Selective excitation of identical conservative port-Hamiltonian systems by a single control

Authors

Dmitry Gromov, Alexander L. Fradkov, Mikhail S. Ananyevskiy

Abstract

A generalization of the results obtained earlier in M. S. Ananyevskiy, A. L. Fradkov, and H. Nijmeijer; Control of mechanical systems with constraints: two pendulums case study, IFAC Proceedings Volumes, vol. 41, no. 2, pp. 7690–7694, 2008. is presented. Three control problems for complex systems consisting of port-Hamiltonian subsystems are formulated. In particular, the problem of exciting a number of identical port-Hamiltonian systems to given (not necessarily equal) energy levels while ensuring strict bounds on the energy levels of remaining systems is studied. Solvability conditions based on speed-gradient control are established. The obtained results are illustrated by numerical simulations.

Citation

• Journal: 2019 18th European Control Conference (ECC)
• Year: 2019
• Volume:
• Issue:
• Pages: 2879–2884
• Publisher: IEEE
• DOI: 10.23919/ecc.2019.8795780

BibTeX

@inproceedings{Gromov_2019,
  title={{Selective excitation of identical conservative port-Hamiltonian systems by a single control}},
  DOI={10.23919/ecc.2019.8795780},
  booktitle={{2019 18th European Control Conference (ECC)}},
  publisher={IEEE},
  author={Gromov, Dmitry and Fradkov, Alexander L. and Ananyevskiy, Mikhail S.},
  year={2019},
  pages={2879--2884}
}

Download the bib file

References

• 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
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• Öttinger, H. C. Beyond Equilibrium Thermodynamics. (2005) doi:10.1002/0471727903 – 10.1002/0471727903
• Gromov, D. Two Approaches to the Description of the Evolution of Thermodynamic Systems. IFAC-PapersOnLine vol. 49 34–39 (2016) – 10.1016/j.ifacol.2016.10.749
• Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
• Castaños, F. & Gromov, D. Passivity-based control of implicit port-Hamiltonian systems with holonomic constraints. Systems & Control Letters vol. 94 11–18 (2016) – 10.1016/j.sysconle.2016.04.004
• Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Automatic Control vol. 36 1228–1240 (1991) – 10.1109/9.100932
• krasovskii, Problems of the Theory of Stability of Motion (Russian) 1959 (1963)
• lasalle, The stability of dynamical systems. SIAM (0)
• fradkov, Speed-gradient scheme and its application in adaptive control problems. Automation and Remote Control (1980)
• pikovsky, Synchronization A Universal Concept in Nonlinear Sciences (2003)
• Ananyevskiy, M. S., Seifullaev, R. E., Nikitin, D. A. & Fradkov, A. L. Synchronization of nonlinear systems over intranet: Cart-pendulum case study. 2014 IEEE Conference on Control Applications (CCA) 1214–1219 (2014) doi:10.1109/cca.2014.6981494 – 10.1109/cca.2014.6981494
• Blekhman, I. I., Fradkov, A. L., Nijmeijer, H. & Pogromsky, A. Yu. On self-synchronization and controlled synchronization. Systems & Control Letters vol. 31 299–305 (1997) – 10.1016/s0167-6911(97)00047-9
• Proskurnikov, A. V. & Fradkov, A. L. Problems and methods of network control. Automation and Remote Control vol. 77 1711–1740 (2016) – 10.1134/s0005117916100015
• fradkov, Cybernetical Physics From Control of Chaos to Quantum Control (2007)
• Ananyevskiy, M. S., Fradkov, A. L. & Nijmeijer, H. Control of mechanical systems with constraints: two pendulums case study. IFAC Proceedings Volumes vol. 41 7690–7694 (2008) – 10.3182/20080706-5-kr-1001.01300
• Liu, T., Jiang, Z.-P. & Hill, D. J. Nonlinear Control of Dynamic Networks. (2018) doi:10.1201/b16759 – 10.1201/b16759
• Ren, W. & Beard, R. W. Distributed Consensus in Multi-Vehicle Cooperative Control. Communications and Control Engineering (Springer London, 2008). doi:10.1007/978-1-84800-015-5 – 10.1007/978-1-84800-015-5
• Wong, D., Steager, E. B. & Kumar, V. Independent Control of Identical Magnetic Robots in a Plane. IEEE Robotics and Automation Letters vol. 1 554–561 (2016) – 10.1109/lra.2016.2522999
• Jadbabaie, A., Jie Lin & Morse, A. S. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control vol. 48 988–1001 (2003) – 10.1109/tac.2003.812781
• Fradkov, A. L. & Pogromsky, A. Yu. Speed gradient control of chaotic continuous-time systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications vol. 43 907–913 (1996) – 10.1109/81.542281
• Hahn, W. Stability of Motion. (Springer Berlin Heidelberg, 1967). doi:10.1007/978-3-642-50085-5 – 10.1007/978-3-642-50085-5
• Dolgopolik, M. V. & Fradkov, A. L. Nonsmooth and discontinuous speed-gradient algorithms. Nonlinear Analysis: Hybrid Systems vol. 25 99–113 (2017) – 10.1016/j.nahs.2017.03.005
• Shiriaev, A. S. & Fradkov, A. L. Stabilization of invariant sets for nonlinear systems with applications to control of oscillations. International Journal of Robust and Nonlinear Control vol. 11 215–240 (2001) – 10.1002/rnc.568.abs
• barbashin, On stability of motion in the large. Dokl Akad Nauk SSSR (1952)
• de Kruijff, J. & Weigand, H. Understanding the Blockchain Using Enterprise Ontology. Lecture Notes in Computer Science 29–43 (2017) doi:10.1007/978-3-319-59536-8_3 – 10.1007/978-3-319-59536-8_3
• Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Automatic Control vol. 36 1228–1240 (1991) – 10.1109/9.100932