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Robust LQG control of uncertain linear systems via simultaneous H2 and H∞ approach

✍ Scribed by Lihua Xie; Yeng Chai Soh

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
211 KB
Volume
18
Category
Article
ISSN
0143-2087

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✦ Synopsis

Linear quadratic control has been well studied in the past 30 years. 1 This control design approach is based on the assumption that the dynamic model of the system under consideration is exactly known and its disturbances are Gaussian white noises with known statistics. However, Doyle 2 has shown that the LQG control design cannot guarantee stability robustness and performance against modelling uncertainty. This has brought to focus the importance of robust control and has attracted significant research interests in the past decade. Several robust control techniques have since been developed, e.g. loop transfer recovery and quadratic stabilization. 3,4 This communication is concerned with linear systems which are subjected to both parametric uncertainty and unstructured unmodelled dynamics. The parametric uncertainty is assumed to be time-varying norm-bounded and appears in both the state and input matrices. The unstructured unmodelled dynamics is characterized by an uncertain loop connected to the system. The problem to be addressed is the design of a robust controller that will guarantee the stability of the system for all admissible uncertainties and optimize the H 2 performance for the nominal system. This problem is referred to as the robust LQG control problem. It will be shown that the robust LQG control problem can be converted into a mixed H 2 and H ∞ problem. A simultaneous H 2 and H ∞ approach of Rotea and Khargonekar 5 can then be used to solve the latter problem. This design methodology is then applied to a simple example which clearly demonstrates the superiority of the proposed design over the nominal LQG control.

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