ℒ<sub>2</sub> neuro‐adaptive tracking control of uncertain port‐controlled Hamiltonian systems
Authors
Aminuddin Qureshi, Sami El Ferik, Frank L. Lewis
Abstract
This study presents a practical method of neural network (NN) adaptive tracking control of uncertain port‐controlled Hamiltonian (PCH) systems. NN is used to compensate for parametric uncertainties and unlike the previous studies, the dynamics of the NN tuning law is driven by both the position as well as the velocity errors owing to the introduction of the information preserving filtering of the Hamiltonian gradient. In addition, the proposed controller achieves the ℒ2 disturbance attenuation objectives as well as preserves the PCH structure of the system in closed loop. Simulation examples demonstrate the efficacy of the proposed approach.
Citation
- Journal: IET Control Theory & Applications
- Year: 2015
- Volume: 9
- Issue: 12
- Pages: 1781–1790
- Publisher: Institution of Engineering and Technology (IET)
- DOI: 10.1049/iet-cta.2014.1144
BibTeX
@article{Qureshi_2015,
title={{ℒ2 neuro‐adaptive tracking control of uncertain port‐controlled Hamiltonian systems}},
volume={9},
ISSN={1751-8652},
DOI={10.1049/iet-cta.2014.1144},
number={12},
journal={IET Control Theory & Applications},
publisher={Institution of Engineering and Technology (IET)},
author={Qureshi, Aminuddin and El Ferik, Sami and Lewis, Frank L.},
year={2015},
pages={1781--1790}
}
References
- 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
- Schaft V.A., ℒ2 ‐Gain and passivity techniques in nonlinear control (1999)
- Secchi C., Control of interactive Robotic interfaces: a port‐Hamiltonian approach (2007)
- Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Trans. Automat. Contr. 45, 1498–1502 (2000) – 10.1109/9.871758
- Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42, 217–227 (2001) – 10.1016/s0167-6911(00)00091-8
- Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39, 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
- Wang, Z. & Goldsmith, P. Modified energy-balancing-based control for the tracking problem. IET Control Theory Appl. 2, 310–322 (2008) – 10.1049/iet-cta:20070124
- Macchelli, A., Melchiorri, C., Secchi, C. & Fantuzzi, C. A variable structure approach to energy shaping. 2003 European Control Conference (ECC) 1309–1314 (2003) doi:10.23919/ecc.2003.7085142 – 10.23919/ecc.2003.7085142
- Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica 43, 403–415 (2007) – 10.1016/j.automatica.2006.09.008
- Shen, T., Ortega, R., Lu, Q., Mei, S. & Tamura, K. Adaptive L2 Disturbance Attenuation Of Hamiltonian Systems With Parametric Perturbation And Application To Power Systems. Asian Journal of Control 5, 143–152 (2003) – 10.1111/j.1934-6093.2003.tb00105.x
- Dirksz, D. A. & Scherpen, J. M. A. Structure Preserving Adaptive Control of Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 57, 2880–2885 (2012) – 10.1109/tac.2012.2192359
- Dirksz, D. A. & Scherpen, J. M. A. Power-based control: Canonical coordinate transformations, integral and adaptive control. Automatica 48, 1045–1056 (2012) – 10.1016/j.automatica.2012.03.003
- Slotine J.J.E., Applied nonlinear control (1991)
- Lewis F.L., Neural network control of robot manipulator and nonlinear systems (1998)
- Igelnik, B. & Yoh-Han Pao. Stochastic choice of basis functions in adaptive function approximation and the functional-link net. IEEE Trans. Neural Netw. 6, 1320–1329 (1995) – 10.1109/72.471375
- Narendra, K. & Annaswamy, A. A new adaptive law for robust adaptation without persistent excitation. IEEE Trans. Automat. Contr. 32, 134–145 (1987) – 10.1109/tac.1987.1104543
- Ioannu P.A., Robust adaptive control (2012)
- Yuzhen Wang, Daizhan Cheng, Chunwen Li & You Ge. Dissipative hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems. IEEE Trans. Automat. Contr. 48, 1428–1433 (2003) – 10.1109/tac.2003.815037
- Yu H., Energy‐shaping and ℒ2 gain disturbance attenuation control of induction motor. Int. J. Innov. Comput. Inf. Control (2012)
- van der Schaft, A. J. L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control. IEEE Trans. Automat. Contr. 37, 770–784 (1992) – 10.1109/9.256331
- Sakurama K., Trajectory tracking control of Hamiltonian and hybrid control systems (2003)
- Dirksz, D. A. & Scherp, J. M. A. Adaptive tracking control of fully actuated port-Hamiltonian mechanical systems. 2010 IEEE International Conference on Control Applications 1678–1683 (2010) doi:10.1109/cca.2010.5611301 – 10.1109/cca.2010.5611301
- Lewis, F. L. & Ge, S. S. Neural Networks in Feedback Control Systems. Mechanical Engineers’ Handbook 791–825 (2005) doi:10.1002/0471777455.ch19 – 10.1002/0471777455.ch19