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Register a new userSupplementary Material to: Realization of Three-port Spring Networks with Inerter for Effective Mechanical Control
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This is a supplementary material to Realization of three-port spring networks with inerter for effective mechanical control [1], which provides the detailed proofs of some results. For more background information, refer to [2]-[32] and references therein.
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This report includes the original manuscript (pp. 2-40) and the supplementary material (pp. 41-48) of Passive Mechanical Realizations of Bicubic Impedances with No More Than Five Elements for Inerter-Based Control Design.
This report presents some supplementary material to the paper entitled Passive controller realization of a biquadratic impedance with double poles and zeros as a seven-element Series-parallel network for effective mechanical control [1].
This is supplementary material to Realizations of a special class of admittances with strictly lower complexity than canonical forms [1], which presents the detailed proofs of some results. For more background information, refer to [2]-[22] and references therein.
This supplement illustrates application of adaptive observer design from (Tyukin et al, 2013) for systems which are not uniquely identifiable. It also provides an example of adaptive observer design for a magnetic bearings benchmark system (Lin, Knospe, 2000).
In this paper, we focus on the influences of the condition number of the regression matrix upon the comparison between two hyper-parameter estimation methods: the empirical Bayes (EB) and the Steins unbiased estimator with respect to the mean square error (MSE) related to output prediction (SUREy). We firstly show that the greatest power of the condition number of the regression matrix of SUREy cost function convergence rate upper bound is always one larger than that of EB cost function convergence rate upper bound. Meanwhile, EB and SUREy hyper-parameter estimators are both proved to be asymptotically normally distributed under suitable conditions. In addition, one ridge regression case is further investigated to show that when the condition number of the regression matrix goes to infinity, the asymptotic variance of SUREy estimator tends to be larger than that of EB estimator.
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