Title: Approximate explicit model predictive control using high-level canonical piecewise-affine functions

Authors: Weiquan Sun; Min Li; Kexin Wang

Addresses: School of Business Administration, Duquesne University, 600 Forbes Avenue, Pittsburgh, PA 15282, USA ' School of Medicine, Indiana University, 975 West Walnut Street, Indianapolis, IN 46202, USA ' State Key Laboratory of Industrial Control Technology, Institute of Industrial Control, Zhejiang University, Hangzhou 310027, China

Abstract: Explicit model predictive control (eMPC) enables conventional MPC to be used to fast sampling systems and implemented by low-cost embedded devices. The primary limitation of eMPC is that the complexities of eMPC solutions are often exponential functions of problem sizes. In this paper, high-level canonical piecewise-affine (HL-CPWA) functions are introduced to approximate eMPC solutions. A HL-CPWA function uses a global and compact functional form to approximate any continuous eMPC controller to arbitrary precision. This guarantees minimal memory storage requirement and fast online computational time to represent and calculate suboptimal eMPC solutions. The HL-CPWA eMPC feedback laws have explicit analytical expressions, which can be easily implemented by elementary 'circuit blocks'. This facilitates the use of constrained MPC in small-scale industrial and consumer electronics applications.

Keywords: explicit MPC; HL-CPWA; high-level canonical piecewise-affine function; general piecewise-affine approximation; MPC; model predictive control; multi-parametric programs; consumer electronics; industrial control.

DOI: 10.1504/IJAAC.2012.045441

International Journal of Automation and Control, 2012 Vol.6 No.1, pp.66 - 80

Received: 18 Jul 2011
Accepted: 13 Aug 2011

Published online: 31 Oct 2014 *

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