Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems

DOI: 10.4236/am.2013.49A006   PDF   HTML     2,757 Downloads   4,576 Views   Citations

Abstract

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

Share and Cite:

B. Su, G. Qi and B. Wyk, "Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems," Applied Mathematics, Vol. 4 No. 9A, 2013, pp. 32-42. doi: 10.4236/am.2013.49A006.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. Hespanha and A. S. Morse, “Switching between Stabi lizing Controllers,” Automatica, Vol. 38, No. 11, 2002, pp. 1905-1917. doi:10.1016/S0005-1098(02)00139-5
[2] S. L. D. Kothare and M. Morari, “Contractive Model Pre dictive Control for Constrained Nonlinear Systems,” IEEE Transactions on Automatic Control, Vol. 45, No. 6, 2000, pp. 1053-1071.
doi:10.1109/9.863592
[3] D. Q. Mayne, J. B. Rawlings and P. O. M. Rao, “Con strained Model Predictive Control: Stability and Optimal ity,” Automatica, Vol. 36, No. 6, 2000, pp. 789-814. doi:10.1016/S0005-1098(99)00214-9
[4] M. S. Branicky, “Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems,” IEEE Transactions on Automatic Control, Vol. 43, No. 4, 1998, pp. 475-482.
doi:10.1109/9.664150
[5] P. Mhaskar, N. H. El-Farra and P. D. Christofides, “Ro bust Hybrid Predictive Control of Nonlinear Systems,” Automatica, Vol. 41, No. 2, 2005, pp. 209-217. doi:10.1016/j.automatica.2004.08.020
[6] P. Mhaskar, N. H. El-Farra and P. D. Christofides, “Stabi lization of Nonlinear Systems with State and Control Con straints Using Lyapunov-Based Predictive Control,” Sys tems and Control Letters, Vol. 55, No. 8, 2006, pp. 650-659. doi:10.1016/j.sysconle.2005.09.014
[7] P. Mhaskar, N. H. El-Farra and P. D. Christofides, “Pre dictive Control of Switched Nonlinear Systems with Sche duled Mode Transitions,” IEEE Transactions on Automa tic Control, Vol. 50, No. 11, 2005, pp. 1670-1680. doi:10.1109/TAC.2005.858692
[8] S. Baili and L. Shaoyuan, “Constrained Predictive Con trol for Nonlinear Switched Systems with Uncertainty,” Acta Automatica Sinica, Vol. 34, No. 9, 2008, pp. 1141-1147
[9] N. H. E1-Farra and P. D. Christofides, “Bounded Robust Control of Constrained Multivariable Nonlinear Proc esses,” Chemical Engineering Science, Vol. 58, No. 13, 2003, pp. 3025-3047. doi:10.1016/S0009-2509(03)00126-X
[10] N. H. E1-Farra, P. Mhaskar and P. D. Christofides, “Out put Feedback Control of Switched Nonlinear Systems Us ing Multiple Lyapunov Functions,” Systems & Control Letters, Vol. 54, No. 12, 2005, pp. 1163-1182. doi:10.1016/j.sysconle.2005.04.005
[11] B. L. Su, S. Y. Li and Q. M. Zhu, “The Design of Predic tive Control with Characterized Set of Initial Condition for Constrained Switched Nonlinear System,” Science in China Series E-Technological Sciences, Vol. 52, No. 2, 2009, pp. 456-466. doi:10.1007/s11431-008-0249-8
[12] G. Y. Qi, Z. Chen and Z. Yuan, “Adaptive High Order Dif ferential Feedback Control for Affine Nonlinear System,” Chaos, Solitons & Fractals, Vol. 37, 2008, pp. 308-315. doi:10.1016/j.chaos.2006.09.027
[13] G. Y. Qi, Z. Chen and Z. Yuan, “Model Free Control of Affine Chaotic System,” Physics Letters A, Vol. 344, No. 2-4, 2005, pp 189-202. doi:10.1016/j.physleta.2005.06.073
[14] G. Y. Qi, M. A. van Wyk and B. J. van Wyk, “Model-Free Differential States Observer for Nonlinear Affine Sys tem,” The 7th IFAC Symposium on Nonlinear Control Systems, 21-24 August 2007, Pretoria, pp. 984-989

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.