Control Theory from the Geometric Viewpoint

By Andrei A. Agrachev, Yuri L. Sachkov. 2004

1,541 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Control and Systems Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3d3429f9a76c4941d7cf57382a61b58d51ef2623

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In Aerospace Engineering

In Control and Systems Engineering

In Geometry and Topology

Citations in the corpus

A Gauss-Bonnet-like formula on two-dimensional almost-Riemannian manifolds (2006, background): “Finally, one can define on M \ Z the Gaussian curvature K associated with g, which is easily expressed in each open set Ω \ Z through the formula (see for instance [3], equation (24.”
Time minimal trajectories for a spin 1∕2 particle in a magnetic field (2005, methodology): “for instance [3, 12] and references therein).”
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].”
Control theory on lie groups (2009, background): “(1) textbooks on control theory [ 1 , 14, 30], sub-Riemannian geometry [28], nonholonomic dynamics [44], and dieren tial geometry and Lie groups [45],”
A Pontryagin Maximum Principle in Wasserstein spaces for constrained optimal control problems (2018, positive): “[3, 15]) and makes an extensive use of the theory of Wasserstein subdifferential calculus [9].”
Time-optimal Control of Spin Systems (2006, neutral): “Since {Ai}i is linearly independent, we find that for each i ∑ j aijzj = 0 ⇐⇒ ∑ j aij 〈Bjw, b〉W = 0.”
Local controllability of 1D linear and nonlinear Schr (2010, neutral): “The controllability of (17) is linked to the rank of the Lie algebra spanned by H0 and H1 (see for instance [5] by Albertini and D’Alessandro, [7] by Altafini, [26] by Brockett, see also [3] by Agrachev and Sachkov, [32] by Coron for a more general discussion).”
Genericity results for singular curves (2006, background): “For a more detailed and self-contained proof of that result, see the textbook [3] and, more specifically, Theorem 20.”
The turnpike property in finite-dimensional nonlinear optimal control (2014, positive): “According to the Pontryagin maximum principle (see [2, 42, 52]), there must exist an absolutely continuous mapping λT (·) : [0, T ] → IR, called adjoint vector, and a real number λT 6 0, with (λT (·), λT ) 6= (0, 0), such that, for almost every t ∈ [0, T ],”
Optimal transportation under nonholonomic constraints (2007, neutral): “O C ] 2 4 N ov”