Geometric control theory

By D. Elliott. IEEE Transactions on Automatic Control, 2000

755 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/71345478367ebe6b67f733e2e421b62e746eca21

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In Computational Mechanics

Citations in the corpus

Equilibria and steering laws for planar formations (2004, background): “(A modern reference for control systems on Lie groups is Jurdjevic [6].”
Invariant Carnot-Caratheodory metrics on $S^3$, $SO(3)$, $SL(2)$ and lens spaces (2007, neutral): “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.”
Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, methodology): “With the controlled part being linear in both the state and the control, it is an example of the wide class of bilinear control systems [154, 212, 311].”
Planning algorithms (2006, methodology): “For further reading on the Hamilton-Jacobi-Bellman equation, see [87, 97, 495, 792, 913].”
Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control (2020, background): “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].”
Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, neutral): “We refer the reader to textbooks such as [1,16,18,19,29,33,38,49,51,52,54] for theoretical results and/or practical applications, essentially for dynamical systems described by ordinary differential equations.”
EQUIVALENCE OF CONTROL SYSTEMS WITH LINEAR SYSTEMS ON LIE GROUPS AND HOMOGENEOUS SPACES (2008, background): “Indeed L0 being Lie-determined, its rank is everywhere equal to the dimension of the zero-time orbit, which is constant, equal to dim(M) or dim(M) − 1 (see [7]).”
Diffeologies, Differential Spaces, and Symplectic Geometry (2012, background): “This generalises a well-known theorem in control theory, called “the orbit theorem” (see [Jur97]).”
On the Geometry of Rolling and Interpolation Curves on Sn, SOn, and Grassmann Manifolds (2007, background): “10) is easily obtained from the equations from [18] by a rotation of coordinates.”
Training Schrödinger’s cat: quantum optimal control (2015, background): “Adapting results from classical linear control systems [191, 390] to bilinear systems with a non-switchable drift term, a rigorous Lie-framework was developed for closed systems [56, 57, 119, 188, 189, 402].”
Time-optimal Control of Spin Systems (2006, neutral): “KRONECKER PRODUCT FORMALISM 29 DEFINITION 1.5.5.”
Navier–Stokes Equations: Controllability by Means of Low Modes Forcing (2005, neutral): “5 (see [14, 2] and references therein).”
Control theory on lie groups (2009, background): “The bibliography contains references of several kinds: (1) textbooks on control theory [1, 14, 30], sub-Riemannian geometry [28], nonholonomic dynamics [44], and differential geometry and Lie groups [45], (2) works on controllability of invariant systems on Lie groups [2, 3, 4, 5, 11, 12, 13, 15, 16”
Time minimal trajectories for a spin 1∕2 particle in a magnetic field (2005, methodology): “Indeed optimal trajectories must satisfy a first order necessary condition for optimality called the Pontryagin Maximum Principle (in the following PMP, see for instance [3, 25]) that generalizes the Weierstraß conditions of Calculus of Variations to problems with non-holonomic constraints.”
On variational approach to differential invariants of rank two distributions (2004, background): “5 Note that distribution D2 appears, when one studies the problem of rolling ball on the plane without slipping and twisting (see Example 4 below and also [13] for the details).”
Quantum Computation as Geometry (2006, methodology): “as the norm associated to a ( right invariant) Riemannian metric whose metric tensor ghas components: gστ = 0 if σ6= τ 1 if σ= τand σis one- or two-body p2 if σ= τand σis three- or more-body. (3) These components are written with respect to a basis for the local tangent space corresponding to the”
A Simple Control Law for UAV Formation Flying (2002, neutral): “Email addresses: justh@isr.umd.edu (E. W. Justh), krishna@isr.umd.edu (P. S. Krishnaprasad).”