Energy-Based Feedback Control for Stochastic Dynamical Systems

Authors

Wassim M. Haddad, Tanmay Rajpurohit, Xu Jin

Abstract

In this paper, we develop an energy-based static and dynamic control framework for stochastic port-controlled Hamiltonian systems. In particular, we obtain constructive sufficient conditions for stochastic feedback stabilization that provide a shaped energy function for the closed-loop system while preserving a Hamiltonian structure at the closed-loop level. In the dynamic control case, energy shaping is achieved by combining the physical energy of the plant and the emulated energy of the controller.

Citation

• Journal: 2018 Annual American Control Conference (ACC)
• Year: 2018
• Volume:
• Issue:
• Pages: 5473–5478
• Publisher: IEEE
• DOI: 10.23919/acc.2018.8431578

BibTeX

@inproceedings{Haddad_2018,
  title={{Energy-Based Feedback Control for Stochastic Dynamical Systems}},
  DOI={10.23919/acc.2018.8431578},
  booktitle={{2018 Annual American Control Conference (ACC)}},
  publisher={IEEE},
  author={Haddad, Wassim M. and Rajpurohit, Tanmay and Jin, Xu},
  year={2018},
  pages={5473--5478}
}

Download the bib file

References

• Khasminskii, R. Stochastic Stability of Differential Equations. Stochastic Modelling and Applied Probability (Springer Berlin Heidelberg, 2012). doi:10.1007/978-3-642-23280-0 – 10.1007/978-3-642-23280-0
• Mao, X. Stochastic Versions of the LaSalle Theorem. Journal of Differential Equations 153, 175–195 (1999) – 10.1006/jdeq.1998.3552
• arapostathis, Ergodic Control of Diffusion Processes (2012)
• Ortega, R., Spong, M. W., Gomez-Estern, F. & Blankenstein, G. Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment. IEEE Trans. Automat. Contr. 47, 1218–1233 (2002) – 10.1109/tac.2002.800770
• Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences (Springer Berlin Heidelberg, 1996). doi:10.1007/3-540-76074-1 – 10.1007/3-540-76074-1
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Ortega, R., van der Schaft, A. J. & Maschke, B. M. Stabilization of port-controlled Hamiltonian systems via energy balancing. Lecture Notes in Control and Information Sciences 239–260 (1999) doi:10.1007/1-84628-577-1_13 – 10.1007/1-84628-577-1_13
• ortega, On output feedback global stabilization of euler-lagrange systems. International Journal of Control (1995)
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Energy-shaping of port-controlled Hamiltonian systems by interconnection. Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304) vol. 2 1646–1651 – 10.1109/cdc.1999.830260
• arnold, Stochastic Differential Equations Theory and Applications (1974)
• Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
• Willems, J. C. Dissipative dynamical systems part I: General theory. Arch. Rational Mech. Anal. 45, 321–351 (1972) – 10.1007/bf00276493
• Rajpurohit, T. & Haddad, W. M. Dissipativity Theory for Nonlinear Stochastic Dynamical Systems. IEEE Trans. Automat. Contr. 62, 1684–1699 (2017) – 10.1109/tac.2016.2598474
• Øksendal, B. Stochastic Differential Equations. Universitext (Springer Berlin Heidelberg, 1995). doi:10.1007/978-3-662-03185-8 – 10.1007/978-3-662-03185-8