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Invariants in Optimal Control: An Exact Solution of the Optimal Stabilization Problem

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Abstract:

The stabilizing optimal feedback is a function onthe separatrix of stable points of the associated Hamiltoniansystem. Three geometric objects - the symplectic form, Hamiltonianvector field, and Lyapunov function, generating the separatrix - are %intrinsic to the optimal control system. They areinvariantly attached to the optimal control system under canonicaltransformations of the phase space. The separatrix equations can be writtenin terms of these invariants through invariant operations.There is a computable representative of the equivalence class,containing the original system. It is its linear approximation system at the stable point.

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Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 21)
Pages:
9-14
Citation:
G. V. Kondratiev, "Invariants in Optimal Control: An Exact Solution of the Optimal Stabilization Problem", Bulletin of Mathematical Sciences and Applications, Vol. 21, pp. 9-14, 2019
Online since:
December 2019
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References:

[1] G. V. Kondratiev, Geometric theory of synthesis of smooth optimal stationary control systems, Fizmatlit, Moscow, Russia, (2003).

[2] V. I. Arnold, A. Weinstein, K. Vogtmann, Mathematical methods of classical mechanics, Springer, (1989).

[3] F. W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, (1983).

[6] R. W. Sharpe, Differential Geometry, Cartan's Generalization of Klein's Erlangen Program, Springer, (1997).

[7] P. J. Olver, Equivalence, Invariants, and Symmetry, Cambridge University Press, (1995).

[9] G. V. Kondratiev , Natural Transformations in Statistics, SciPress, International Frontier Science Letters, vol. 6, (2015).

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