Power-series approximations for the optimal feedback control of noisy nonlinear systems |
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Authors: | Y. Nishikawa N. Sannomiya H. Itakura |
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Affiliation: | (1) Department of Electrical Engineering, Kyoto University, Kyoto, Japan |
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Abstract: | Power-series methods are developed for designing approximately optimal state regulators for a nonlinear system subject to white Gaussian random disturbances. The performance index of the control is an ensemble average of a quadratic form. A perfect observation of the system state is assumed. When the system nonlinearity is small and it is characterized by a polynomial function of the state, a definite method is presented to construct a suboptimal feedback control of a power-series form in a small nonlinearity parameter. If the variance of noise is small, an alternative method is also applicable which yields a suboptimal control in a power series with respect to a variance parameter. A simple one-dimensional problem is examined to make comparison between controls of the two different forms. |
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Keywords: | Noisy nonlinear systems white Gaussian noise polynomial nonlinearity suboptimal feedback control small-parameter method series expansion |
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