On optimal trajectory tracking for mechanical systems with unilateral constraints

Mark Rijnen; Alessandro Saccon; Henk Nijmeijer

doi:10.1109/CDC.2015.7402602

On optimal trajectory tracking for mechanical systems with unilateral constraints

Mark Rijnen, Alessandro Saccon, Henk Nijmeijer

Dynamics and Control

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

9 Citations (Scopus)

11 Downloads (Pure)

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 language	English
Title of host publication	54th IEEE Conference on Decision and Control (CDC 2015), December 15-18, 2015. Osaka, Japan
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	2561-2566
Number of pages	6
ISBN (Electronic)	978-1-4799-7885-4
ISBN (Print)	978-1-4799-7884-7
DOIs	https://doi.org/10.1109/CDC.2015.7402602
Publication status	Published - 2015
Event	54th IEEE Conference on Decision and Control (CDC 2015) - "Osaka International Convention Center", Osaka, Japan Duration: 15 Dec 2015 → 18 Dec 2015 Conference number: 54 http://www.cdc2015.ctrl.titech.ac.jp/

Conference

Conference	54th IEEE Conference on Decision and Control (CDC 2015)
Abbreviated title	CDC 2015
Country	Japan
City	Osaka
Period	15/12/15 → 18/12/15
Internet address	http://www.cdc2015.ctrl.titech.ac.jp/

Access to Document

10.1109/CDC.2015.7402602

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title = "On optimal trajectory tracking for mechanical systems with unilateral constraints",

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.",

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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 proceeding › Conference contribution › Academic › peer-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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