article · PAMM · 2017

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

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Abstract

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 ( 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)

Cite this paper

APA 7

Glaas, D., & Leyendecker, S. (2017). Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control. PAMM, 17(1), 149–150. https://doi.org/10.1002/pamm.201710044

MLA 9

Glaas, Daniel, and Sigrid Leyendecker. “Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control.” PAMM, vol. 17, no. 1, 2017, pp. 149–50, https://doi.org/10.1002/pamm.201710044.

Chicago

Glaas, Daniel, and Sigrid Leyendecker. 2017. “Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control.” PAMM 17 (1): 149–50. https://doi.org/10.1002/pamm.201710044.

Harvard

Glaas, D. and Leyendecker, S. (2017) ‘Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control’, PAMM, 17(1), pp. 149–150. Available at: https://doi.org/10.1002/pamm.201710044.

BibTeX

@article{glaas2017variational,
  title = {{Variational integrator for constrained mechanical systems with pulsed disturbances and optimal feedback control}},
  author = {Glaas, Daniel and Leyendecker, Sigrid},
  journal = {PAMM},
  volume = {17},
  number = {1},
  pages = {149--150},
  year = {2017},
  doi = {10.1002/pamm.201710044}
}

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