Abstract
In this paper, we investigate morphisms of tautological control systems. Given a tautological control system \(\mathfrak {H}\) on the manifold N and a mapping \(\Phi : M \rightarrow N\), we study existence of tautological control system \(\mathfrak {G}\) on the manifold M such that there exists a trajectory-preserving morphism \((\Phi , \Phi ^\#)\) from \(\mathfrak {G}\) to \(\mathfrak {H}\). Sufficient conditions are given such that reachability of \(\mathfrak {H}\) implies the reachability of \(\mathfrak {G}\). Correspondence between the notion of lifting ordinary control systems and morphisms of tautological control systems are examined. We give an application of the above results to the class of second-order type control systems, where the special structure of second-order type leads to additional results.
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Acknowledgements
The author would like to thank the reviewers whose remarks and suggestions have improved the final version of the paper. This work is supported by the Startup Foundation for Introducing Talent of NUIST (No. 2017r003).
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Xia, Q. Morphisms of tautological control systems. Math. Control Signals Syst. 29, 12 (2017). https://doi.org/10.1007/s00498-017-0201-1
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DOI: https://doi.org/10.1007/s00498-017-0201-1