Suris, Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products. Huffmann, Mesh refinement in direct transcription methods for optimal control. Betts, Survey of numerical methods for trajectory optimization. Bär, Ein Kollokationsverfahren zur numerischen Lösung allgemeiner Mehrpunktrandwertaufgaben mit Schalt- und Sprungbedingungen mit Anwendungen in der Optimalen Steuerung und der Parameteridentifizierung. Russell, A collocation solver for mixed order systems of boundary value problems. LA - eng KW - Optimal control discrete mechanics discrete variational principle convergence optimal control UR - ER. TI - Discrete mechanics and optimal control: An analysis* JO - ESAIM: Control, Optimisation and Calculus of Variations DA - 2011/5// PB - EDP Sciences VL - 17 IS - 2 SP - 322 EP - 352 AB.
TY - JOUR AU - Ober-Blöbaum, Sina AU - Junge, Oliver AU - Marsden, Jerrold E. The numerical performance of DMOC and its relationship to other existing optimal control methods are investigated. We show that the DMOC (Discrete Mechanics and Optimal Control) approach is equivalent to a finite difference discretization of Hamilton's equations by a symplectic partitioned Runge-Kutta scheme and employ this fact in order to give a proof of convergence. The resulting optimization algorithm lets the discrete solution directly inherit characteristic structural properties from the continuous one like symmetries and integrals of the motion. The approach proposed in this paper is to directly discretize the variational description of the system's motion. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. The optimal control of a mechanical system is of crucial importance in many application areas. MarsdenĮSAIM: Control, Optimisation and Calculus of Variations Sina Ober-Blöbaum Oliver Junge Jerrold E. Discrete mechanics and optimal control: An analysis*
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