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RekingQin

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zhao0426

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zhao0426

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18Â¥2011-07-12 10:45:32
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fcqian

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ÏÂÃæÊÇÎÒÃÇÑо¿¹¤×÷µÄÒ»²¿·Ö£¬ÒѾ­±»IEEE Trans. Automatica Control ¼ÓÃ

As the performance index of the linear-quadratic-Gaussian (LQG)
problem is governed by the non-central generalized Chi-square
distribution, solely controlling the expected value of the
performance index, as the traditional LQG theory aims at, is
insufficient to deliver a satisfactory solution in some
situations. While the risk sensitive control does control a specific
weighting sum of various moments of the performance index, the
single degree of freedom in adjusting the weighting coefficients
in this specific weighting sum of various moments of the performance index
often prevents the risk sensitive control from generating a desired
pattern of high order moment-distribution. We achieve in this
paper the complete statistical characterization of the performance
index for the discrete-time LQG formulation. More specifically, we derive
a recursive relationship to obtain cumulants of various orders
of the performance index successively. Parameterized in feedback
gain, the optimal feedback control law can be computed off-line by
solving a static polynomial optimization problem, thus serving two
design goals: i) To shape the probability density function (PDF)
of the performance index to attain, at least approximately, a given desired pattern by
regulating cumulants of various orders, and ii) to improve the
performance measure of an incumbent solution (generated by the risk sensitive control, for example) by adjusting the
levels of cumulants of various orders.
19Â¥2011-08-17 09:13:12
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