Time optimisation problem for switched stochastic systems with multi-switching times
- Author(s): Xiaomei Liu 1 ; Kanjian Zhang 1 ; Shengtao Li 2 ; Shumin Fei 1 ; Haikun Wei 1
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View affiliations
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Affiliations:
1:
Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing 210096, People's Republic of China;
2: School of Information Science and Engineering, Shandong Normal University, Jinan 250014, People's Republic of China
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Affiliations:
1:
Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing 210096, People's Republic of China;
- Source:
Volume 8, Issue 16,
06 November 2014,
p.
1732 – 1740
DOI: 10.1049/iet-cta.2014.0053 , Print ISSN 1751-8644, Online ISSN 1751-8652
In this study, a time optimisation problem is solved for a class of linear time-invariant switched stochastic systems with multi-switching times using the calculus of variations. The objective of authors’ study is to minimise a cost functional defined on the system state, where the sequence of active subsystems is pre-specified and the switching times are the only control variables. The gradient of the cost functional with respect to the switching times is derived, which has an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instants. The proposed method is applied on a two-tank system, which is a practical example of switched systems. Combining with another numerical example with three switching times case, the viability of the proposed method is further demonstrated.
Inspec keywords: switching theory; stochastic systems; gradient methods
Other keywords: control variables; multiswitching times; time optimisation problem; optimal switching instants; variations; cost functional; two-tank system; gradient descent algorithms; calculus; active subsystems; linear time-invariant switched stochastic systems; switched systems
Subjects: Optimisation techniques; Switching theory; Time-varying control systems
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