Developments in Control Theory Towards Glocal Control by Li Qiu, Jie Chen, Tetsuya Iwasaki, Hisaya Fujioka

By Li Qiu, Jie Chen, Tetsuya Iwasaki, Hisaya Fujioka

A suite of study articles devoted to the sixtieth birthday of Prof. Shinji Hara of the college of Tokyo, highlighting papers on keep watch over concept and its purposes. - appropriate for researchers, PhD scholars and skilled engineers operating within the box of regulate engineering.

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It turns out that the well-known separation principle for LQG control fails to generalize to QLQG, and this is caused by the fact that minimizing the quantization error at each time instant separately does not lead to a minimum cost globally. Here we consider the QLQG problem for a scalar system and present an adaptive quantization scheme. Using this scheme, we show that the quantization distortion order is R2À2R for a large bit rate R. This means that the separation principle holds approximately when the bit rate is sufficient.

The reference input r(t) is assumed to be a vector of wide sense stationary (WSS) random processes with zero mean and finite power, whose power spectrum matrix Gr(s) is rational and admits the spectral factorization Gr ¼ Y$ r Yr : Without loss of generality, we assume that the spectral factor Yr is stable and minimum phase. , s2r ¼ kYr k22 51. 2, which have their own noise levels but share a common input power specification. We assume that the channel noise n ¼ (n1(t), . . , nm(t))T is a vector of uncorrelated white noise processes ni(t).

Vol. 1, pp. 656–661, 2002 5. T. Asai, ‘Improved worst-case L2 gain analysis for systems with switching and dynamic uncertainly based on LMIs’, Trans. ISCIE, vol. 16, no. 2, pp. 94–100, 2003 (in Japanese) 6. T. Asai, ‘Necessary and sufficient conditions for analysis of L2 gain across switching’, Trans. SICE, vol. 41, no. 5, pp. 437–443, 2005 (in Japanese) 7. T. Asai, ‘LMI-based synthesis for robust attenuation of disturbance responses due to switching’, Proc. 42nd IEEE Conf. , vol. 5, pp. 5277– 5282, 2003 8.

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