Sampled–data model predictive control: Adaptive time–mesh refinement algorithms and guarantees of stability

• Type: Article in International Scientific Journal
• Date: 2019

Authors

L.T. Paiva (Author) FEUP; Fernando A. C. C. Fontes (Author) FEUP

Journal

Title: Discrete and Continuous Dynamical Systems - Series B

Vol. 24 No. 5

Pages: 2335-2364

ISSN: 1531-3492

Publisher: American Institute of Mathematical Sciences

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00Q-EEP

DOI: 10.3934/dcdsb.2019098

Abstract (EN): This article addresses the problem of controlling a constrained, continuous-time, nonlinear system through Model Predictive Control (MPC). In particular, we focus on methods to efficiently and accurately solve the underlying optimal control problem (OCP). In the numerical solution of a nonlinear OCP, some form of discretization must be used at some stage. There are, however, benefits in postponing the discretization process and maintain a continuous-time model until a later stage. This is because that way we can exploit additional freedom to select the number and the location of the discretization node points. We propose an adaptive time-mesh refinement (AMR) algorithm that iteratively finds an adequate time-mesh satisfying a pre-defined bound on the local error estimate of the obtained trajectories. The algorithm provides a time-dependent stopping criterion, enabling us to impose higher accuracy in the initial parts of the receding horizon, which are more relevant to MPC. Additionally, we analyze the conditions to guarantee closed-loop stability of the MPC framework using the AMR algorithm. The numerical results show that the proposed AMR strategy can obtain solutions as fast as methods using a coarse equidistant-spaced mesh and, on the other hand, as accurate as methods using a fine equidistant-spaced mesh. Therefore, the OCP can be solved, and the MPC law obtained, faster and/or more accurately than with discrete-time MPC schemes using equidistant-spaced meshes.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 30