TY - GEN
T1 - Norm vanishment and its applications in constrained control - Part II
T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
AU - Zhou, Bin
AU - Lin, Zongli
AU - Duan, Guang Ren
PY - 2009
Y1 - 2009
N2 - In Part I of this paper, we introduced the notion of ℒ ∞-vanishment and established several kinds of characterizations of this notion. Based on this notion, ℒ∞ low gain feedback was reconsidered and a systematic approach to ℒ∞ low gain feedback design was proposed. In this second part of the paper, we consider the parallel notion of ℒ2-vanishment. We establish several characterizations of the ℒ2-vanishment property, based on which a new design approach referred to as the ℒ2 low gain feedback approach is developed. Just as the ℒ∞ low gain design is useful in the control of linear systems subject to actuator magnitude saturation, the ℒ2 low gain feedback is instrumental in the control of systems with control energy constraints. As applications of ℒ2 low gain feedback, the problem of semi-global stabilization of linear systems with energy constraints and the problem of linear time-delay system with energy constraints are solved in this paper. The notion of ℒ2-vanishment and the resulting ℒ2 low gain feedback are also extended to nonlinear systems. As in the ℒ ∞ low gain feedback considered in Part I, a systematic approach is also developed for ℒ2 low gain feedback design in this second part of the paper. Finally, an example involving a linearized model of the relative motion with respect to another in a circular orbit around the Earth is used to illustrate the effectiveness of the results developed in this paper.
AB - In Part I of this paper, we introduced the notion of ℒ ∞-vanishment and established several kinds of characterizations of this notion. Based on this notion, ℒ∞ low gain feedback was reconsidered and a systematic approach to ℒ∞ low gain feedback design was proposed. In this second part of the paper, we consider the parallel notion of ℒ2-vanishment. We establish several characterizations of the ℒ2-vanishment property, based on which a new design approach referred to as the ℒ2 low gain feedback approach is developed. Just as the ℒ∞ low gain design is useful in the control of linear systems subject to actuator magnitude saturation, the ℒ2 low gain feedback is instrumental in the control of systems with control energy constraints. As applications of ℒ2 low gain feedback, the problem of semi-global stabilization of linear systems with energy constraints and the problem of linear time-delay system with energy constraints are solved in this paper. The notion of ℒ2-vanishment and the resulting ℒ2 low gain feedback are also extended to nonlinear systems. As in the ℒ ∞ low gain feedback considered in Part I, a systematic approach is also developed for ℒ2 low gain feedback design in this second part of the paper. Finally, an example involving a linearized model of the relative motion with respect to another in a circular orbit around the Earth is used to illustrate the effectiveness of the results developed in this paper.
UR - https://www.scopus.com/pages/publications/77950835066
U2 - 10.1109/CDC.2009.5400858
DO - 10.1109/CDC.2009.5400858
M3 - 会议稿件
AN - SCOPUS:77950835066
SN - 9781424438716
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 7984
EP - 7989
BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 15 December 2009 through 18 December 2009
ER -