Data-driven method for dimension reduction of nonlinear randomly vibrating systems
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DOI: 10.1007/s11071-021-06601-1
Abstract: Data-driven identification of nonlinear differential equations turns out to be an inefficient, and sometimes even impossible, for high-dimensional randomly vibrating systems. The mathematical formulism of stochastic averaging, moreover, is restricted by the difficulty of determining… read more here.
Keywords: dimension reduction; vibrating systems; stochastic averaging; randomly vibrating ... See more keywords
Stabilized principal interval decomposition method for model reduction of nonlinear convective systems with moving shocks
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DOI: 10.1007/s40314-018-0718-z
Abstract: An efficient and reliable model order reduction of nonlinear systems poses a challenge for nonstationary problems with convective, non-periodic, and non-equilibrium dynamics. To that end, we put forth a localized basis selection strategy based on… read more here.
Keywords: interval decomposition; model; reduction nonlinear; principal interval ... See more keywords
Geometric Theory of Reduction of Nonlinear Control Systems
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DOI: 10.1134/s0965542518020045
Abstract: The foundations of a differential geometric theory of nonlinear control systems are described on the basis of categorical concepts (isomorphism, factorization, restrictions) by analogy with classical mathematical theories (of linear spaces, groups, etc.). read more here.
Keywords: control systems; nonlinear control; theory reduction; reduction nonlinear ... See more keywords