A connection between optimal control and IDA-PBC design

Authors

Abstract

This paper discusses the relations between Interconnection and Damping Assignment - Passivity Based Control (IDA-PBC) design and Linear Quadratic (LQ) optimal control. It is first investigated how a given optimal control affect the closed-loop system design and, on the other hand, how an optimal criterion may be used as a guideline for IDA-PBC parameters design. The case of a trivial relation between the optimal control gain and the desired total power in the IDA-PBC design is investigated in this work while some other choices could be further considered. The proposed method is successfully illustrated via the example of a linearized pendulum.

Keywords

Port-Controlled Hamiltonian (PCH) systems; Interconnection; Damping Assignment Passivity Based Control (IDA-PBC) parameterization; linear quadratic (LQ) optimal control

Citation

Journal: IFAC-PapersOnLine
Year: 2018
Volume: 51
Issue: 3
Pages: 205–210
Publisher: Elsevier BV
DOI: 10.1016/j.ifacol.2018.06.054
Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018

BibTeX

@article{Vu_2018,
  title={{A connection between optimal control and IDA-PBC design}},
  volume={51},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2018.06.054},
  number={3},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Vu, N.M. Trang and Lefèvre, L.},
  year={2018},
  pages={205--210}
}

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References

Boyd, S., El Ghaoui, L., Feron, E. & Balakrishnan, V. Linear Matrix Inequalities in System and Control Theory. (1994) doi:10.1137/1.9781611970777 – 10.1137/1.9781611970777
Castaños, F., Ortega, R., van der Schaft, A. & Astolfi, A. Asymptotic stabilization via control by interconnection of port-Hamiltonian systems. Automatica vol. 45 1611–1618 (2009) – 10.1016/j.automatica.2009.03.015
Fujimoto, K., Horiuchi, T. & Sugie, T. Optimal control of Hamiltonian systems with input constraints via iterative learning. 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) 4387–4392 doi:10.1109/cdc.2003.1272188 – 10.1109/cdc.2003.1272188
Hamroun, B., Dimofte, A., Lefèvre, L. & Mendes, E. Control by Interconnection and Energy-Shaping Methods of Port Hamiltonian Models. Application to the Shallow Water Equations. European Journal of Control vol. 16 545–563 (2010) – 10.3166/ejc.16.545-563
Kotyczka, P. & Lohmann, B. Parametrization of IDA-PBC by assignment of local linear dynamics. 2009 European Control Conference (ECC) 4721–4726 (2009) doi:10.23919/ecc.2009.7075146 – 10.23919/ecc.2009.7075146
Macchelli, A. Boundary energy shaping of linear distributed port-Hamiltonian systems. European Journal of Control vol. 19 521–528 (2013) – 10.1016/j.ejcon.2013.10.002
Macchelli, (2014)
Macchelli, A. & Melchiorri, C. Control by interconnection of mixed port Hamiltonian systems. IEEE Transactions on Automatic Control vol. 50 1839–1844 (2005) – 10.1109/tac.2005.858656
Macchelli, A., van der Schaft, A. J. & Melchiorri, C. Port Hamiltonian formulation of infinite dimensional systems II. Boundary control by interconnection. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) 3768-3773 Vol.4 (2004) doi:10.1109/cdc.2004.1429325 – 10.1109/cdc.2004.1429325
Mikles, (2007)
Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 53 2527–2542 (2008) – 10.1109/tac.2008.2006930
Rodríguez, H. & Ortega, R. Stabilization of electromechanical systems via interconnection and damping assignment. International Journal of Robust and Nonlinear Control vol. 13 1095–1111 (2003) – 10.1002/rnc.804
Rodriguez, H., van der Schaft, A. J. & Ortega, R. On stabilization of nonlinear distributed parameter port-controlled Hamiltonian systems via energy shaping. Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228) vol. 1 131–136 – 10.1109/cdc.2001.980086
(2009)
Minh Trang Vu, N. & Lefèvre, L. Finite rank distributed control for the resistive diffusion equation using damping assignment. Evolution Equations & Control Theory vol. 4 205–220 (2015) – 10.3934/eect.2015.4.205
Vu, N. M. T., Nouailletas, R., Lefèvre, L. & Felici, F. Plasma q-profile control in tokamaks using a damping assignment passivity-based approach. Control Engineering Practice vol. 54 34–45 (2016) – 10.1016/j.conengprac.2016.05.003