Simultaneous design of H∞ model predictive controller and persistent dwell time switching signal for a class of nonlinear switched systems with unstabilizable sub-systems

Document Type : Original Article

Authors

Department of Electrical Engineering, Shahid Beheshti university, Velenjak, Tehran, Iran

Abstract

In this paper, simultaneous design of the model predictive control and persistent dwell time switching signal is investigated for a class of discrete-time nonlinear switched systems. In the proposed design, the assumption of stabilizability of all sub-systems is removed. The suggested methodology introduces an online framework that guarantees the H∞ performance against external disturbances. Multiple Lyapunov functions are used to ensure the overal stability of the control system. Also, two different types of cost functions are defined, including cost function with finite predictive horizon for unstabilizable sub-systems and cost function with infinite predictive horizon for stabilizable sub-systems. The sequence of applying constraints in the developed LMI problem is chosen in such a way that the rate of energy variations in different sub-systems can be adjusted and the asymptotic stability of the whole system is guaranteed. This design reduces the conservative aspects of other model predictive schemes in which arbitrary switching signal and switched Lyapunov function are used. Finally, to validate the proposed design, a chemical system is developed, and the performance of the proposed design is evaluated.

Keywords

Main Subjects

References

[1] Z. Sun and S. Ge S, "Stability Theory of Switched Dynamical Systems", Springer, 2005.
[2] H. Yang, B. Jiang and V. Cocquempot, "A survey of results and perspectives on stabilization of switched nonlinear systems with unstable modes", Nonlinear Analysis: Hybrid Systems vol.13, pp. 45-60, 2014.
[3] S. Ebadollahi and S. Saki, "Wind turbine torque oscillation reduction using soft switching multiple model predictive control based on the gap metric and Kalman filter estimator", IEEE Transactions on Industrial Electronics vol. 65 no. 5, pp. 3890-3898, 2017.
[4] Saki S and Bolandi H, "Optimal direct adaptive soft switching multi-model predictive control using the gap metric for spacecraft attitude control in a wide range of operating points", Aerospace Science and Technology vol. 77, pp. 235-243 2018.
[5] I. Nodozi and M. Rahmani M, "LMI-based model predictive control for switched nonlinear system", Journal of Process Control, vol. 59 pp. 49-58, 2017.
[6] M. Benallouch, G. Schutz, D. Fiorelli and M. Boutayeb, "H∞ model predictive control for discrete-time switched linear systems with application to drinking water supply network", Journal of Process Control, vol. 24, no. 6, pp. 924-938, 2014.
[7] H. Lin and P. Antsaklis, "Stability and stabilizability of switched linear systems: a survey of recent results", IEEE Transactions on Automatic control, vol. 45 no. 2, pp. 308-322, 2009.
[8] H. Sun and S. Ge, "Switched Linear Systems", Springer, 2005.
 [9] S. Shi, Z. Shi and Z. Fei, "Asynchronous control for switched systems by using persistent dwell time modeling", Systems & Control Letters, vol, 133, pp.104523, 2019.
 [10] Y. Fan, M. Wang, G. Sun, W. Yi and G. Liu, "Quasi-time-dependent robust H∞ static output feedback control for uncertain discrete-time switched systems with mode-dependent persistent dwell-time", Journal of the Franklin Ins., vol. 357, no. 15, pp. 10329-10352, 2020.
[11] A. Ladel, A. Benzaouia, R. Outbib and M. Ouladsine, "Robust fault tolerant control of continuous-time switched systems: An LMI approach", Nonlinear Analysis: Hybrid Systems, vol. 39, pp. 100950, 2021.
[12] Z. Huang, J. Xia, X. Chen, H. Shen and J. Wang, "Adaptive Tracking Control for Persistent Dwell-Time Switched Nonlinear Systems with Uncertainty", IEEE Access 7, pp.109924-109933, 2019.
[13] W. Wu, S. Tong and Y. Li, "Fuzzy adaptive tracking control for switched nonlinear systems with full time-varying state constraints", Neurocomputing, vol. 352, pp.1-11, 2019.
[14] محسن قلعه نوئی، محمدرضا اکبرزاده توتونچی و ناصر پریز، «پایدارسازی محلی کلاسی از سیستم­های غیرخطی سوئیچ ضربه­ای با محدودیت نُرم سیگنال کنترل: رویکرد نامساوی­های ماتریسی»، مجله مهندسی برق دانشگاه تبریز، جلد 49، شماره 4، صفحه 1793-1781.
[15]  مریم بلوچ ­زاده، علی کریم پور و ناصر پریز، «کنترل زیربهینه سیستم­های سوئیچ­شونده خطی نامعین»، مجله مهندسی برق دانشگاه تبریز، جلد 50، شماره 4، صفحه 1909-1918.
[16] M. Müller, P. Martius  and F. Allgöwer, "Model predictive control of switched nonlinear systems under average dwell-time", Journal of Process Control, vol. 22, no. 9, pp.1702-1710, 2012.
 [17]M. Aminsafaee and M. Shafiei, "Stabilization of uncertain nonlinear discrete-time switched systems with state delays: A constrained robust model predictive control approach", Journal of Vibration and Control, vol. 25, no. 14, pp. 2079-2090, 2019.
[18] A. Taghieh and M. Shafiei, "Observer-based robust model predictive control of switched nonlinear systems with time delay and parametric uncertainties", Journal of Vibration and Control, 2021.
[19] C. Yuan, Y. Gu, W. Zeng and P. Stegagno, "Switching Model Predictive Control of Switched Linear Systems with Average Dwell Time", In 2020 American Control Conference, Denver, USA, pp. 2888-2893, 2020.
 [20]Y. Qi, W. Yu, J. Huang and Y. Yu, "Model predictive control for switched systems with a novel mixed time/event-triggering mechanism", Nonlinear Analysis: Hybrid Systems, vol. 42, pp. 101081, 2022.
[21] Y. Ma, and X. Hui, "Design of a new model predictive control for Lipschitz non-linear delayed switched systems with application to water pollution system", Multiscale and Multidisciplinary Modeling, Experiments and Design, pp. 1-10, 2023.
[22] H. Zhao, H. Yang, Z. Wang, and H. Li, "Nonlinear switched model predictive control with multiple Lyapunov functions for trajectory tracking and obstacle avoidance of nonholonomic systems”, International Journal of Robust and Nonlinear Control, 2023.
 [23] L. Jia, Y. Li, J. Du, S. Yuan, "Robust L2/L∞ control for uncertain singular systems with time varying delay", Prog Nat Sci, vol. 18, no. 8, pp. 1015–21, 2008.
 

Files

Share

How to cite

Statistics