Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control

Variational integrator for constrained mechanical systems with pulsed disturbances and optimal... 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 (qopt, popt) and according control input uopt 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 uR. Adding uopt and uR 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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710044
Publisher site
See Article on Publisher Site

Abstract

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 (qopt, popt) and according control input uopt 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 uR. Adding uopt and uR 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)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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