Weighted multiple model adaptive control with self-tuning model

ZHANG Yu-zhen; LI Qing; ZHANG Wei-cun

doi:10.13374/j.issn2095-9389.2018.11.013

Volume 40 Issue 11

Nov. 2018

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Engineering > 2018 > 40(11): 1389-1401

ZHANG Yu-zhen, LI Qing, ZHANG Wei-cun. Weighted multiple model adaptive control with self-tuning model[J]. Chinese Journal of Engineering, 2018, 40(11): 1389-1401. doi: 10.13374/j.issn2095-9389.2018.11.013

Citation:

ZHANG Yu-zhen, LI Qing, ZHANG Wei-cun. Weighted multiple model adaptive control with self-tuning model[J]. Chinese Journal of Engineering, 2018, 40(11): 1389-1401. doi: 10.13374/j.issn2095-9389.2018.11.013

Citation:

PDF( 1033 KB)

Weighted multiple model adaptive control with self-tuning model

doi: 10.13374/j.issn2095-9389.2018.11.013

School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Received Date: 2017-11-07

Abstract

Abstract

The issues of model set construction and weighting algorithm analysis in multiple model adaptive control of discrete-time systems with large parameter uncertainty are considered in this paper. First, to improve system performance by reducing the calculation burden and relaxing the convergence conditions for the classical weighting algorithm, a new weighting algorithm is adopted, which is based on the model output errors of the multi-model adaptive control system with a self-tuning model. Second, the weighting algorithm convergence is analyzed in two cases:when the model set contains the true model of plant and it tends to the fixed model, and when the model set does not contain the true model of plant and it tends to the self-tuning model. Third, according to the virtual equivalent system (VES) concept and methodology, the stability of weighted multiple model adaptive control (WMMAC) with a self-tuning model is presented under a unified framework. The analysis procedures for linear time-invariant (LTI) and parameter jump plants are independent of specific local control methods and weighting algorithm, which only require that each local controller stabilizes the corresponding local model, the output of the formed closed-loop system tracks the reference signal, and the weighting algorithm is convergent. The principal contributions of the paper are the analysis of global stability and the convergence of the overall system with a self-tuning model. Compared with the stability results of WMMAC in the early stage, the constraint condition that the model set only has fixed models is relaxed, which can enlarge the application range of the stability results in theory. In addition, because of the introduction of a self-tuning controller, the control performance of the system is significantly improved when the real model of the plant is not included in the model set. Finally, computer simulation results verify the feasibility and effectiveness of the proposed method.
- discrete-time system,
- multiple model adaptive control,
- weighting algorithm,
- stability,
- convergence

FullText(HTML)

References(30)

References

[1]	Narendra K S, Xiang C. Adaptive control of discrete-time systems using multiple models. IEEE Trans Autom Control, 2000, 45(9):1669
[2]	Magill D. Optimal adaptive estimation of sampled stochastic processes. IEEE Trans Autom Control, 1965, 10(4):434
[3]	Lainiotis D G. Partitioning:a unifying framework for adaptive systems, I:Estimation. Proc. IEEE, 1976, 64(8):1126
[4]	Lainiotis D G. Partitioning:a unifying framework for adaptive systems, Ⅱ:Control. Proc. IEEE, 1976, 64(8):1182
[5]	Athans M, Castanon D, Dunn K, et al. The stochastic control of the F-8C aircraft using a multiple model adaptive control (MMAC) method-Part Ⅰ:equilibrium flight. IEEE Trans Autom Control, 1977, 22(5):768
[6]	Lane D W, Maybeck P S. Multiple model adaptive estimation applied to the LAMBDA URV for failure detection and identification//Proceedings of the 33rd IEEE Conference on Decision and Control. Lake Buena Vista, 1994:678
[7]	Yu C, Roy R J, Kaufman H, et al. Multiple-model adaptive predictive control of mean arterial pressure and cardiac output. IEEE Trans Biomed Eng, 1992, 39(8):765
[8]	Moose R L, Vanlandingham H F, McCabe D H. Modeling and estimation for tracking maneuvering targets. IEEE Trans Aerospace Electron Syst, 1979, 15(3):448
[9]	Li X R, Bar-Shalom Y. Design of an interacting multiple model algorithm for air traffic control tracking. IEEE Trans Control Syst Technol, 1993, 1(3):186
[10]	Badr A, Binder Z, Hagras A N, et al. A multi-model tracking controller for distributed control systems. IFAC Proc Vol, 1984, 17(2):2823
[11]	Martin J F, Schneider A M, Smith N T. Multiple-model adaptive control of blood pressure using sodium nitroprusside. IEEE Trans Biomed Eng, 1987, 34(8):603
[12]	He W G, Kaufman H, Roy R. Multiple model adaptive control procedure for blood pressure control. IEEE Trans Biomed Eng, 1986, 33(1):10
[13]	Chaudhuri B, Majumder R, Pal B C. Application of multiple-model adaptive control strategy for robust damping of interarea oscillations in power system. IEEE Trans Control Syst Technol, 2004, 12(5):727
[14]	Narendra K S, Balakrishnan J. Improving transient response of adaptive control systems using multiple models and switching. IEEE Trans Autom Control, 1994, 39(9):1861
[15]	Narendra K S, Balakrishnan J, Ciliz M K. Adaptation and learning using multiple models, switching, and tuning. IEEE Control Syst, 1995, 15(3):37
[16]	Narendra K S, Balakrishnan J. Adaptive control using multiple models. IEEE Trans Autom Control, 1997, 42(2):171
[21]	Kuipers M, Ioannou P. Multiple model adaptive control with mixing. IEEE Trans Autom Control, 2010, 55(8):1822
[22]	Kuipers M, Ioannou P. Multiple model adaptive control with mixing:A pedagogical example//Proceedings of 47th IEEE Conference on Decision and Control. Cancun, 2009:3239
[23]	Kuipers M, Ioannou P. Practical robust adaptive control:Benchmark example//Proceedings of 2008 American Control Conference. Seattle, 2008:5168
[24]	Baldi S, Ioannou P, Mosca E. Multiple model adaptive mixing control:the discrete-time case. IEEE Trans Autom Control, 2012, 57(4):1040
[25]	Baldi S, Ioannou P A, Mosca E. Discrete-time adaptive mixing control with stability-preserving interpolation:the output regulation problem. IFAC Proc Vol, 2011, 44(1):102
[28]	Han Z, Narendra K S. Second level adaptation using multiple models//Proceedings of 2011 American Control Conference. San Francisco, 2011:2350
[29]	Han Z, Narendra K S. Multiple adaptive models for control//Proceedings of 49th IEEE Conference on Decision and Control. Atlanta, 2010:60
[30]	Zhou Y H, Zhang Z L. High-speed train control based on multiple-model adaptive control with second-level adaptation. Vehicle Syst Dyn, 2014, 52(5):637
[34]	Zhang W C. Stable weighted multiple model adaptive control:discrete-time stochastic plant. Int J Adaptive Control Signal Process, 2013, 27(7):562
[35]	Fekri S, Athans M, Pascoal A. Issues, progress and new results in robust adaptive control. Int J Adaptive Control Signal Process, 2006, 20(10):519
[40]	Zhang W C, Chu T G, Wang L. A new theoretical framework for self-tuning control. Int J Inform Technol, 2005, 11(11):123
[41]	Zhang W C. On the stability and convergence of self-tuning control-virtual equivalent system approach. Int J Control, 2010, 83(5):879
[43]	Zhang W C. Further results on stable weighted multiple model adaptive control:Discrete-time stochastic plant. Int J Adapt Control Signal Process, 2016, 29(12):1497
[44]	Shorten R, Wirth F, Mason O, et al. Stability criteria for switched and hybrid systems. SIAM Rev, 2007, 49(4):545