Optimal control with stabilization for a class of hybrid dynamical systems

Bin Liu; David J. Hill; Chunxia Dou

doi:10.1109/CCDC.2012.6242978

Optimal control with stabilization for a class of hybrid dynamical systems

Bin Liu^*, David J. Hill, Chunxia Dou

^*Corresponding author for this work

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

Abstract

This paper studies the optimal control with stabilization issue for a class of hybrid dynamical systems (HDS) with hybrid performance functional (HPF). By employing Lyapunov function method and the recent results of stability of HDS, the optimal control conditions for the HDS has been derived with respect to the HPF. Under the state feedback control, the closed-loop HDS is globally asymptotically stable (GAS) and at the same time the HPF can achieve the desirable maximal (minimal) value. The results are then used to study the case of linear HDS with hybrid quadratic performance functional (HQPF). The matrix inequality conditions are derived to design the linear feedback controller under which the closed-loop linear HDS is GAS and the HQPF is optimized. Finally, one example is given for illustration.

Original language	English
Title of host publication	Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012
Pages	614-619
Number of pages	6
DOIs	https://doi.org/10.1109/CCDC.2012.6242978
Publication status	Published - 2012
Event	2012 24th Chinese Control and Decision Conference, CCDC 2012 - Taiyuan, China Duration: 23 May 2012 → 25 May 2012

Publication series

Name	Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012

Conference

Conference	2012 24th Chinese Control and Decision Conference, CCDC 2012
Country/Territory	China
City	Taiyuan
Period	23/05/12 → 25/05/12

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10.1109/CCDC.2012.6242978

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title = "Optimal control with stabilization for a class of hybrid dynamical systems",

abstract = "This paper studies the optimal control with stabilization issue for a class of hybrid dynamical systems (HDS) with hybrid performance functional (HPF). By employing Lyapunov function method and the recent results of stability of HDS, the optimal control conditions for the HDS has been derived with respect to the HPF. Under the state feedback control, the closed-loop HDS is globally asymptotically stable (GAS) and at the same time the HPF can achieve the desirable maximal (minimal) value. The results are then used to study the case of linear HDS with hybrid quadratic performance functional (HQPF). The matrix inequality conditions are derived to design the linear feedback controller under which the closed-loop linear HDS is GAS and the HQPF is optimized. Finally, one example is given for illustration.",

keywords = "HDS, Optimal control, global asymptotic stability (GAS), hybrid performance functional (HPF)",

author = "Bin Liu and Hill, {David J.} and Chunxia Dou",

year = "2012",

doi = "10.1109/CCDC.2012.6242978",

language = "English",

isbn = "9781457720727",

series = "Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012",

pages = "614--619",

booktitle = "Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012",

note = "2012 24th Chinese Control and Decision Conference, CCDC 2012 ; Conference date: 23-05-2012 Through 25-05-2012",

}

Liu, B, Hill, DJ & Dou, C 2012, Optimal control with stabilization for a class of hybrid dynamical systems. in Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012., 6242978, Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012, pp. 614-619, 2012 24th Chinese Control and Decision Conference, CCDC 2012, Taiyuan, China, 23/05/12. https://doi.org/10.1109/CCDC.2012.6242978

Optimal control with stabilization for a class of hybrid dynamical systems. / Liu, Bin; Hill, David J.; Dou, Chunxia.
Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012. 2012. p. 614-619 6242978 (Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012).

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

TY - GEN

T1 - Optimal control with stabilization for a class of hybrid dynamical systems

AU - Liu, Bin

AU - Hill, David J.

AU - Dou, Chunxia

PY - 2012

Y1 - 2012

N2 - This paper studies the optimal control with stabilization issue for a class of hybrid dynamical systems (HDS) with hybrid performance functional (HPF). By employing Lyapunov function method and the recent results of stability of HDS, the optimal control conditions for the HDS has been derived with respect to the HPF. Under the state feedback control, the closed-loop HDS is globally asymptotically stable (GAS) and at the same time the HPF can achieve the desirable maximal (minimal) value. The results are then used to study the case of linear HDS with hybrid quadratic performance functional (HQPF). The matrix inequality conditions are derived to design the linear feedback controller under which the closed-loop linear HDS is GAS and the HQPF is optimized. Finally, one example is given for illustration.

AB - This paper studies the optimal control with stabilization issue for a class of hybrid dynamical systems (HDS) with hybrid performance functional (HPF). By employing Lyapunov function method and the recent results of stability of HDS, the optimal control conditions for the HDS has been derived with respect to the HPF. Under the state feedback control, the closed-loop HDS is globally asymptotically stable (GAS) and at the same time the HPF can achieve the desirable maximal (minimal) value. The results are then used to study the case of linear HDS with hybrid quadratic performance functional (HQPF). The matrix inequality conditions are derived to design the linear feedback controller under which the closed-loop linear HDS is GAS and the HQPF is optimized. Finally, one example is given for illustration.

KW - HDS

KW - Optimal control

KW - global asymptotic stability (GAS)

KW - hybrid performance functional (HPF)

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U2 - 10.1109/CCDC.2012.6242978

DO - 10.1109/CCDC.2012.6242978

M3 - Conference contribution

SN - 9781457720727

T3 - Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012

SP - 614

EP - 619

BT - Proceedings of the 2012 24th Chinese Control and Decision Conference, CCDC 2012

T2 - 2012 24th Chinese Control and Decision Conference, CCDC 2012

Y2 - 23 May 2012 through 25 May 2012

ER -

Optimal control with stabilization for a class of hybrid dynamical systems

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