Control analysis and design via randomised coordinate polynomial minimisation

A relevant family of control analysis and design problems can be reduced to the minimisation of a multivariate polynomial objective over a semialgebraic set. Such control problem formulations, however, are nonconvex in general and hard to solve in practice. In this paper, we propose a novel approach...

Full description

Saved in:
Bibliographic Details
Published in:International journal of control Vol. 95; no. 1; pp. 158 - 172
Main Authors: Calafiore, Giuseppe C., Novara, Carlo, Possieri, Corrado
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.01.2022
Taylor & Francis Ltd
Subjects:
Design analysis
Iterative methods
Nonlinear control
optimal control
optimisation methods
Optimization
Polynomials
Predictive control
randomised algorithms
robustness
Space rendezvous
ISSN:0020-7179, 1366-5820
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A relevant family of control analysis and design problems can be reduced to the minimisation of a multivariate polynomial objective over a semialgebraic set. Such control problem formulations, however, are nonconvex in general and hard to solve in practice. In this paper, we propose a novel approach to polynomial control design based on iterations that involve either a fast coordinate-wise minimisation or a univariate minimisation along a randomly chosen direction. We provide a detailed iteration complexity analysis of the method, and we prove its convergence in probability to the global optimum. The practical effectiveness of the proposed method is also illustrated via a comparison with state-of-the-art tools available in the literature. An example of application to an automated space rendezvous manoeuvre is finally presented, showing how the method can be particularly relevant in the context of nonlinear model predictive control.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2020.1782476