Solving optimal control problems by exploiting inherent dynamical systems structures
type: Item
instance of: scholarly article
title: Solving optimal control problems by exploiting inherent dynamical systems structures
zbMATH Open document ID: 1264.37013
author: Sina Ober-Blöbaum
author: Marin Kobilarov
author: Kathrin Flasskamp
published in: Journal of Nonlinear Science
publication date: 2012-10-29T00:00:00Z
review text: The paper proposes a method combining local optimization and motion planning techniques based on exploiting inherent dynamical systems structures, such as symmetries and invariant manifolds. Prior to the optimal control, the dynamical system is analyzed for structural properties that can be used to compute pieces of trajectories that are stored in a motion planning library. In the context of mechanical systems, these motion planning candidates, named primitives, are given by relative equilibria induced by symmetries and motion on stable or unstable manifolds. The existence of controlled relative equilibria is studied with Lagrangian mechanics and symmetry reduction techniques. The approach is illustrated by two numerical examples.
Mathematics Subject Classification ID: 37J15
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 70Q05
zbMATH DE Number: 6100217
zbMATH Keywords: Lagrangian mechanics
zbMATH Keywords: optimal control
zbMATH Keywords: invariant manifolds
reviewed by: Bozhidar Cheshankov
describes a project that uses: SODAS
describes a project that uses: GAIO
MaRDI profile type: Publication
full work available at URL: s00332-012-9140-7
OpenAlex ID: W1987533373
cites work: Survey of Numerical Methods for Trajectory Optimization
cites work: Q2762557
cites work: Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden. With scientific input from P. S. Krishnaprasad, R. M. Murray, and D. Zenkov.
cites work: Controlled Lagrangians and the stabilization of mechanical systems. I: The first matching theorem.
cites work: Q3155754
cites work: Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
cites work: Nonlinear dynamics of the 3D pendulum
cites work: Q5713497
cites work: Optimal control applications in electric power systems
cites work: Low Energy Transit Orbits in the Restricted Three-Body Problems
cites work: Q4544293
cites work: On target for Venus -- set oriented computation of energy efficient low thrust trajectories
cites work: A multi-objective approach to the design of low thrust space trajectories using optimal control
cites work: Multicriteria Optimization
cites work: Almost-invariant sets and invariant manifolds - connecting probabilistic and geometric descriptions of coherent structures in flows
cites work: An SQP method for the optimal control of large-scale dynamical systems
cites work: Connecting orbits and invariant manifolds in the spatial restricted three-body problem
cites work: Evaluating Derivatives
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Distinguished material surfaces and coherent structures in three-dimensional fluid flows
cites work: Lagrangian coherent structures and mixing in two-dimensional turbulence
cites work: Q4840149
cites work: Geometric discretization of nonholonomic systems with symmetries
cites work: Low energy transfer to the Moon
cites work: A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS
cites work: Planning Algorithms
cites work: Discrete mechanics and optimal control for constrained systems
cites work: Q4279738
cites work: Q4297015
cites work: Q4249020
cites work: Lagrangian reduction and the double spherical pendulum
cites work: Discrete mechanics and variational integrators
cites work: Multisymplectic geometry, variational integrators, and nonlinear PDEs
cites work: Reduction theory and the Lagrange-Routh equations.
cites work: Optimal transition maneuvers for a class of V/STOL aircraft
cites work: Complete search in continuous global optimization and constraint satisfaction
cites work: Discrete mechanics and optimal control: An analysis
cites work: Numerical approximations of strong (un)stable manifolds
cites work: Hamiltonian systems near relative equilibria
cites work: Halo orbit mission correction maneuvers using optimal control
cites work: Stability of relative equilibria. I: The reduced energy-momentum method
cites work: Q3149379
cites work: Numerical Bifurcation of Hamiltonian Relative Periodic Orbits
cites work: Stochastic global optimization.
DOI: 10.1007/S00332-012-9140-7
description: scientific article; zbMATH DE number 6100217