Decentralized robust adaptive output feedback stabilization for interconnected nonlinear systems with uncertainties. (English) Zbl 1346.93322
Summary: Based on adaptive nonlinear damping, a novel decentralized robust adaptive output feedback stabilization comprising a decentralized robust adaptive output feedback controller and a decentralized robust adaptive observer is proposed for a large-scale interconnected nonlinear system with general uncertainties, such as unknown nonlinear parameters, bounded disturbances, unknown nonlinearities, unmodeled dynamics, and unknown interconnections, which are nonlinear function of not only states and outputs but also unmodeled dynamics coming from other subsystems. In each subsystem, the proposed stabilization only has two adaptive parameters, and it is not needed to generate an additional dynamic signal or estimate the unknown parameters. Under certain assumptions, the proposed scheme guarantees that all the dynamic signals in the interconnected nonlinear system are bounded. Furthermore, the system states and estimate errors can approach arbitrarily small values by choosing the design parameters appropriately large. Finally, simulation results illustrate the effectiveness of the proposed scheme.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93A14 | Decentralized systems |
| 93C40 | Adaptive control/observation systems |
| 93C10 | Nonlinear systems in control theory |
| 93C41 | Control/observation systems with incomplete information |
Keywords:
decentralized robust adaptive output feedback stabilization; interconnected nonlinear systems; uncertaintiesReferences:
| [1] | Zheng, D.-Z., Decentralized output feedback stabilization of a class of nonlinear interconnected systems, IEEE Transactions on Automatic Control, 34, 12, 1297-1300 (1989) · Zbl 0689.93052 · doi:10.1109/9.40781 |
| [2] | Gavel, D. T.; Siljak, D. D., Decentralized adaptive control: structural conditions for stability, IEEE Transactions on Automatic Control, 34, 4, 413-426 (1989) · Zbl 0681.93001 · doi:10.1109/9.28016 |
| [3] | Liu, Y.; Li, X.-Y., Decentralized robust adaptive control of nonlinear systems with unmodeled dynamics, IEEE Transactions on Automatic Control, 47, 5, 848-856 (2002) · Zbl 1364.93401 · doi:10.1109/tac.2002.1000285 |
| [4] | Wu, Q. H.; Jiang, L.; Wen, J. Y., Decentralized adaptive control of interconnected non-linear systems using high gain observer, International Journal of Control, 77, 8, 703-712 (2004) · Zbl 1061.93060 · doi:10.1080/00207170410001711648 |
| [5] | Hovakimyan, N.; Lavretsky, E.; Calise, A.; Sattigeri, R., Decentralized adaptive output feedback control via input/output inversion, International Journal of Control, 79, 12, 1538-1551 (2006) · Zbl 1125.93360 · doi:10.1080/00207170600852000 |
| [6] | Stankovic, S. S.; Stipanovic, D. M.; Siljak, D. D., Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems, Automatica, 43, 5, 861-867 (2007) · Zbl 1117.93057 · doi:10.1016/j.automatica.2006.11.010 |
| [7] | Swarnakar, A.; Marquez, H. J.; Chen, T., A new scheme on robust observer-based control design for interconnected systems with application to an industrial utility boiler, IEEE Transactions on Control Systems Technology, 16, 3, 539-547 (2008) · doi:10.1109/TCST.2007.908217 |
| [8] | Stanković, S.; Šiljak, D. D., Robust stabilization of nonlinear interconnected systems by decentralized dynamic output feedback, Systems & Control Letters, 58, 4, 271-275 (2009) · Zbl 1159.93355 · doi:10.1016/j.sysconle.2008.11.003 |
| [9] | Kalsi, K.; Lian, J.; Zak, S. H., Decentralized dynamic output feedback control of nonlinear interconnected systems, IEEE Transactions on Automatic Control, 55, 8, 1964-1970 (2010) · Zbl 1368.93545 · doi:10.1109/tac.2010.2050715 |
| [10] | Hua, C.; Guan, X., Output feedback stabilization for time-delay nonlinear interconnected systems using neural networks, IEEE Transactions on Neural Networks, 19, 4, 673-688 (2008) · doi:10.1109/TNN.2007.912318 |
| [11] | Mehraeen, S.; Jagannathan, S.; Crow, M. L., Decentralized dynamic surface control of large-scale interconnected systems in strict-feedback form using neural networks with asymptotic stabilization, IEEE Transactions on Neural Networks, 22, 11, 1709-1722 (2011) · doi:10.1109/TNN.2011.2140381 |
| [12] | Wu, H., Decentralized adaptive robust control for a class of large scale systems with uncertainties in the interconnections, International Journal of Control, 76, 3, 253-265 (2003) · Zbl 1048.93060 · doi:10.1080/0020717031000079427 |
| [13] | Wu, H., Decentralised adaptive robust control of uncertain large-scale non-linear dynamical systems with time-varying delays, IET Control Theory & Applications, 6, 5, 629-640 (2012) · doi:10.1049/iet-cta.2011.0015 |
| [14] | Lavaei, J., Decentralized implementation of centralized controllers for interconnected systems, IEEE Transactions on Automatic Control, 57, 7, 1860-1865 (2012) · Zbl 1369.93236 · doi:10.1109/tac.2011.2180089 |
| [15] | Fan, H.; Han, L.; Wen, C.; Xu, L., Decentralized adaptive output-feedback controller design for stochastic nonlinear interconnected systems, Automatica, 48, 11, 2866-2873 (2012) · Zbl 1252.93054 · doi:10.1016/j.automatica.2012.08.022 |
| [16] | Liu, D.; Wang, D.; Li, H., Decentralized stabilization for a class of continuous-time nonlinear interconnected systems using online learning optimal control approach, IEEE Transactions on Neural Networks and Learning Systems, 25, 2, 418-428 (2014) · doi:10.1109/TNNLS.2013.2280013 |
| [17] | Barmish, B. R.; Galimidi, A. R., Robustness of luenberger observers: linear systems stabilized via nonlinear control, Automatica, 22, 4, 413-423 (1986) · Zbl 0598.93045 · doi:10.1016/0005-1098(86)90046-4 |
| [18] | Jiang, Z.-P.; Praly, L., Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties, Automatica, 34, 7, 825-840 (1998) · Zbl 0951.93042 · doi:10.1016/s0005-1098(98)00018-1 |
| [19] | Liu, Y., Robust adaptive observer for nonlinear systems with unmodeled dynamics, Automatica, 45, 8, 1891-1895 (2009) · Zbl 1185.93021 · doi:10.1016/j.automatica.2009.04.002 |
| [20] | Yang, Q.; Liu, Y., Adaptive state estimation of multi-input and multi-output non-linear systems with general uncertainties both in the state and output equations, IET Control Theory & Applications, 10, 3, 354-362 (2016) · doi:10.1049/iet-cta.2015.0092 |
| [21] | Khalil, H. K., Adaptive output feedback control of nonlinear systems represented by input-output models, IEEE Transactions on Automatic Control, 41, 2, 177-188 (1996) · Zbl 0842.93033 · doi:10.1109/9.481517 |
| [22] | Sussmann, H. J.; Kokotovic, P. V., The peaking phenomenon and the global stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 36, 4, 424-440 (1991) · Zbl 0749.93070 · doi:10.1109/9.75101 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
