TY - GEN

T1 - Spectral MIMO H∞-Optimization Problem

AU - Veremey, Evgeny

AU - Knyazkin, Yaroslav

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020

Y1 - 2020

N2 - This paper is devoted to the problem of spectral H∞-optimal control synthesis for LTI plants. This problem is significant in situations when spectral features of the external disturbance are not completely given. H∞-optimization problem has been paid very serious attention for the past decades and it can be solved with the help of well-known numerical methods, based on Riccati equations or linear matrix equations (LMI), but these approaches are not absolutely universal, because there are irregular situations, such as problems with no noisy measurement signal. Implementation of the spectral methods, based on parameterization of the set of transfer functions of the closed-loop system and polynomial factorization makes possible to avoid mentioned difficulties, but most of the research in this area are devoted to the plants with scalar control signal that significantly restricts its area of implementation. The approach, proposed in this paper, makes possible to overcome these difficulties. Some theoretical aspects, including matrix Nevanlinna-Pick rational function interpolation, are discussed and computational scheme for the optimal control design is formulated. Applicability and effectiveness are illustrated by the numerical example with implementation of MATLAB package.

AB - This paper is devoted to the problem of spectral H∞-optimal control synthesis for LTI plants. This problem is significant in situations when spectral features of the external disturbance are not completely given. H∞-optimization problem has been paid very serious attention for the past decades and it can be solved with the help of well-known numerical methods, based on Riccati equations or linear matrix equations (LMI), but these approaches are not absolutely universal, because there are irregular situations, such as problems with no noisy measurement signal. Implementation of the spectral methods, based on parameterization of the set of transfer functions of the closed-loop system and polynomial factorization makes possible to avoid mentioned difficulties, but most of the research in this area are devoted to the plants with scalar control signal that significantly restricts its area of implementation. The approach, proposed in this paper, makes possible to overcome these difficulties. Some theoretical aspects, including matrix Nevanlinna-Pick rational function interpolation, are discussed and computational scheme for the optimal control design is formulated. Applicability and effectiveness are illustrated by the numerical example with implementation of MATLAB package.

KW - H infinity control

KW - Interpolation

KW - Linear-quadratic problem

KW - Optimization

UR - http://www.scopus.com/inward/record.url?scp=85081045590&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/830b8316-8dca-37e9-a25d-87d5445487da/

U2 - 10.1007/978-3-030-37436-5_10

DO - 10.1007/978-3-030-37436-5_10

M3 - Conference contribution

AN - SCOPUS:85081045590

SN - 9783030374358

T3 - Communications in Computer and Information Science

SP - 119

EP - 131

BT - Convergent Cognitive Information Technologies - 3rd International Conference, Convergent 2018, Revised Selected Papers

A2 - Sukhomlin, Vladimir

A2 - Zubareva, Elena

PB - Springer Nature

T2 - 3rd International Scientific Conference on Convergent Cognitive Information Technologies, Convergent 2018

Y2 - 29 November 2018 through 2 December 2018

ER -