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Time-Invariant Control in LQ Optimal Tracking: An Alternative to Output Regulation

Bernhard, Sebastian (2021)
Time-Invariant Control in LQ Optimal Tracking: An Alternative to Output Regulation.
20th IFAC World Congress. Toulouse, France (09.-14.07.2017)
doi: 10.26083/tuprints-00019112
Conference or Workshop Item, Secondary publication, Publisher's Version

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Item Type: Conference or Workshop Item
Type of entry: Secondary publication
Title: Time-Invariant Control in LQ Optimal Tracking: An Alternative to Output Regulation
Language: English
Date: 2021
Place of Publication: Darmstadt
Year of primary publication: 2017
Publisher: Elsevier
Event Title: 20th IFAC World Congress
Event Location: Toulouse, France
Event Dates: 09.-14.07.2017
DOI: 10.26083/tuprints-00019112
Corresponding Links:
Origin: Secondary publication service

We propose a new time-invariant control for linear quadratic tracking problems with references and disturbances generated by linear exo-systems. The control consists of a static feedback and a static pre-filter similar as in output regulation theory (ORT). Instead of forcing the tracking error to converge to zero, a tolerated steady-state error is balanced against the necessary input-energy via a quadratic cost. For the first time in this context, we deduce a time-invariant control from algebraic equations such that necessary optimality conditions are satisfied on infinite horizons. Then, we prove strong optimality for bounded exo-system states. Hence, any other steady-state solution will lead to infinite additional cost. On finite horizons and for arbitrary exo-systems, we prove that our control is an agreeable plan as it approximates the computational expensive, time-varying optimal control of any suitably large horizon. Since our control applies for any initial conditions of the plant and the exo-system, it is well suited for a practical resource-efficient implementation. In this regard, a presented algorithm allows for an easy to carry out control design. Finally, an industrial application indicates the unified treatment of square, under- and over-actuated systems by our approach in contrast to ORT.

Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-191122
Additional Information:

Erscheint auch in: IFAC-PapersOnLine, Volume 50, Issue 1, Pages 4912-4919, ISSN: 2405-8963

Classification DDC: 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering
Divisions: 18 Department of Electrical Engineering and Information Technology > Institut für Automatisierungstechnik und Mechatronik > Control Methods and Robotics (from 01.08.2022 renamed Control Methods and Intelligent Systems)
Date Deposited: 13 Jul 2021 12:07
Last Modified: 09 Aug 2023 11:57
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19112
PPN: 483252832
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