期刊
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
卷 58, 期 4, 页码 2288-2311出版社
SIAM PUBLICATIONS
DOI: 10.1137/19M1269944
关键词
terminal constraint; uncertain initial data; probabilistic constraint; optimal control; boundary control; wave equation
资金
- DFG in the Collaborative Research Centre [CRC/Transregio 154]
- FMJH Program Gaspard Monge in optimization and operations research
- EDF
In optimal control problems, often initial data are required that are not known exactly in practice. In order to take into account this uncertainty, we consider optimal control problems for a system with an uncertain initial state. A finite terminal time is given. On account of the uncertainty of the initial state, it is not possible to prescribe an exact terminal state. Instead, we are looking for a control that steers the system into a given neighborhood of the desired terminal state with sufficiently high probability. This neighborhood is described in terms of an inequality for the terminal energy. The probabilistic constraint in the considered optimal control problem leads to optimal controls that are robust against the inevitable uncertainties of the initial state. Numerical examples with optimal Neumann control of the wave equation are presented.
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