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Bifurcation of controllability regions in a plane by separatrix splitting

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Abstract

For a nonlinear controlled dynamic system of the form where u(t) is a bounded piecewise-continuous control and m ≤ u(t) ≤ n, the article studies bifurcations (qualitative changes) of controllability (reachability) regions due to merging and subsequent splitting of separatrices of the equilibrium states of auxiliary autonomous systems. Conditions for continuous and discontinuous changes of the controllability (reachability) regions are established. Bifurcations of controllability regions of Duffing equations are considered as an illustration.

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References

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Authors
  1. N. N. Butenina
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  2. Z. G. Pavlyuchonok
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Additional information

Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 70–81, 1993.

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Butenina, N.N., Pavlyuchonok, Z.G. Bifurcation of controllability regions in a plane by separatrix splitting. Comput Math Model 7, 319–327 (1996). https://doi.org/10.1007/BF01128163

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  • DOI: https://doi.org/10.1007/BF01128163

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