Journal
INTERNATIONAL JOURNAL OF CONTROL
Volume 90, Issue 8, Pages 1604-1611Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207179.2016.1214879
Keywords
Optimal control; switched stochastic systems; calculus of variation
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Funding
- Major Program of National Natural Science Foundation of China [11190015]
- National Natural Science Foundation of China [61374006]
- Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province [BS2015DX016]
- Science and Technology Plan Project of Colleges and Universities in Shandong Province [J16LN23]
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In this paper, we solve an optimal control problem for a class of time-invariant switched stochastic systems with multi-switching times, where the objective is to minimise a cost functional with different costs defined on the states. In particular, we focus on problems in which a pre-specified sequence of active subsystems is given and the switching times are the only control variables. Based on the calculus of variation, we derive the gradient of the cost functional with respect to the switching times on an especially simple form, which can be directly used in gradient descent algorithms to locate the optimal switching instants. Finally, a numerical example is given, highlighting the validity of the proposed methodology.
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