E. I. Atamas’, A. V. Il’in, S. K. Korovin, V. V. Fomichev
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引用次数: 0
Abstract
A new methodology for solving inverse dynamics problem is developed. The methodology
is based on using a mathematical model of a dynamical system and robust stabilization methods
for a system under uncertainty.
Most exhaustively the theory is described for linear finite-dimensional
time-invariant scalar systems and multiple-input multiple-output systems.
The study shows that with this approach, the zero dynamics of the original system
is of crucial significance. This dynamics, if exists, is assumed to be exponentially stable.
It is established that zero-dynamics, relative order, and the corresponding
equations of motion cannot be defined correctly in multiple-input multiple-output systems. For
correct inverse transformation of the solution of the problem, additional assumptions have to be
introduced, which generally limits the inverse system category.
Special attention is given to the synthesis of elementary (minimal) inverters, i.e.,
least-order dynamical systems that solve the transformation problem.
It is also established that the inversion methods sustain the efficiency with finite
parameter variations in the initial system as well as with uncontrolled exogenous impulses having
no impact on the system’s internal dynamics.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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