Robust MPC Method for BMI Based Wheelchair
Author(s)
Tohru Kawabe
ABSTRACT
In this paper, robust MPC (Model Predictive Control) with adaptive DA converter method for the wheelchair using EEG (Electroencephalogram) based BMI (Brain Machine Interface) is discussed. The method is developed to apply to the obstacle avoidance system of wheelchair. This paper is the 1st stage for the development of the BMI based wheelchair in practical use. The robust MPC method is realized by using the minimax optimization with bounded constraint conditions. Some numerical examples are also included to demonstrate the effectiveness of the proposed methodas the former stage of the real experiments.
In this paper, robust MPC (Model Predictive Control) with adaptive DA converter method for the wheelchair using EEG (Electroencephalogram) based BMI (Brain Machine Interface) is discussed. The method is developed to apply to the obstacle avoidance system of wheelchair. This paper is the 1st stage for the development of the BMI based wheelchair in practical use. The robust MPC method is realized by using the minimax optimization with bounded constraint conditions. Some numerical examples are also included to demonstrate the effectiveness of the proposed methodas the former stage of the real experiments.
KEYWORDS
Wheelchair, Brain Machine Interface, Model Predictive Control, Adaptive DA Converter, Minimax Optimization
Wheelchair, Brain Machine Interface, Model Predictive Control, Adaptive DA Converter, Minimax Optimization
Cite this paper
nullT. Kawabe, "Robust MPC Method for BMI Based Wheelchair," Intelligent Control and Automation, Vol. 2 No. 4, 2011, pp. 340-350. doi: 10.4236/ica.2011.24039.
nullT. Kawabe, "Robust MPC Method for BMI Based Wheelchair," Intelligent Control and Automation, Vol. 2 No. 4, 2011, pp. 340-350. doi: 10.4236/ica.2011.24039.
References
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[1] C. E. Garcia, D. M. Prett and M. Morari, “Model Predictive Control: Theory and Practice—A Survey,” Automatica, Vol. 25, No. 3, 1989, pp. 335-348. doi:10.1016/0005-1098(89)90002-2 [2] J. Ackermann, “Sampled-Data Control Systems: Analysis and Synthesis, Robust System Design,” Springer-Verlag, Berlin, 1985. [3] P. T. Kabamba, “Control of Linear Systems Using Generalized Sampled-Data Hold Functions,” IEEE Transactions on Automatic Control, Vol. 32, No. 9, 1987, pp. 772-783. doi:10.1109/TAC.1987.1104711 [4] B. D. O. Anderson, “Controller Design: Moving from Theory to Practice,” IEEE Control Systems Magazine, Vol. 13, No. 4, 1983, pp. 16-25. doi:10.1109/37.229554 [5] Y. Yamamoto, “A Function Space Approach to Sampled-Data Control Systems and Tracking Problems,” IEEE Transactions on Automatic Control, Vol. 39, No. 4, 1994, pp. 703-713. doi:10.1109/9.286247 [6] D. R. Ramirez and E. F. Camacho, “Piecewise Affinity of Min-Max MPC with Bounded Additiveuncertainties and a Quadratic Criterion,” Automatica, Vol. 42, No. 2, 2006, pp. 295-302. doi:10.1016/j.automatica.2005.09.009 [7] A. Grancharova and T. A. Johansen, “Computation, Approximation and Stability of Explicit Feedback Min-Max-Nonlinear Model Predictive Control,” Automatica, Vol. 45, No. 5, 2009, pp. 1134-1143. doi:10.1016/j.automatica.2008.12.023 [8] P. J. Campo and M. Morari, “Robust Model Predictive Control,” Proceedings of 1987 American Control Conference, Minneapolis, 10-12 June 1987, pp. 1021-1026. [9] Z. Q. Zheng and M. Morari, “Robust Stability of Constrained Model Predictive Control,” Proceedings of 1987 American Control Conference, San Francisco, 2-4 June 1993, pp. 379-383. [10] M. V. Kothare, V. Balakrishnan and M. Morari, “Robust Constrained Model Predictive Control using Linear MatrixInequalities,” Automatica, Vol. 32, No. 10, 1996, pp. 1361-1379. doi:10.1016/0005-1098(96)00063-5 [11] F. A. Cuzzola, J. C. Geromel and M. Morari, “An Improved Discrete-Time Robust Approach for Constrained Model Predictive Control,” Proceedings of 2001 European Control Conference, Porto, 4-7 September 2001, pp. 2759-2764. [12] J. C. Allwright and G. C. Papavasiliou, “On Linear Programming and Robust Model-Predictive Control Using Impulse-Responses,” System & Control Letters, Vol. 18, No. 2, 1992, pp. 159-164. doi:10.1016/0167-6911(92)90020-S [13] J. H. Lee and Z. Yu, “Worst-Case Formulation of Model Predictive Control for Systems with Bounded Parameters,” Automatica, Vol. 33, No. 5, 1997, pp. 768-781. doi:10.1016/S0005-1098(96)00255-5 [14] A. Bemporad and M. Morari, “Robust Model Predictive Control: A Survey,” In: A. Garulli, A. Tesi and A. Vicino, Eds., Robustness in Identification and Control, Lecture Notes in Control and Information Sciences, Vol. 245, Springer-Verlag, 1999, pp. 207-226. [15] A. Bemporad and A. Garulli, “Output-Feedback Predictive Control of Constrained Linear Systems via Set-Membership State Estimation,” International Journal of Control, Vol. 73, No. 8, 2000, pp. 655-665. doi:10.1080/002071700403420 [16] P. O. M. Scokaert and D. Q. Mayne, “Min-Max Feedback Model Predictive Control for Constrained Linear Systems,” IEEE Transactions on Automatic Control, Vol. 43, No. 8, 1998, pp. 1136-1142. doi:10.1109/9.704989 [17] D. Q. Mayne, J. B. Rawlings, C. V. Rao and M. Scokaert, “Constrained Model Predictive Control: Stability and Optimality,” Automatica, Vol. 36, No. 6, 2000, pp. 789-814. doi:10.1016/S0005-1098(99)00214-9 [18] S. Waldert, T. Pistohl, C. Braun, T. Ball, A. Aertsen and C. Mehring, “A Review on Directional Information in Neural Signals for Brain-Machine Interfaces,” Journal of Physiology Paris, Vol. 103, No. 3-5, 2009, pp. 244-254. doi:10.1016/j.jphysparis.2009.08.007 [19] R. Heliot and J. M. Carmena, “Brain-Machine Interfaces,” Encyclopedia of Behavioral Neuroscience, 2010, pp. 221-225. http://www.sciencedirect.com/science/article/pii/B9780080453965002098 [20] T. N. Lal, M. Schroder, T. Hinterberger, J. Weston and M. Bogdan, “Support Vector Channel Selection in BCI,” IEEE Transactions on Biomedical Engineering, Vol. 51, No. 6, 2004, pp. 1003-1010. doi:10.1109/TBME.2004.827827 [21] J. del R. Millan, M. Franze, J. Mourino, F. Cincotti and F. Babiloni, “Relevant EEG Features for the Classification of Spontaneous Motor-Related Tasks,” Biological Cybernetics, Vol. 86, No. 2, 2002, pp. 89-95. doi:10.1007/s004220100282 [22] V. N. Vapnik, “Statistical Learning Theory,” John Wiley & Sons, New York, 1998. [23] C. T. Suand and C. H. Yang, “Feature Selection for the SVM: An Application to Hypertension Diagnosis,” Expert Systems with Applications, Vol. 34, No. 1, 2008, pp. 754-763. doi:10.1016/j.eswa.2006.10.010 [24] M. Sampei and M. Ishikawa, “State Estimation and Output Feedback Control of Nonholonomic Mobile Systems using Time-Scale Transformation,” Transactions of the Institute of Systems, Control and Information Engineers, Vol. 13, No. 3, 2000, pp. 124-133. [25] R. Fierro and F. L. Lewis, “Control of a Nonholonomic Mobile Robot: Backstepping Kinematics into Dynamics,” Journal of Robotic Systems, Vol. 14, No. 3, 1997, pp. 149-163. doi:10.1002/(SICI)1097-4563(199703)14:3<149::AID-ROB1>3.0.CO;2-R [26] J. Tang, K. Watanabe, M. Nakamura and N. Koga, “Fuzzy Gaussian Neural Network Controller and Its Application to the Control of a Mobile Robot,” Transactions of Japan Society of Mechanical Engineers, Series C, Vol. 59, No. 564, 1993, pp. 2290-2297. [27] S. Boyd and C. H. Barratt, “Linear Controller Design: Limits of Performance,” Prentice-Hall, Upper Saddle River, 1991. [28] K. Zhou, J. C. Doyle and K. Glover, “Robust and Optimal Control,” Prentice-Hall, Upper Saddle River, 1996.