Singular Trajectories and Their Role in Control Theory
By Bernard Bonnard, M. Chyba. IEEE Transactions on Automatic Control, 2003
437 citations recorded by the source corpus.
Subfields: Aerospace Engineering, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/357d59e328dd90766fa1a1fb4f836d6b9c459ae1
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Aerospace Engineering
- Ugo V. Boscain
- Paolo Mason
- María Barbero-Liñán
- Miguel C. Muñoz-Lecanda
- Mario Sigalotti
- Andrew D. Lewis
- Francesco Bullo
- Andrei A. Agrachev
In Applied Mathematics
- Ugo V. Boscain
- Andrei A. Agrachev
- Mario Sigalotti
- Andrew D. Lewis
- Francesco Bullo
- Dominique Sugny
- Christiane P. Koch
- Davide Barilari
Citations in the corpus
- Geometric Approach to Pontryagin’s Maximum Principle (2008, background): “The understanding of this Maximum Principle never finishes as shows the continuous wide number of references in this topic [1, 2, 6, 8, 9, 12, 17, 19, 20, 21, 28, 31, 32, 33] and references therein.”
- Geometric control of mechanical systems (2004, positive): “We refer the reader to the book of Bonnard and Chyba [2003] for a detailed discussion of singular controlled extremals. In the paper of Chyba, Leonard, and Sontag [2003], it is shown that for mechanical systems, there can be singular extremals that are optimal.”
- Invariant Carnot-Caratheodory metrics on $S^3$, $SO(3)$, $SL(2)$ and lens spaces (2007, neutral): “For a deep analysis of abnormal extremals in sub-Riemannian geometry, see [8, 15].”
- Time minimal trajectories for a spin 1∕2 particle in a magnetic field (2005, background): “Second, one should manage with some special solutions of the PMP, the so called abnormal and singular extremals (see for instance [8]).”
- A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds (2006, background): “The di‐culties in studying tangency points are related with those appearing in non-contact sub-Riemannian geometry (see [2, 6 ]).”
- Training Schrödinger’s cat: quantum optimal control (2015, background): “Examples of geometric optimal control applications involving singular arcs [34] in NMR are relaxation-optimized polarization transfer experiments [205, 206, 291, 395], minimal-time controls for the saturation of spins, [238], for maximizing contrast in MRI [240] and for maximizing the achievable sig”