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...

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Vydané v:International journal of control Ročník 95; číslo 1; s. 158 - 172
Hlavní autori: Calafiore, Giuseppe C., Novara, Carlo, Possieri, Corrado
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Abingdon Taylor & Francis 02.01.2022
Taylor & Francis Ltd
Predmet:
Design analysis
Iterative methods
Nonlinear control
optimal control
optimisation methods
Optimization
Polynomials
Predictive control
randomised algorithms
robustness
Space rendezvous
ISSN:0020-7179, 1366-5820
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Abstract 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.
AbstractList 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.
Author Calafiore, Giuseppe C.
Possieri, Corrado
Novara, Carlo
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  surname: Possieri
  fullname: Possieri, Corrado
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  organization: Istituto di Analisi dei Sistemi ed Informatica 'A. Ruberti', Consiglio Nazionale delle Ricerche (IASI-CNR)
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SubjectTerms Design analysis
Iterative methods
Nonlinear control
optimal control
optimisation methods
Optimization
Polynomials
Predictive control
randomised algorithms
robustness
Space rendezvous
Title Control analysis and design via randomised coordinate polynomial minimisation
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