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Differential-geometric and invariance properties of the equations of maximum principle (MP). (English) Zbl 1298.49069

Stefani, Gianna (ed.) et al., Geometric control theory and sub-Riemannian geometry. Proceedings of the meeting on geometric control theory and sub-Riemannian geometry, dedicated to Andrei A. Agrachev on the occasion of his 60th birthday, Cortona, Italy, May 21–25, 2012. Cham: Springer (ISBN 978-3-319-02131-7/hbk; 978-3-319-02132-4/ebook). Springer INdAM Series 5, 167-175 (2014).
Summary: An invariant formulation of the Pontryagin Maximum Principle (PMP) is given. It is proved that the Pontryagin derivative \(\mathcal P_{X}\) coincides on vector fields \(X \in \mathrm{Vect} M\), (\(M\) – the configuration space of the problem), with the Lie bracket \(ad_{X}\), and the flow generated on the cotangent bundle \(T^* M\) by the vector field \(\mathcal P_{X}\) is bundle-preserving.
For the entire collection see [Zbl 1287.49001].

MSC:

49Q99 Manifolds and measure-geometric topics
49K27 Optimality conditions for problems in abstract spaces
49K15 Optimality conditions for problems involving ordinary differential equations
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