Synthesis of optimal H∞ controllers via LQG-based loop shaping design

Ciann Dong Yang; Chia Yuan Chang; Yun Ping Sun

Synthesis of optimal H_∞ controllers via LQG-based loop shaping design

Ciann Dong Yang, Chia Yuan Chang, Yun Ping Sun

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In this paper, synthesis of optimal H_∞ controllers is formulated as a loop-shaping problem where the desired closed-loop shape to be pursued is a flat frequency response of the largest singular value. Weighted H₂ optimization technique used in LQG/LTR is exploited in the loop shaping procedures to generate a sequence of H₂ controllers converging to the optimal H_∞ controller. The resulting optimal H_∞ controller not only has the inherent robust property due to H_∞ criterion but also possesses the nice H₂ control structure, being easy to compute and implement. A flight control example is demonstrated to show that the numerical accuracy of the present LQG-based H_∞ synthesis is comparable to the conventional H_∞ approach, i.e., γ-iteration.

Original language	English
Title of host publication	Proceedings of the IEEE Conference on Decision and Control
Editors	Anon
Publication status	Published - 1996 Dec 1
Event	Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4) - Kobe, Jpn Duration: 1996 Dec 11 → 1996 Dec 13

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	1
ISSN (Print)	0191-2216

Other

Other	Proceedings of the 1996 35th IEEE Conference on Decision and Control. Part 3 (of 4)
City	Kobe, Jpn
Period	96-12-11 → 96-12-13

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Cite this

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title = "Synthesis of optimal H∞ controllers via LQG-based loop shaping design",

abstract = "In this paper, synthesis of optimal H∞ controllers is formulated as a loop-shaping problem where the desired closed-loop shape to be pursued is a flat frequency response of the largest singular value. Weighted H2 optimization technique used in LQG/LTR is exploited in the loop shaping procedures to generate a sequence of H2 controllers converging to the optimal H∞ controller. The resulting optimal H∞ controller not only has the inherent robust property due to H∞ criterion but also possesses the nice H2 control structure, being easy to compute and implement. A flight control example is demonstrated to show that the numerical accuracy of the present LQG-based H∞ synthesis is comparable to the conventional H∞ approach, i.e., γ-iteration.",

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AB - In this paper, synthesis of optimal H∞ controllers is formulated as a loop-shaping problem where the desired closed-loop shape to be pursued is a flat frequency response of the largest singular value. Weighted H2 optimization technique used in LQG/LTR is exploited in the loop shaping procedures to generate a sequence of H2 controllers converging to the optimal H∞ controller. The resulting optimal H∞ controller not only has the inherent robust property due to H∞ criterion but also possesses the nice H2 control structure, being easy to compute and implement. A flight control example is demonstrated to show that the numerical accuracy of the present LQG-based H∞ synthesis is comparable to the conventional H∞ approach, i.e., γ-iteration.

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