Robust H∞ Filtering and Controller Design for Linear Stochastic Systems
Keywords:
Controller, Disturbance, Noise, Robustness, Stochastic systems
Abstract
Some stochastic process can be studied as linear process. In this case, conventional linear control method cannot be used directly. Thus it is important to propose methods that are compatible with these systems. In this paper, $H\infty$ filtering and controller proposed for robust control of linear stochastic systems. In the following, proposed method applied to mathematical model of twin rotor multi inputs-multi outputs system. The investigation of results show good noise and disturbance attenuation, robustness and closed loop stability. Also estimation error improved approximately from 30 to 50 percentages in comparison with other conventional methods.References
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Control, IEEE Transactions on, vol. 34, pp. 831- 847 (1989).
2. K. M. Nagpal and P. P. Khargonekar, ”Filteringand smoothing in an H∞ setting,” Automatic Control, IEEE Transactions on, vol. 36, pp. 152- 166 (1991).
3. A. Fattouh, O. Sename, and J. Dion, ”H∞ observer design for time-delay systems,” Proc. 37th IEEE Confer. on Decision & Control, pp. 4545-4546 (1998).
4. A. Pila, U. Shaked, and C. E. de Souza, ”H∞ filtering for continuous-time linear systems with delay,” Automatic Control, IEEE Transactions on, vol. 44, pp. 1412-1417 (1999).
5. M. Basin, S. Elvira-Ceja, and E. N. Sanchez, ”Mean-square H∞ filtering for stochastic systems: Application to a 2DOF helicopter,” Signal Processing, vol. 92, pp. 801-806 (2012).
6. H. Dong, Z. Wang, and H. Gao, ”Robust filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts,” Signal Processing, IEEE Transactions on, vol. 58, pp. 1957-1966 (2010).
7. H. Dong, Z. Wang, D. W. Ho, and H. Gao, ”Variance-Constrained Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements: The Finite-Horizon Case,” Signal Processing, IEEE Transactions on, vol. 58, pp. 2534-2543 (2010).
8. Pham, V.-C. and Juang, J.-C. , ”Robust and Efficient Slam Via Compressed H8 Filtering. Asian Journal of Control,” vol. 16, pp.878889 (2014).
9. Gao, H. and Wang, C. , ”LMI APPROACH TO ROBUST FILTERING FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR DISTURBANCES,” Asian Journal of Control, vol. 7, pp. 8190 (2005).
10. Xu, S. and Chen, T., ”Robust H8 Filtering For Uncertain Stochastic Time-Delay Systems,” (2003).
11. A.-G. Wu, J. Dong, and G.-R. Duan, ”Robust H∞ estimation for linear time-delay systems: An improved LMI approach,” International Journal of Control, Automation and Systems, vol. 7, pp. 668- 673 (2009).
12. P. Neveux and E. Blanco, ”RobustH∞filtering by means of lead-lag controller,” in Proc. 17th IFAC World Congress, pp. 450-455 (2009).
13. A. Wu and G. Duan, ”Robust H∞ estimation for continuous-time polytopic uncertain systems,” Journal of Control Theory and Applications, vol. 3, pp. 393-398 (2005).
14. M. Dridi, G. Scorletti, D. Tournier, M. Smaoui, and X. Lin-Shi, ”Weighted H∞ filtering versus observation: Application to signal differentiation,” in American Control Conference (ACC), pp. 1404-1409 (2010).
15. R. Orjuela, B. Marx, J. Ragot, and D. Maquin, ”Proportional-Integral observer design for nonlinear uncertain systems modelled by a multiple model approach,” in Decision and Control, CDC 2008. 47th IEEE Conference on, pp. 3577-3582 (2008).
16. Z. Lendek, R. Babuska, and B. De Schutter, ”Stability analysis and observer design for decentralized TS fuzzy systems,” in Fuzzy Systems, 2008. FUZZ-IEEE 2008.(IEEE World Congress on Computational Intelligence). IEEE International Conference on, pp. 631-636 (2008)
17. X. Li and H. Gao, ”Reduced-Order Generalized H? Filtering for Linear Discrete-Time Systems with Application to Channel Equalization,” (2014).
18. M. Sheikhan and M. M. Bagheri, ”Robust state estimator design for uncertain linear systems using optimization techniques,” Neural Computing and Applications, vol. 23, pp. 1395-1406 (2013).
19. Z. Wang and H. Qiao, ”H∞ reliable control of uncertain linear state delayed systems,” Journal of dynamical and control systems, vol. 10, pp. 55-76 (2004).
20. J. Zhang and W. Tang, ”Output feedback H∞ control for uncertain piecewise linear systems,” Journal of dynamical and control systems, vol. 14, pp. 121-144 (2008).
21. R. Xie, X. Wang, and Y. Li, ”H infinity state feedback control for the stabilization of the three Euler angles of helicopter based on LMI,” in Intelligent Computation Technology and Automation (ICICTA), 2008 International Conference on, pp. 375-379 (2008).
22. W. Yuan and J. Katupitiya, ”Centralized Robust Controllers Using Signal-based H∞ and - Synthesis for an Unmanned Helicopter,” (2012).
23. A. Rabhi, M. Chadli, and C. Pegard, ”Robust fuzzy control for stabilization of a quadrotor,” in Advanced Robotics (ICAR), 2011 15th International Conference on, pp. 471-475 (2011).
24. A. H. Jazwinski, ”Stochastic processes and filtering theory: Courier Dover Publications,”(2007.
25. V. S. Pugachev and I. N. Sinitsyn, ”Stochastic systems: theory and applications: World Scientific,” (2001).
26. C.-C. Luo, R.-F. Liu, C.-D. Yang, and Y.-H. Chang, ”Helicopter H∞ control design with robust flying quality,” Aerospace science and technology, vol. 7, pp. 159-169, (2003).
27. Astrom KJ. ”Introduction to stochastic control theory. Courier Dover Publications,” (2012).
28. F. Minyue, C. E. De Souza, and L. Zhi-Quan, ”Finite-horizon robust Kalman filter design,” Signal Processing, IEEE Transactions on, vol. 49,pp. 2103-2112 (2001).
Published
2017-01-30
How to Cite
Azimi, M. M. (2017). Robust H∞ Filtering and Controller Design for Linear Stochastic Systems. Majlesi Journal of Mechatronic Systems, 5(4). Retrieved from https://ms.majlesi.info/index.php/ms/article/view/291
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