TY - JOUR

T1 - SDP-based approximation of stabilising solutions for periodic matrix Riccati differential equations

AU - Gusev, S.V.

AU - Shiriaev, A.S.

AU - Freidovich, L.B.

PY - 2016

Y1 - 2016

N2 - © 2016 Taylor & Francis Numerically finding stabilising feedback control laws for linear systems of periodic differential equations is a nontrivial task with no known reliable solutions. The most successful method requires solving matrix differential Riccati equations with periodic coefficients. All previously proposed techniques for solving such equations involve numerical integration of unstable differential equations and consequently fail whenever the period is too large or the coefficients vary too much. Here, a new method for numerical computation of stabilising solutions for matrix differential Riccati equations with periodic coefficients is proposed. Our approach does not involve numerical solution of any differential equations. The approximation for a stabilising solution is found in the form of a trigonometric polynomial, matrix coefficients of which are found solving a specially constructed finite-dimensional semidefinite programming (SDP) problem. This problem is obtained using maximality property

AB - © 2016 Taylor & Francis Numerically finding stabilising feedback control laws for linear systems of periodic differential equations is a nontrivial task with no known reliable solutions. The most successful method requires solving matrix differential Riccati equations with periodic coefficients. All previously proposed techniques for solving such equations involve numerical integration of unstable differential equations and consequently fail whenever the period is too large or the coefficients vary too much. Here, a new method for numerical computation of stabilising solutions for matrix differential Riccati equations with periodic coefficients is proposed. Our approach does not involve numerical solution of any differential equations. The approximation for a stabilising solution is found in the form of a trigonometric polynomial, matrix coefficients of which are found solving a specially constructed finite-dimensional semidefinite programming (SDP) problem. This problem is obtained using maximality property

U2 - 10.1080/00207179.2015.1131850

DO - 10.1080/00207179.2015.1131850

M3 - Article

VL - 89

SP - 1396

EP - 1405

JO - International Journal of Control

JF - International Journal of Control

SN - 0020-7179

IS - 7

ER -