Control and Estimation of Distributed Parameter Systems Internationa
Consisting of 16 refereed original contributions, this volume presents a diversified collection of recent results in control of distributed parameter systems. Topics addressed include - optimal control in fluid mechanics - numerical methods for optimal co
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Control and Estimation of Distributed Parameter Systems International Conference in Maria Trost (Austria), July 15-21, 2001
Edited by W. Desch F. Kappel K. Kunisch
Springer Basel AG
Editors: W. Desch. F. K appel and K. Kunisch Universi ttil Oraz InstituI rur Mathematik HcinrichstraBe 36 8010 Graz Austria e-mails: [email protected] [email protected] karl [email protected]
2000 Mat hematies Subjec i Classification 35L05. 35Q72. 47006.49J40. 49K40. 49NOS. 62H30. 6SC20. 65M99. 65P99.
68U99. 76D05. 93A15. 93 B07. 93C". 93DI5
A CIP eatalogue record fo r thi s book is available fro m the Li brary of Congrcss. Washington D.C .• USA
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ISDN 978·3·0J~8·9399·2 This work is subjectlo copyright. AII righlS are reserved. whether Ihe whole or part of thc material is conccmcd. spe «
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FIGURE 11. Comparison of tracking controls/state estimators on Example 2, with noise.
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H.T. Banks, S.C. Beeler, and H.T. Tran
6. Conclusions In this paper we have considered the method for feedback control of nonlinear systems using the state-dependent Riccati equation and extended it into a feedback tracking control method. We have also modified the state estimation method for nonlinear systems established in the literature to include a nonlinear gain function found through a state-dependent Riccati equation. Application of these new techniques to two selected example problems provided significant control authority and distinct advantages in comparison with the linear methods. As mentioned in earlier sections, there are some drawbacks and restrictions to the new techniques which must be considered. The power series solution of the SDRE method grows inaccurate when the states move farther from the origin, something which is of particular concern in a tracking problem. In solving the tracking variable equation by coupling it with a nominal state equation, one tacitly assumes a good prediction of the actual state behavior for the control to be effective. There are limitations on the types of problems to which the SDRE approach can be applied and on the types of signals which can be tracked, and the SDRE for obtaining the nonlinear state estimation gain uses only a linearized version of the measurement function . While these are nontrivial factors to consider, the methods described here for tracking control and state estimation are still applicable to a large class of important control problems, and their performance on the chosen examples provides improvement (in places dramatic improvement) when compared to previously established control techniques.
7. Acknowledgment This research was supported in part by a DOD/AFOSR MURI Grant AFOSR F49620-95-1-0447 and in part by AFOSR Grant F49620-96-1-0292
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