Optimal Syntheses for Control Systems on 2-D Manifolds

By Ugo Boscai, Benedetto Piccoli. 2004

229 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/180009dc4f7e6b5238e4ebc00d8094cc9562f68e

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Citations in the corpus

Training Schrödinger’s cat: quantum optimal control (2015, background): “Mathematical tools that were developed recently [4, 34, 44, 188] allowed to solve problems of increasing difficulty including fundamental control problems for closed [42, 43, 91, 92, 135, 209] and open quantum systems [35, 205, 238, 291, 400, 461].”
On the Hausdorff volume in sub-Riemannian geometry (2010, background): “The following characterization is a corollary of Pontryagin Maximum Principle (PMP for short, see for instance [6, 15, 29, 37]):”
The turnpike property in finite-dimensional nonlinear optimal control (2014, background): “[51]). More recently, turnpike phenomena have been also put in evidence in optimal control problems coming from biology, such as in [17], in relation with singular arcs (see also [39]). Note that, in [12], the word "turnpike" refers to the set of points where singular trajectories can stay”
Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control (2020, methodology): “Many reference textbooks have been published on the subject both on mathematical results and engineering applications [28, 29, 30, 31, 26, 32, 33, 34, 36, 35].”
Time minimal trajectories for a spin 1∕2 particle in a magnetic field (2005, background): “On the other side, for M/E > 1, the time optimal trajectory steering the state one to the state two is bang-bang with exactly one switching.”
Invariant Carnot-Caratheodory metrics on $S^3$, $SO(3)$, $SL(2)$ and lens spaces (2007, unknown): “Solutions to the optimal control problem (8) are computed via the Pontryagin Maximum Principle (PMP for short, see for instance [3, 11, 21, 24]) that is a first order necessary condition for optimality and generalizes the Weierstraß conditions of Calculus of Variations.”