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Equivalence-Based Model of Dimension-Varying Linear Systems. (arXiv:1810.03520v1 [math.DS])
来源于:arXiv
Dimension-varying linear systems are investigated. First, a dimension-free
state space is proposed. A cross dimensional distance is constructed to glue
vectors of different dimensions together to form a cross-dimensional
topological space. This distance leads to projections over different
dimensional Euclidean spaces and the corresponding linear systems on them,
which provide a connection among linear systems with different dimensions.
Based on these projections, an equivalence of vectors and an equivalence of
matrices over different dimensions are proposed. It follows that the dynamics
on quotient space is obtained, which provides a proper model for
cross-dimensional systems. Finally, using the lift of dynamic systems on
quotient space to Euclidean spaces of different dimensions, a cross-dimensional
model is proposed to deal with the dynamics of dimension-varying process of
linear systems. On the cross-dimensional model a control is designed to realize
the transfer between models on E 查看全文>>