Adjustment Optimization for a Model of Differential Realization of a Multidimensional Second-Order System

We study the problem of calculating the preferred differential realization system in the space of similar plant-controller-observer models induced by transformation groups over an identified second-order dynamical system. We prove theorems on the existence of a transforming matrix (an a posteriori b...

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Bibliographic Details
Published in:Differential equations 2019-10, Vol.55 (10), p.1390-1396
Main Authors: Rusanov, V. A., Daneev, A. V., Linke, Yu. E.
Format: Article
Language:English
Subjects:
Control Theory
Difference and Functional Equations
Differential equations
Eigenvalues
Eigenvectors
Existence theorems
Mathematics
Mathematics and Statistics
Optimization
Ordinary Differential Equations
Partial Differential Equations
Transformations (mathematics)
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Summary:We study the problem of calculating the preferred differential realization system in the space of similar plant-controller-observer models induced by transformation groups over an identified second-order dynamical system. We prove theorems on the existence of a transforming matrix (an a posteriori basis of the configuration space) in the transformation groups GL n (ℝ) and SO n minimizing the mismatch between the positional force matrix and its reference rated parameters. Based on Morse theory, we construct a nonlinear matrix characteristic equation of the optimal SO n -adjustment process. The results have applications in the differential precise modeling of forced oscillations and generate statements of the problem in the infinite-dimensional case.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266119100148