Optimal control of LQG problem with an explicit trade-off between mean and variance

Fucai Qian, Guo Xie, Ding Liu and Wenfang Xie

International Journal of Systems Science, 2011, vol. 42, issue 12, 1957-1964

Abstract: For discrete-time linear-quadratic Gaussian (LQG) control problems, a utility function on the expectation and the variance of the conventional performance index is considered. The utility function is viewed as an overall objective of the system and can perform the optimal trade-off between the mean and the variance of performance index. The nonlinear utility function is first converted into an auxiliary parameters optimisation problem about the expectation and the variance. Then an optimal closed-loop feedback controller for the nonseparable mean–variance minimisation problem is designed by nonlinear mathematical programming. Finally, simulation results are given to verify the algorithm's effectiveness obtained in this article.

Date: 2011
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DOI: 10.1080/00207721003764133

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