TY - JOUR

T1 - Structured optimal feedback in multi-agent systems

T2 - A static output feedback perspective

AU - Zeng, Shen

AU - Allgöwer, Frank

N1 - Publisher Copyright:
© 2016 Elsevier Ltd

PY - 2017/2/1

Y1 - 2017/2/1

N2 - In this paper we demonstrate how certain structured feedback gains necessarily emerge as the optimal controller gains in two linear optimal control formulations for multi-agent systems. We consider the cases of linear optimal synchronization and linear optimal centroid stabilization. In the former problem, the considered cost functional integrates squared synchronization error and input, and in the latter, the considered cost functional integrates squared sum of the states and input. Our approach is to view the structures in the feedback gains in terms of a static output feedback with suitable output matrices and to relate this fact with the optimal control formulations. We show that the two considered problems are special cases of a more general case in which the optimal feedback to a linear quadratic regulator problem with cost functionals integrating squared outputs and inputs is a static output feedback. A treatment in this light leads to a very simple and general solution which significantly generalizes a recent result for the linear optimal synchronization problem. We illustrate the general problem in a geometric light.

AB - In this paper we demonstrate how certain structured feedback gains necessarily emerge as the optimal controller gains in two linear optimal control formulations for multi-agent systems. We consider the cases of linear optimal synchronization and linear optimal centroid stabilization. In the former problem, the considered cost functional integrates squared synchronization error and input, and in the latter, the considered cost functional integrates squared sum of the states and input. Our approach is to view the structures in the feedback gains in terms of a static output feedback with suitable output matrices and to relate this fact with the optimal control formulations. We show that the two considered problems are special cases of a more general case in which the optimal feedback to a linear quadratic regulator problem with cost functionals integrating squared outputs and inputs is a static output feedback. A treatment in this light leads to a very simple and general solution which significantly generalizes a recent result for the linear optimal synchronization problem. We illustrate the general problem in a geometric light.

KW - Linear quadratic optimal control

KW - Multi-agent systems

KW - Static output feedback

UR - http://www.scopus.com/inward/record.url?scp=85001943988&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2016.10.021

DO - 10.1016/j.automatica.2016.10.021

M3 - Article

AN - SCOPUS:85001943988

SN - 0005-1098

VL - 76

SP - 214

EP - 221

JO - Automatica

JF - Automatica

ER -