TY - JOUR

T1 - Optimization of the H-2 Norm for Single-Delay Systems, With Application to Control Design and Model Approximation

AU - Gomez, Marco A.

AU - Egorov, Alexey V.

AU - Mondie, Sabine

AU - Michiels, Wim

PY - 2019/2/1

Y1 - 2019/2/1

N2 - We propose a novel approach for the optimization of the H-2 norm for time-delay systems, grounded in its characterization in terms of the delay Lyapunov matrix. We show how the partial derivatives of the delay Lyapunov matrix with respect to system or controller parameters can be semianalytically computed, by solving a delay Lyapunov equation with inhomogeneous terms. It allows us to obtain the gradient of the H-2 norm and in turn to use it in a gradient-based optimization framework. We demonstrate the potential of the approach on two classes of problems, the design of robust controllers and the computation of approximate models of reduced dimension. Thereby, a major advantage is the flexibility: in the former class of applications, the order or structure of the controller can be prescribed, including recently proposed delay-based controllers. For the latter class of applications, approximate models described by both ordinary and delay differential equations (e.g., inhering the structure of the original system) can be synthesized.

AB - We propose a novel approach for the optimization of the H-2 norm for time-delay systems, grounded in its characterization in terms of the delay Lyapunov matrix. We show how the partial derivatives of the delay Lyapunov matrix with respect to system or controller parameters can be semianalytically computed, by solving a delay Lyapunov equation with inhomogeneous terms. It allows us to obtain the gradient of the H-2 norm and in turn to use it in a gradient-based optimization framework. We demonstrate the potential of the approach on two classes of problems, the design of robust controllers and the computation of approximate models of reduced dimension. Thereby, a major advantage is the flexibility: in the former class of applications, the order or structure of the controller can be prescribed, including recently proposed delay-based controllers. For the latter class of applications, approximate models described by both ordinary and delay differential equations (e.g., inhering the structure of the original system) can be synthesized.

KW - Delay Lyapunov matrix

KW - H-2-norm optimization

KW - model reduction

KW - time-delay systems

KW - LINEAR-SYSTEMS

KW - REDUCTION

KW - STABILITY

KW - STABILIZATION

KW - COMPUTATION

KW - EQUATIONS

UR - http://www.scopus.com/inward/record.url?scp=85046726166&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/optimization-mathcal-h2-norm-singledelay-systems-application-control-design-model-approximation

U2 - 10.1109/TAC.2018.2836019

DO - 10.1109/TAC.2018.2836019

M3 - Article

AN - SCOPUS:85046726166

VL - 64

SP - 804

EP - 811

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 2

M1 - 8358743

ER -