EBSCO Logo
Connecting you to content on EBSCOhost
Results
Title

A double‐layer Jacobi method for partial differential equation‐constrained nonlinear model predictive control.

Authors

Deng, Haoyang; Ohtsuka, Toshiyuki

Abstract

This paper presents a real‐time optimization method for nonlinear model predictive control (NMPC) of systems governed by partial differential equations (PDEs). The NMPC problem to be solved is formulated by discretizing the PDE system in space and time by using the finite difference method. The proposed method is called the double‐layer Jacobi method, which exploits both the spatial and temporal sparsities of the PDE‐constrained NMPC problem. In the upper layer, the NMPC problem is solved by ignoring the temporal couplings of either the state or costate (Lagrange multiplier corresponding to the state equation) equations so that the spatial sparsity is preserved. The lower‐layer Jacobi method is a linear solver dedicated to PDE‐constrained NMPC problems by exploiting the spatial sparsity. Convergence analysis indicates that the convergence of the proposed method is related to the prediction horizon. Results of a numerical experiment of controlling a heat transfer process show that the proposed method can be two orders of magnitude faster than the conventional Newton's method exploiting the banded structure of NMPC problems.

Subjects

NEWTON-Raphson method; FINITE difference method; JACOBI method; PARTIAL differential equations; PREDICTION models

Publication

Optimal Control - Applications & Methods, 2024, Vol 45, Issue 5, p1971

ISSN

0143-2087

Publication type

Academic Journal

DOI

10.1002/oca.3132

EBSCO Connect | Privacy policy | Terms of use | Copyright | Manage my cookies
Journals | Subjects | Sitemap
© 2025 EBSCO Industries, Inc. All rights reserved