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Output Feedback Stabilization for MIMO Semi-linear Stochastic Systems with Transient Optimisation

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Abstract

This paper investigates the stabilisation problem and consider transient optimisation for a class of the multi-input-multi-output (MIMO) semi-linear stochastic systems. A control algorithm is presented via an m-block backstepping controller design where the closed-loop system has been stabilized in a probabilistic sense and the transient performance is optimisable by optimised by searching the design parameters under the given criterion. In particular, the transient randomness and the probabilistic decoupling will be investigated as case studies. Note that the presented control algorithm can be potentially extended as a framework based on the various performance criteria. To evaluate the effectiveness of this proposed control framework, a numerical example is given with simulation results. In summary, the key contributions of this paper are stated as follows: 1) one block backstepping-based output feedback control design is developed to stabilize the dynamic MIMO semi-linear stochastic systems using a linear estimator; 2) the randomness and probabilistic couplings of the system outputs have been minimized based on the optimisation of the design parameters of the controller; 3) a control framework with transient performance enhancement of multi-variable semi-linear stochastic systems has been discussed.

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References

  1. M. Krstic, I. Kanellakopoulos, P. V. Kokotovic. Nonlinear and Adaptive Control Design, New York, USA: Wiley, 1995.

    MATH  Google Scholar 

  2. S. J. Liu, J. F. Zhang, Z. P. Jiang. Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems. Automatica, vol. 43, no. 2, 238–251, 2007. DOI: https://doi.org/10.1016/j.automatica.2006.08.028.

    MathSciNet  MATH  Google Scholar 

  3. F. Wang, Z. Liu, Y. Zhang, C. L. P. Chen. Adaptive quantized controller design via backstepping and stochastic small-gain approach. IEEE Transactions on Fuzzy Systems, vol. 24, no. 2, 330–343, 2016. DOI: 10.1109/TFUZZ.2015.2454232.

    Google Scholar 

  4. S. C. Tong, T. Wang, Y. M. Li, H. G. Zhang. Adaptive neural network output feedback control for stochastic non-linear systems with unknown dead-zone and unmodeled dynamics. IEEE Transactions on Cybernetics, vol. 44, no. 6, 910–921, 2014. DOI: https://doi.org/10.1109/TCYB.2013.2276043.

    Google Scholar 

  5. X. J. Xie, N. Duan. Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system. IEEE Transactions on Automatic Control, vol. 55, no. 5, 1197–1202, 2010. DOI: https://doi.org/10.1109/TAC.2010.2043004.

    MathSciNet  MATH  Google Scholar 

  6. W. S. Chen, L. C. Jiao, J. Li, R. H. Li. Adaptive NN backstepping output-feedback control for stochastic nonlinear strict-feedback systems with time-varying delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 40, no. 3, 939–950, 2010. DOI: https://doi.org/10.1109/TSMCB.2009.2033808.

    Google Scholar 

  7. P. Jagtap, M. Zamani. Backstepping design for incremental stability of stochastic Hamiltonian systems with jumps. IEEE Transactions on Automatic Control, vol. 63, no. 1, 255–261, 2018. DOI: https://doi.org/10.1109/TAC.2017.2720592.

    MathSciNet  MATH  Google Scholar 

  8. H. Q. Wang, K. F. Liu, X. P. Liu, B. Chen, C. Lin. Neural-based adaptive output-feedback control for a class of non-strict-feedback stochastic nonlinear systems. IEEE Transactions on Cybernetics, vol. 45, no. 9, 1977–1987, 2015. DOI: https://doi.org/10.1109/TCYB.2014.2363073.

    Google Scholar 

  9. Y. T. Chang. Block backstepping control of MIMO systems. IEEE Transactions on Automatic Control, vol. 56, no. 5, 1191–1197, 2011. DOI: https://doi.org/10.1109/TAC.2011.2109435.

    MathSciNet  MATH  Google Scholar 

  10. C. C. Cheng, G. I. Su, C. W. Chien. Block backstepping controllers design for a class of perturbed non-linear systems with m blocks. IET Control Theory & Applications, vol. 6, no. 13, 2021–2030, 2012. DOI: https://doi.org/10.1049/iet-cta.2011.0431.

    MathSciNet  Google Scholar 

  11. Q. C. Zhang, J. L. Zhou, H. Wang, T. Y. Chai. Output feedback stabilization for a class of multi-variable bilinear stochastic systems with stochastic coupling attenuation. IEEE Transactions on Automatic Control, vol. 62, no. 6, 2936–2942, 2017. DOI: https://doi.org/10.1109/TAC.2016.2604683.

    MathSciNet  MATH  Google Scholar 

  12. Q. C. Zhang, X. Yin. Observer-based parametric decoupling controller design for a class of multi-variable non-linear uncertain systems. Systems Science & Control Engineering, vol. 6, no. 1, 258–267, 2018. DOI: https://doi.org/10.1080/21642583.2018.1483276.

    Google Scholar 

  13. Q. C. Zhang, J. L. Zhou, H. Wang, T. Y. Chai. Minimized coupling in probability sense for a class of multivariate dynamic stochastic control systems. In Proceedings of the 54th IEEE Conference on Decision and Control, IEEE, Osaka, Japan, pp. 1846–1851, 2015. DOI: https://doi.org/10.1109/CDC.2015.7402479.

    Google Scholar 

  14. Q. C. Zhang, L. Hu. Probabilistic decoupling control for stochastic non-linear systems using EKF-based dynamic set-point adjustment. In Proceedings of the UKACC 12th International Conference on Control, IEEE, Sheffield, UK, pp. 330–335, 2018. DOI: https://doi.org/10.1109/CONTROL.2018.8516784.

    Google Scholar 

  15. Q. C. Zhang, Z. Wang, H. Wang. Parametric covariance assignment using a reduced-order closed-form covariance model. Systems Science & Control Engineering, vol. 4, no. 1, 78–86, 2016. DOI: https://doi.org/10.1080/21642583.2016.1185045.

    MathSciNet  Google Scholar 

  16. Q. C. Zhang, F. Sepulveda. A statistical description of pairwise interaction between nerve fibres? In Proceedings of the 8th International IEEE/EMBS Conference on Neural Engineering, IEEE, Shanghai, China, pp. 194–198, 2017. DOI: https://doi.org/10.1109/NER.2017.8008324.

    Google Scholar 

  17. Q. C. Zhang, F. Sepulveda. A model study of the neural interaction via mutual coupling factor identification. In Proceedings of the 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, IEEE, Seogwipo, South Korea, pp. 3329–3332, 2017. DOI: https://doi.org/10.1109/EMBC.2017.8037569.

  18. H. Wang. Minimum entropy control of non-Gaussian dynamic stochastic systems. IEEE Transactions on Automatic Control, vol. 47, no. 2, 398–403, 2002. DOI: https://doi.org/10.1109/9.983388.

    MathSciNet  MATH  Google Scholar 

  19. H. Yue, H. Wang. Minimum entropy control of closed-loop tracking errors for dynamic stochastic systems. IEEE Transactions on Automatic Control, vol. 48, no. 1, 118–122, 2003. DOI: https://doi.org/10.1109/TAC.2002.806663.

    MathSciNet  MATH  Google Scholar 

  20. M. Ren, J. Zhang, M. Jiang, M. Yu, J. Xu. Minimum (h, ϕ)-entropy control for non-Gaussian stochastic networked control systems and its application to a networked DC motor control system. IEEE Transactions on Control Systems Technology, vol. 23, no. 1, 406–411, 2015. DOI: https://doi.org/10.1109/TCST.2014.2324978.

    Google Scholar 

  21. J. H. Zhang, L. L. Du, M. F. Ren, G. L. Hou. Minimum error entropy filter for fault detection of networked control systems. Entropy, vol. 14, no. 3, 505–516, 2012. DOI: https://doi.org/10.3390/e14030505.

    MATH  Google Scholar 

  22. L. Guo, H. Wang. Minimum entropy filtering for multivariate stochastic systems with non-Gaussian noises. IEEE Transactions on Automatic Control, vol. 51, no. 4, 695–700, 2006. DOI: https://doi.org/10.1109/TAC.2006.872771.

    MathSciNet  MATH  Google Scholar 

  23. L. Guo, L. P. Yin, H. Wang, T. Y. Chai. Entropy optimization filtering for fault isolation of nonlinear non-Gaussian stochastic systems. IEEE Transactions on Automatic Control, vol. 54, no. 4, 804–810, 2009. DOI: https://doi.org/10.1109/TAC.2008.2009599.

    MathSciNet  MATH  Google Scholar 

  24. L. Guo, H. Wang, T. Chai. Fault detection for non-linear non-Gaussian stochastic systems using entropy optimization principle. Transactions of the Institute of Measurement and Control, vol. 28, no. 2, 145–161, 2006. DOI: https://doi.org/10.1191/0142331206tm169oa.

    Google Scholar 

  25. L. N. Yao, J. F. Qin, H. Wang, B. Jiang. Design of new fault diagnosis and fault tolerant control scheme for non-Gaussian singular stochastic distribution systems. Automatica, vol. 48, no. 9, 2305–2313, 2012. DOI: https://doi.org/10.1016/j.automatica.2012.06.036.

    MathSciNet  MATH  Google Scholar 

  26. . D. Yang, A. Armaou. Feedback control of semi-linear distributed parameter systems using advanced pod method. In Proceedings of the 54th IEEE Conference on Decision and Control, IEEE, Osaka, Japan, pp. 4680–4687, 2015. DOI: https://doi.org/10.1109/CDC.2015.7402949.

    Google Scholar 

  27. Q. C. Zhang, L. Hu, J. Gow. Output feedback stabilization for dynamic MIMO semi-linear stochastic systems with output randomness attenuation. In Proceedings of the 24th International Conference on Automation and Computing, IEEE, Newcastle upon Tyne, UK, pp. 1–6, 2018. DOI: https://doi.org/10.23919/IConAC.2018.8748997.

  28. Q. C. Zhang, A. P. Wang. Decoupling control in statistical sense: Minimised mutual information algorithm. International Journal of Advanced Mechatronic Systems, vol. 7, no. 2, 61–70, 2016. DOI: https://doi.org/10.1504/IJAMECHS.2016.082625.

    Google Scholar 

  29. J. Bao, H. Yue, W. E. Leithead, J. Q. Wang. Feedforward control for wind turbine load reduction with pseudo-LIDAR measurement. International Journal of Automation and Computing, vol. 15, no. 2, 142–155, 2018. DOI: https://doi.org/10.1007/s11633-017-1103-x.

    Google Scholar 

  30. P. Cross, X. D. Ma. Model-based and fuzzy logic approaches to condition monitoring of operational wind turbines. International Journal of Automation and Computing, vol. 12, no. 1, 25–34, 2015. DOI: https://doi.org/10.1007/s11633-014-0863-9.

    Google Scholar 

  31. F. Qin, Q. L. Zhang, W. X. Zhang, Y. Yang, J. L. Ding, X. W. Dai. Link quality estimation in industrial temporal fading channel with augmented Kalman filter. IEEE Transactions on Industrial Informatics, vol. 15, no. 4, 1936–1946, 2019. DOI: https://doi.org/10.1109/TII.2018.2859919.

    Google Scholar 

  32. C. G. Yang, G. Z. Peng, Y. N. Li, R. X. Cui, L. Cheng, Z. J. Li. Neural networks enhanced adaptive admittance control of optimized robot-environment interaction. IEEE Transactions on Cybernetics, vol. 49, no. 7, 2568–2579, 2019. DOI: https://doi.org/10.1109/TCYB.2018.2828654.

    Google Scholar 

  33. C. G. Yang, J. Luo, Y. P. Pan, Z. Liu, C. Y. Su. Personalized variable gain control with tremor attenuation for robot teleoperation. IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 10, 1759–1770, 2018. DOI: https://doi.org/10.1109/TSMC.2017.2694020.

    Google Scholar 

  34. R. Khasminskii. Stochastic Stability of Differential Equations, Berlin, Heidelberg, Germany: Springer, 2011. DOI: https://doi.org/10.1007/978-3-642-23280-0.

    Google Scholar 

  35. T. M. Cover, J. A. Thomas. Elements of Information Theory, New York, USA: John Wiley & Sons, 2012.

    MATH  Google Scholar 

  36. Y. Y. Zhou, Q. C. Zhang, H. Wang, P. Zhou, T. Y. Chai. EKF-based enhanced performance controller design for nonlinear stochastic systems. IEEE Transactions on Automatic Control, vol. 63, no. 4, 1155–1162, 2018. DOI: https://doi.org/10.1109/TAC.2017.2742661.

    MathSciNet  MATH  Google Scholar 

  37. Y. Y. Zhou, Q. C. Zhang, H. Wang. Enhanced performance controller design for stochastic systems by adding extra state estimation onto the existing closed loop control. In Proceedings of the UKACC 11th International Conference on Control, IEEE, Belfast, UK, pp. 1–6, 2016. DOI: https://doi.org/10.1109/CONTROL.2016.7737531.

    Google Scholar 

  38. X. W. Dai, Z. W. Gao, T. Breikin, H. Wang. High-gain observer-based estimation of parameter variations with delay alignment. IEEE Transactions on Automatic Control, vol. 57, no. 3, 726–732, 2012. DOI: https://doi.org/10.1109/TAC.2011.2169635.

    MathSciNet  MATH  Google Scholar 

  39. M. F. Ren, Q. C. Zhang, J. H. Zhang. An introductory survey of probability density function control. Systems Science & Control Engineering, vol. 7, no. 1, 158–170, 2019. DOI: https://doi.org/10.1080/21642583.2019.1588804.

    Google Scholar 

  40. Y. Liu, H. Wang, C. H. Hou. UKF based nonlinear filtering using minimum entropy criterion. IEEE Transactions on Signal Processing, vol. 61, no. 20, 4988–4999, 2013. DOI: https://doi.org/10.1109/TSP.2013.2274956.

    MathSciNet  MATH  Google Scholar 

  41. Q. C. Zhang, A. P. Wang, H. Wang. Minimum mutual information control for multi-variable non-Gaussian stochastic systems. In Proceedings of International Conference on Advanced Mechatronic Systems, IEEE, Beijing, China, pp. 497–502, 2015. DOI: https://doi.org/10.1109/ICAMechS.2015.7287161.

    Google Scholar 

  42. C. G. Yang, Y. M. Jiang, W. He, J. Na, Z. J. Li, B. Xu. Adaptive parameter estimation and control design for robot manipulators with finite-time convergence. IEEE Transactions on Industrial Electronics, vol. 65, no. 10, 8112–8123, 2018. DOI: https://doi.org/10.1109/TIE.2018.2803773.

    Google Scholar 

  43. X. W. Dai, Z. W. Gao, T. Breikin, H. Wang. Zero assignment for robust H2/H∞ fault detection filter design. IEEE Transactions on Signal Processing, vol. 57, no. 4, 1363–1372, 2009. DOI: https://doi.org/10.1109/TSP.2008.2010598.

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

We would like to thank the editor and the reviewers for their valuable comments. This work was supported by Higher Education Innovation Fund (No. HEIF 2018-2020), De Montfort University, Leicester, UK.

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Authors and Affiliations

  1. School of Engineering and Sustainable Development, De Montfort University, Leicester, LE1 9BH, UK

    Qi-Chun Zhang & John Gow

  2. School of Computer Science and Informatics, De Montfort University, Leicester, LE1 9BH, UK

    Liang Hu

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  1. Qi-Chun Zhang
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Correspondence to Qi-Chun Zhang.

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Recommended by Associate Editor Xian-Dong Ma

Qi-Chun Zhang received the B. Eng. in automation in 2008 and the M. Sc. degree in control theory and control engineering in 2010, respectively, from Northeastern University, China. He also received the Ph. D. degree in electrical and electronic engineering from University of Manchester, UK in 2016. Currently, he is senior lecturer in dynamics and control at De Montfort University in Leicester, UK, where his research is supported by vice-chancellor 2020 scheme. Before joining De Montfort University in 2017, he was a senior research officer at University of Essex, UK. From 2011–2013, he was an academic visitor at Control Systems Centre, University of Manchester, UK. He serves over 20 international journals as an active reviewer.

His research interests include stochastic dynamic systems, probabilistic coupling analysis, decoupling control, performance optimisation, brain-computer interface and computational modelling for peripheral nervous systems.

Liang Hu received the B. Eng. and M. Eng. degrees in control engineering from Harbin Institute of Technology, China in 2008 and 2010, respectively, and the Ph. D. degree in computer science from Brunel University London, UK in 2016. He has been a lecturer in intelligent transport systems at De Montfort University, UK since 2018. Prior to that, he did the postdoctoral research at Queen’s University Belfast and Loughborough University, UK.

His research interests include signal processing, control and decision and their applications in autonomous systems and intelligent transport systems.

John Gow received the M. Eng. degree in electronic and electrical engineering from Loughborough University, UK in 1993, and the Ph. D. degree in power electronics from Loughborough University, UK in 1998. He subsequently continued research in the area of power conversion systems for building integrated and large scale solar photovoltaic installations. Subsequent industrial opportunities in power electronics and embedded control led to him acting as a senior design engineer developing hardware and software for digital signal processing (DSP) and microcontroller based embedded control systems along with power chains for inverters, industrial drives and uninterruptible power supplies. He developed a working knowledge of radio-frequency (RF) hardware design through an industrial position developing hardware for radio frequency identification systems as well as a lifelong interest in amateur radio. He now works as associate professor of electronic engineering at De Montfort University, UK.

His research interests include power electronics, high speed embedded systems for control applications and software radio.

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Zhang, QC., Hu, L. & Gow, J. Output Feedback Stabilization for MIMO Semi-linear Stochastic Systems with Transient Optimisation. Int. J. Autom. Comput. 17, 83–95 (2020). https://doi.org/10.1007/s11633-019-1193-8

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  • DOI: https://doi.org/10.1007/s11633-019-1193-8

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