization problem whose solution is a piecewise affine (PWA) map from the measured state to the optimal control input. The primary limitation of this optimal `explicit solution¿ is that the complexity can grow quickly with problem size, and so in this paper we seek to compute approximate explicit control laws that can trade-off complexity for approximation error. This computation is accomplished in a two-phase process: First, inner and outer polyhedral approximations of the the convex cost function of the parametric problem are computed with an algorithm based on an extension to the classic double-description method; a convex hull approach. The proposed method has two main advantages from a control point of view: it is an incremental approach, meaning that an approximation of any specified complexity can be produced and it operates on implicitly-defined convex sets, meaning that the optimal solution of the parametric problem is not required. In the second phase of the algorithm, a feasible approximate control law is computed that has the cost function derived in the first phase. For this purpose, a new interpolation method is introduced based on recent work on barycentric interpolation. The resulting control law is continuous, although non-linear and defined over a non-simplical polytopic partition of the state space. The non-simplical nature of the partition generates significantly simpler approximate control laws than current competing methods, as demonstrated on computational examples.
Starting Page	4724
Ending Page	4730
File Size	231016
Page Count	7
File Format	PDF
ISBN	9781424431236
ISSN	01912216
DOI	10.1109/CDC.2008.4738794
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-12-09
Publisher Place	Mexico
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimal control Cost function Interpolation Predictive models Size control Control systems Approximation algorithms Measurement standards Optimization methods Approximation error
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
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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