Premium
Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control
Author(s) -
Glaas Daniel,
Leyendecker Sigrid
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710044
Subject(s) - variational integrator , control theory (sociology) , optimal control , riccati equation , integrator , algebraic riccati equation , mathematics , discrete time and continuous time , trajectory , controller (irrigation) , differential equation , mathematical analysis , mathematical optimization , control (management) , computer science , physics , bandwidth (computing) , artificial intelligence , computer network , statistics , agronomy , astronomy , biology
An approach to minimize the control costs and ensuring a stable deviation control is the Riccati controller and we use it to control constrained dynamical systems (differential algebraic equations of Index 3) with pulsed disturbances. To describe their discrete dynamics, a constrained variational integrator [1] is used. Using a discrete version of the Lagrange‐d'Alembert principle yields a forced constrained discrete Euler‐Lagrange equation in a position‐momentum form that depends on the current and future time steps [2]. The desired optimal trajectory ( q opt , p opt ) and according control input u opt is determined solving the discrete mechanics and optimal control (DMOC) algorithm [3] based on the variational integrator. Then, during time stepping of the perturbed system, the discrete Riccati equation yields the optimal deviation control input u R . Adding u opt and u R to the discrete Euler‐Lagrange equation causes a structure preserving trajectory as both DMOC and Riccati equations are based on the same variational integrator. Furthermore, coordinate transformations are implemented (minimal, redundant and nullspace) enabling the choice of different coordinates in the feedback loop and in the optimal control problem. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)