Abstract
We shall deal with the dynamic polysystems and nonlinear control systems on C∞-smooth connected n-dimensional Riemannian manifolds. Dynamical polysystem on a manifold M (see [12]) is a family \( \Im \) of complete C∞-smooth vector fields on M. Trajectories of \( \Im \) are piecewise smooth curves γ: [t1, t2]→M, such that for some partitioning t1=t 0 ≤ τ1≤… τN=t2 of [t1,t2] the restriction of γ on any [τ1, τi+1] is a trajectory of some vector field from \( \Im \). For any x∈M put \( {\Im_X} \) for {f(x)|f∈ \( \Im \) }; evidently \( {\Im_X} \) — is a subset of tangent space TxM to M at point x.
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© 1991 Birkhäuser Boston
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Sarychev, A.V. (1991). Nonlinear Control Systems: Topological Properties of Trajectory Space. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_32
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_32
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