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Discrete mechanics and optimal control / Sina Ober-Blöbaum. 2008
Inhalt
Introduction
Optimal control
Optimal control problem
Problem formulation
Necessary conditions for optimality
Solution methods for optimal control problems
Indirect methods
Direct methods
Solution methods for nonlinear constrained optimization problems
Local optimality conditions
Sequential Quadratic Programming (SQP)
Discussion of direct methods
Variational mechanics
Lagrangian mechanics
Basic definitions and concepts
Discrete Lagrangian mechanics
Hamiltonian mechanics
Basic definitions and concepts
Discrete Hamiltonian mechanics
Forcing and control
Forced Lagrangian systems
Forced Hamiltonian systems
Legendre transform with forces
Noether's theorem with forcing
Discrete variational mechanics with control forces
Discrete Legendre transforms with forces
Discrete Noether's theorem with forcing
Discrete mechanics and optimal control (DMOC)
Optimal control of a mechanical system
Lagrangian optimal control problem
Hamiltonian optimal control problem
Transformation to Mayer form
Optimal control of a discrete mechanical system
Discrete Optimal Control Problem
Transformation to Mayer form
Fixed boundary conditions
Correspondence between discrete and continuous optimal control problem
Exact discrete Lagrangian and forcing
Order of consistency
Discrete problem as direct solution method
High-order discretization
Quadrature approximation
High-order discrete optimal control problem
Correspondence to Runge-Kutta discretizations
Adjoint system
Continuous setting
Discrete setting
The transformed adjoint system
Convergence
Implementation, applications and extension
Implementation
Comparison to existing methods
Low thrust orbital transfer
Two-link manipulator
Application: Trajectory planning
A group of hovercraft
Perfect underwater glider
Application: Optimal control of multi-body systems
The falling cat
A gymnast (three-link mechanism)
Reconfiguration of formation flying spacecraft -- a decentralized approach
Optimal control of constrained mechanical systems in multi-body dynamics
Constrained dynamics and optimal control
Optimization problem
Constrained Lagrange-d'Alembert principle
Null space method
Reparametrization
Constrained discrete dynamics and optimal control
Discrete constrained Lagrange-d'Alembert principle
Discrete null space method
Nodal reparametrization
Boundary conditions
Discrete constrained optimization problem
Optimal control for rigid body dynamics
Constrained formulation of rigid body dynamics
Actuation of the rigid body
Kinematic pairs
Applications
Optimal control of a rigid body with rotors
Biomechanics: The optimal pitch
Conclusions and outlook
Definitions
Adjoint system
Convergence proof
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