On optimal trajectory tracking for mechanical systems with unilateral constraints

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Abstract

This paper addresses the optimal trajectory tracking problem for hybrid systems with discontinuous state trajectories. We consider state-triggered jumps in the state evolution. The tracking of a given reference trajectory is complicated by the fact that the time instants at which the closed-loop dynamics actually jumps differ from those at which the reference trajectory jumps. A recently introduced hybrid feedback tracking controller is used to cope with these differences. A method to design the corresponding time-varying feedback gains such that they minimize a cost criterion in a linear quadratic regulator (LQR) like idea is described in this work. The effectiveness of the proposed control law is investigated numerically by comparison with classic proportional feedback and constant gain hybrid feedback control for a mechanical system with a unilateral position constraint, namely a controlled mass interacting with a rigid obstacle.
Original languageEnglish
Title of host publication54th IEEE Conference on Decision and Control (CDC 2015), December 15-18, 2015. Osaka, Japan
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages2561-2566
Number of pages6
ISBN (Electronic)978-1-4799-7885-4
ISBN (Print)978-1-4799-7884-7
DOIs
Publication statusPublished - 2015
Event54th IEEE Conference on Decision and Control (CDC 2015) - "Osaka International Convention Center", Osaka, Japan
Duration: 15 Dec 201518 Dec 2015
Conference number: 54
http://www.cdc2015.ctrl.titech.ac.jp/

Conference

Conference54th IEEE Conference on Decision and Control (CDC 2015)
Abbreviated titleCDC 2015
CountryJapan
CityOsaka
Period15/12/1518/12/15
Internet address

Fingerprint

Trajectories
Feedback
Hybrid systems
Feedback control
Controllers
Costs

Cite this

Rijnen, M., Saccon, A., & Nijmeijer, H. (2015). On optimal trajectory tracking for mechanical systems with unilateral constraints. In 54th IEEE Conference on Decision and Control (CDC 2015), December 15-18, 2015. Osaka, Japan (pp. 2561-2566). [7402602] Piscataway: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2015.7402602
Rijnen, Mark ; Saccon, Alessandro ; Nijmeijer, Henk. / On optimal trajectory tracking for mechanical systems with unilateral constraints. 54th IEEE Conference on Decision and Control (CDC 2015), December 15-18, 2015. Osaka, Japan. Piscataway : Institute of Electrical and Electronics Engineers, 2015. pp. 2561-2566
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Rijnen, M, Saccon, A & Nijmeijer, H 2015, On optimal trajectory tracking for mechanical systems with unilateral constraints. in 54th IEEE Conference on Decision and Control (CDC 2015), December 15-18, 2015. Osaka, Japan., 7402602, Institute of Electrical and Electronics Engineers, Piscataway, pp. 2561-2566, 54th IEEE Conference on Decision and Control (CDC 2015), Osaka, Japan, 15/12/15. https://doi.org/10.1109/CDC.2015.7402602

On optimal trajectory tracking for mechanical systems with unilateral constraints. / Rijnen, Mark; Saccon, Alessandro; Nijmeijer, Henk.

54th IEEE Conference on Decision and Control (CDC 2015), December 15-18, 2015. Osaka, Japan. Piscataway : Institute of Electrical and Electronics Engineers, 2015. p. 2561-2566 7402602.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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N2 - This paper addresses the optimal trajectory tracking problem for hybrid systems with discontinuous state trajectories. We consider state-triggered jumps in the state evolution. The tracking of a given reference trajectory is complicated by the fact that the time instants at which the closed-loop dynamics actually jumps differ from those at which the reference trajectory jumps. A recently introduced hybrid feedback tracking controller is used to cope with these differences. A method to design the corresponding time-varying feedback gains such that they minimize a cost criterion in a linear quadratic regulator (LQR) like idea is described in this work. The effectiveness of the proposed control law is investigated numerically by comparison with classic proportional feedback and constant gain hybrid feedback control for a mechanical system with a unilateral position constraint, namely a controlled mass interacting with a rigid obstacle.

AB - This paper addresses the optimal trajectory tracking problem for hybrid systems with discontinuous state trajectories. We consider state-triggered jumps in the state evolution. The tracking of a given reference trajectory is complicated by the fact that the time instants at which the closed-loop dynamics actually jumps differ from those at which the reference trajectory jumps. A recently introduced hybrid feedback tracking controller is used to cope with these differences. A method to design the corresponding time-varying feedback gains such that they minimize a cost criterion in a linear quadratic regulator (LQR) like idea is described in this work. The effectiveness of the proposed control law is investigated numerically by comparison with classic proportional feedback and constant gain hybrid feedback control for a mechanical system with a unilateral position constraint, namely a controlled mass interacting with a rigid obstacle.

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Rijnen M, Saccon A, Nijmeijer H. On optimal trajectory tracking for mechanical systems with unilateral constraints. In 54th IEEE Conference on Decision and Control (CDC 2015), December 15-18, 2015. Osaka, Japan. Piscataway: Institute of Electrical and Electronics Engineers. 2015. p. 2561-2566. 7402602 https://doi.org/10.1109/CDC.2015.7402602