Full‐order observer design for quadratic port‐controlled Hamiltonian systems

Authors

Michael Rojas, Christian Granados‐Salazar, Gerardo Espinosa‐Pérez

Abstract

The full‐order observer design problem for a particular class of port‐controlled Hamiltonian systems is approached in this paper. The proposed full‐order observer scheme belongs to the structure preserving class of dynamic estimators as it preserves the natural stability properties of the approached class of systems that are useful for the convergence analysis and exhibits a structure that is a copy of the original system plus an output corrective term. Due to the physical interpretation of port‐controlled Hamiltonian systems, the proposed full‐order observer is attractive because the estimated states have an immediate practical meaning. The class approached in this paper considers both linear and nonlinear dissipation terms, a quadratic Hamiltonian function and internal interconnections between two components of the state vector modulated by another state component that correspond to quadratic nonlinearities. This features lead to several structural properties that allow to carry out the convergence analysis in a relatively simple way and leads to a simple tuning procedure. The usefulness of the contribution is illustrated considering two practical applications: the Lorenz oscillator and the permanent magnet synchronous motor.

Citation

• Journal: Asian Journal of Control
• Year: 2025
• Volume:
• Issue:
• Pages:
• Publisher: Wiley
• DOI: 10.1002/asjc.3647

BibTeX

@article{Rojas_2025,
  title={{Full‐order observer design for quadratic port‐controlled Hamiltonian systems}},
  ISSN={1934-6093},
  DOI={10.1002/asjc.3647},
  journal={Asian Journal of Control},
  publisher={Wiley},
  author={Rojas, Michael and Granados‐Salazar, Christian and Espinosa‐Pérez, Gerardo},
  year={2025}
}

Download the bib file

References

• López‐Caamal, F. & Moreno, J. A. A quasicontinuous multivariable super‐twisting observer for 2n states systems with Lipschitz nonlinearities. Intl J Robust & Nonlinear 33, 8992–9017 (2022) – 10.1002/rnc.6357
• Ortiz, N., Linares, E., Santillan, R., López‐Estrada, F. & Estrada‐Manzo, V. Convex unknown input observer for sensor fault estimation of nonlinear descriptor systems via linear matrix inequalities. Asian Journal of Control 26, 2297–2307 (2024) – 10.1002/asjc.3354
• Liu, Y., Sun, H. & Hou, L. Distributed extended state observer design and output feedback anti‐disturbance control for nonlinear interconnected systems: A dynamic memory event‐triggered mechanism. Asian Journal of Control 26, 227–245 (2023) – 10.1002/asjc.3197
• Guo, B., Dian, S., Zhao, T. & You, X. Distributed observer design for interconnected nonlinear systems with faults and disturbances based on dynamic event conditions. Asian Journal of Control 25, 4414–4434 (2023) – 10.1002/asjc.3107
• Adil, A. et al. On high-gain observer design for nonlinear systems with delayed output measurements. Automatica 141, 110281 (2022) – 10.1016/j.automatica.2022.110281
• Cao, L., Li, H., Wang, N. & Zhou, Q. Observer-Based Event-Triggered Adaptive Decentralized Fuzzy Control for Nonlinear Large-Scale Systems. IEEE Trans. Fuzzy Syst. 27, 1201–1214 (2019) – 10.1109/tfuzz.2018.2873971
• Bernard, P., Mimmo, N. & Marconi, L. On the Semi-Global Stability of an EK-Like Filter. IEEE Control Syst. Lett. 5, 1771–1776 (2021) – 10.1109/lcsys.2020.3044030
• Besancon, G. & Tsiclea, A. Regularization approach for an immersion-based observer design. 2018 European Control Conference (ECC) 1951–1956 (2018) doi:10.23919/ecc.2018.8550112 – 10.23919/ecc.2018.8550112
• Rajamani, R. Observers for Lipschitz nonlinear systems. IEEE Trans. Automat. Contr. 43, 397–401 (1998) – 10.1109/9.661604
• Astolfi, A., Karagiannis, D. & Ortega, R. Nonlinear and Adaptive Control with Applications. Communications and Control Engineering (Springer London, 2008). doi:10.1007/978-1-84800-066-7 – 10.1007/978-1-84800-066-7
• Bernard, P., Andrieu, V. & Astolfi, D. Observer design for continuous-time dynamical systems. Annual Reviews in Control 53, 224–248 (2022) – 10.1016/j.arcontrol.2021.11.002
• Willems, J. C. Dissipative dynamical systems part I: General theory. Arch. Rational Mech. Anal. 45, 321–351 (1972) – 10.1007/bf00276493
• Arcak, M. & Kokotović, P. Nonlinear observers: a circle criterion design and robustness analysis. Automatica 37, 1923–1930 (2001) – 10.1016/s0005-1098(01)00160-1
• Moreno, J. A. Observer Design for Nonlinear Systems: A Dissipative Approach. IFAC Proceedings Volumes 37, 681–686 (2004) – 10.1016/s1474-6670(17)30549-9
• Maschke B. M., Nonlinear control systems design 1992 (1993)
• Granados-Salazar, C., Rojas, M. & Espinosa-Pérez, G. Observer design for a class of nonlinear Hamiltonian systems based on energy function structure. IFAC-PapersOnLine 58, 178–183 (2024) – 10.1016/j.ifacol.2024.08.277
• Pfeifer, M., Caspart, S., Strehle, F. & Hohmann, S. Full-Order Observer Design for a Class of Nonlinear Port-Hamiltonian Systems. IFAC-PapersOnLine 54, 149–154 (2021) – 10.1016/j.ifacol.2021.11.070
• Venkatraman, A. & van der Schaft, A. J. Full-order observer design for a class of port-Hamiltonian systems. Automatica 46, 555–561 (2010) – 10.1016/j.automatica.2010.01.019
• Vu, N. M. T., Pham, T. H., Prodan, I. & Lefèvre, L. Port-Hamiltonian observer for state-feedback control design. 2023 European Control Conference (ECC) 1–6 (2023) doi:10.23919/ecc57647.2023.10178222 – 10.23919/ecc57647.2023.10178222
• Vincent, B., Hudon, N., Lefèvre, L. & Dochain, D. Port-Hamiltonian observer design for plasma profile estimation in tokamaks. IFAC-PapersOnLine 49, 93–98 (2016) – 10.1016/j.ifacol.2016.10.761
• Biedermann, B. & Meurer, T. Observer design for a class of nonlinear systems combining dissipativity with interconnection and damping assignment. Intl J Robust & Nonlinear 31, 4064–4080 (2021) – 10.1002/rnc.5461
• Yaghmaei, A. & Yazdanpanah, M. J. Structure Preserving Observer Design for Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 64, 1214–1220 (2019) – 10.1109/tac.2018.2847904
• Zucco, J. P. T., Ramirez, H., Wu, Y. & Le Gorrec, Y. Linear Matrix Inequality Design of Exponentially Stabilizing Observer-Based State Feedback Port-Hamiltonian Controllers. IEEE Trans. Automat. Contr. 68, 6184–6191 (2023) – 10.1109/tac.2022.3227927
• Zenfari, S., Laabissi, M. & Achhab, M. E. Proportional observer design for port Hamiltonian systems using the contraction analysis approach. Int. J. Dynam. Control 10, 403–408 (2021) – 10.1007/s40435-021-00830-3
• Sun, W., Wang, Z., Lv, X., Alsaadi, F. E. & Liu, H. H∞ observer design for networked Hamiltonian systems with sensor saturations and missing measurements. Information Sciences 593, 577–590 (2022) – 10.1016/j.ins.2022.02.010
• Zenfari, S., Laabissi, M. & Achhab, M. E. Observer Design for a Class of Discrete Port Hamiltonian Systems. J Control Autom Electr Syst 34, 963–970 (2023) – 10.1007/s40313-023-01017-1
• Bonnard, B. Quadratic control systems. Math. Control Signal Systems 4, 139–160 (1991) – 10.1007/bf02551263
• Pavlov, A. & Marconi, L. Incremental passivity and output regulation. Systems & Control Letters 57, 400–409 (2008) – 10.1016/j.sysconle.2007.10.008
• Ortega, R., Romero, J. G., Borja, P. & Donaire, A. PID Passivity‐Based Control of Nonlinear Systems with Applications. (2021) doi:10.1002/9781119694199 – 10.1002/9781119694199
• Khalil H., Nonlinear systems (2002)
• Rojas, M., Granados-Salazar, C. & Espinosa-Pérez, G. Observer Design for a Class of Nonlinear Hamiltonian Systems. IFAC-PapersOnLine 54, 125–130 (2021) – 10.1016/j.ifacol.2021.11.066
• Moon, S., Baik, J.-J. & Seo, J. M. Chaos synchronization in generalized Lorenz systems and an application to image encryption. Communications in Nonlinear Science and Numerical Simulation 96, 105708 (2021) – 10.1016/j.cnsns.2021.105708
• Shah, D., Espinosa–Pérez, G., Ortega, R. & Hilairet, M. An asymptotically stable sensorless speed controller for non‐salient permanent magnet synchronous motors. Intl J Robust & Nonlinear 24, 644–668 (2012) – 10.1002/rnc.2910
• van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
• Ortega, R., Cisneros, R., Wang, L. & van der Schaft, A. Indirect adaptive control of nonlinearly parameterized nonlinear dissipative systems. Intl J Robust & Nonlinear 32, 5105–5119 (2022) – 10.1002/rnc.6078
• Dashkovskiy, S. N., Efimov, D. V. & Sontag, E. D. Input to state stability and allied system properties. Autom Remote Control 72, 1579–1614 (2011) – 10.1134/s0005117911080017
• Zhao, Y., Zhang, W., Su, H. & Yang, J. Observer-Based Synchronization of Chaotic Systems Satisfying Incremental Quadratic Constraints and Its Application in Secure Communication. IEEE Trans. Syst. Man Cybern, Syst. 50, 5221–5232 (2020) – 10.1109/tsmc.2018.2868482
• Mahboobi, S. H., Shahrokhi, M. & Pishkenari, H. N. Observer-based control design for three well-known chaotic systems. Chaos, Solitons & Fractals 29, 381–392 (2006) – 10.1016/j.chaos.2005.08.042
• Khodarahmi, M. & Maihami, V. A Review on Kalman Filter Models. Arch Computat Methods Eng 30, 727–747 (2022) – 10.1007/s11831-022-09815-7