TY - GEN

T1 - Strictly Positive Realness-Based Feedback Gain Design Under Imperfect Input-Output Feedback Linearization in Prioritized Control Problem

AU - An, Sang Ik

AU - Park, Gyunghoon

AU - Lee, Dongheui

N1 - Publisher Copyright:
© 2023 IEEE.

PY - 2023

Y1 - 2023

N2 - The prioritized control problem is a process to find a control strategy for a dynamical system with prioritized multiple outputs, so that it can operate outside its nonsingular domain. Singularity typically leads to imperfect inversion in the prioritized control problem, which in turn results in imperfect input-output feedback linearization. In this paper, we propose a method based on the Kalman-Yakubovich-Popov lemma that compensates nonlinear feedback terms caused by the imperfect inversion of the prioritized control problem. In order to realize this idea, we prove existence of a feedback gain matrix that gives a strictly positive real transfer function whose output matrix is identical to the feedback gain matrix. Our proof is constructive so that a set of such matrices can be found. Also, we provide a numerical approach that gives a larger set of feedback gain matrices and validate the result with numerical examples.

AB - The prioritized control problem is a process to find a control strategy for a dynamical system with prioritized multiple outputs, so that it can operate outside its nonsingular domain. Singularity typically leads to imperfect inversion in the prioritized control problem, which in turn results in imperfect input-output feedback linearization. In this paper, we propose a method based on the Kalman-Yakubovich-Popov lemma that compensates nonlinear feedback terms caused by the imperfect inversion of the prioritized control problem. In order to realize this idea, we prove existence of a feedback gain matrix that gives a strictly positive real transfer function whose output matrix is identical to the feedback gain matrix. Our proof is constructive so that a set of such matrices can be found. Also, we provide a numerical approach that gives a larger set of feedback gain matrices and validate the result with numerical examples.

UR - http://www.scopus.com/inward/record.url?scp=85184828150&partnerID=8YFLogxK

U2 - 10.1109/CDC49753.2023.10383658

DO - 10.1109/CDC49753.2023.10383658

M3 - Conference contribution

AN - SCOPUS:85184828150

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 2622

EP - 2629

BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 62nd IEEE Conference on Decision and Control, CDC 2023

Y2 - 13 December 2023 through 15 December 2023

ER -