Grey Qualitative Modeling and Control Method for Subjective Uncertain Systems

Peng Wang; Shu-Jie Li; Yan Lv; Zong-Hai Chen

doi:10.1007/s11633-014-0820-7

February 2015

Article Contents

Peng Wang, Shu-Jie Li, Yan Lv and Zong-Hai Chen. Grey Qualitative Modeling and Control Method for Subjective Uncertain Systems. International Journal of Automation and Computing, vol. 12, no. 1, pp. 70-76, 2015. doi: 10.1007/s11633-014-0820-7

Cite as: Peng Wang, Shu-Jie Li, Yan Lv and Zong-Hai Chen. Grey Qualitative Modeling and Control Method for Subjective Uncertain Systems. International Journal of Automation and Computing, vol. 12, no. 1, pp. 70-76, 2015. doi: 10.1007/s11633-014-0820-7

Grey Qualitative Modeling and Control Method for Subjective Uncertain Systems

Department of Automation, University of Science and Technology of China, Hefei 230027, China

Received: 2012-08-21

Fund Project:

This work was supported by National Natural Science Foundation of China (No. 61075073 and 61375079).

Abstract

A new approach to model and control an unknown system using subjective uncertain rules is proposed. This method is established by combining the grey system theory and the qualitative simulation method. The proposed approach mainly contains three steps. In the first step, subjective uncertain rules are accumulated gradually during cognizing the system; the mapping relations between the system inputs and outputs are built and represented using the grey qualitative matrix in the second step; in the third step, the generalized whitening function is defined to realize the transformation between qualitative and quantitative information. Besides the theoretical results, two sets of simulations based on a water level control system are conducted comparatively to demonstrate the effectiveness of the proposed method. The water level expectation is set to be constant in the first set, while it changes in the second set. The simulation results show that the proposed method tracks the water level expectation well. By combining the proposed method with proportional-integral-derivative (PID) or fuzzy logic controller (FLC), it can be concluded that the system can reach the stable state more quickly and the overshoot can also be reduced compared to using PID or FLC alone.
- Uncertain system,
- qualitative modeling,
- knowledge representation,
- subjective uncertainty,
- grey qualitative method

References

[1]	L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, vol. 8, no. 3, pp. 199-249, 1975.
[2]	L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-II. Information Sciences, vol. 8, no. 4, pp. 301-357, 1975.
[3]	L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences, vol. 9, no. 1, pp. 43-80, 1975.
[4]	L. A. Zadeh. Toward a generalized theory of uncertainty (GTU)-An outline. Information Sciences, vol. 172, no. 1, pp. 1-40, 2005.
[5]	L. A. Zadeh. Is there a need for fuzzy logic? Information Sciences, vol. 178, no. 13, pp. 2751-2779, 2008.
[6]	L. A. Zadeh. Toward extended fuzzy logic-A first step. Fuzzy Sets and Systems, vol. 160, no. 21, pp. 3175-3181, 2009.
[7]	B. Kuipers. Qualitative simulation. Artificial Intelligence, vol. 29, no. 3, pp. 289-338, 1986.
[8]	B. Kuipers. Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge, Cambridge, MA: The MIT Press, 1994.
[9]	B. Kuipers. Qualitative simulation as causal explanation. IEEE Transactions on Systems, Man and Cybernetics, vol. 17, no. 3, pp. 432-444, 1987.
[10]	B. J. Kuipers, C. Chiu, D. T. D. Molle, D. R. Throop. Higher-order derivative constraints in qualitative simulation. Artificial Intelligence, vol. 51, no. 1-3, pp. 343-379, 1991.
[11]	D. Berleant, B. J. Kuipers. Qualitative and quantitative simulation: Bridging the gap. Artificial Intelligence, vol. 95, no. 2, pp. 215-255, 1997.
[12]	J. L. Deng. Control problems of grey systems. Systems & Control Letters, vol. 1, no. 5, pp. 288-294, 1982.
[13]	H. V. Trivedi, J. K. Singh. Application of grey system theory in the development of a runoff prediction model. Biosystems Engineering, vol. 92, no. 4, pp. 521-526, 2005.
[14]	H. X. Li, X. H. Yuan, J. Y. Wang, Y. C. Li. The normal numbers of the fuzzy systems and their classes. Science China Information Sciences, vol. 53, no. 11, pp. 2215-2229, 2010.
[15]	H. X. Li. Probability representations of fuzzy systems. Science in China, Series F, vol. 49, no. 3, pp. 339-363, 2006.
[16]	J. L. Deng. Introduction to grey system theory. The Journal of Grey System, vol. 1, no. 1, pp. 1-24, 1989.
[17]	J. C. Helton. Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. Journal of Statistical Computation and Simulation, vol. 57, no. 1-4, pp. 3-76, 1997.
[18]	Y. L. Huang, Z. H. Chen, W. S. Gui. Grey qualitative simulation. Journal of Grey System, vol. 16, no. 1, pp. 5-20, 2004.
[19]	C. L. Chen, D. Y. Dong, Z. H. Chen, H. B. Wang. Qualitative control for mobile robot navigation based on reinforcement learning and grey system. The Mediterranean Journal of Measurement and Control, vol. 4, no. 1, pp. 1-7, 2008.
[20]	C. L. Chen, D. Y. Dong, Z. H. Chen, H. B. Wang. Grey systems for intelligent sensors and information processing. Journal of Systems Engineering and Electronics, vol. 19, no. 4, pp. 659-665, 2008.
[21]	J. S. Brown, J. De Kleer. The origin, form, and logic of qualitative physical laws. In Proceedings of International Joint Conference on Artificial Intelligence, Karlsruhe, Germany, pp. 1158-1169, 1983.

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通讯作者: 陈斌, bchen63@163.com

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Grey Qualitative Modeling and Control Method for Subjective Uncertain Systems

Department of Automation, University of Science and Technology of China, Hefei 230027, China

Received: 2012-08-21

Fund Project:

This work was supported by National Natural Science Foundation of China (No. 61075073 and 61375079).

Key words:

Abstract: A new approach to model and control an unknown system using subjective uncertain rules is proposed. This method is established by combining the grey system theory and the qualitative simulation method. The proposed approach mainly contains three steps. In the first step, subjective uncertain rules are accumulated gradually during cognizing the system; the mapping relations between the system inputs and outputs are built and represented using the grey qualitative matrix in the second step; in the third step, the generalized whitening function is defined to realize the transformation between qualitative and quantitative information. Besides the theoretical results, two sets of simulations based on a water level control system are conducted comparatively to demonstrate the effectiveness of the proposed method. The water level expectation is set to be constant in the first set, while it changes in the second set. The simulation results show that the proposed method tracks the water level expectation well. By combining the proposed method with proportional-integral-derivative (PID) or fuzzy logic controller (FLC), it can be concluded that the system can reach the stable state more quickly and the overshoot can also be reduced compared to using PID or FLC alone.

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[1]	L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, vol. 8, no. 3, pp. 199-249, 1975.
[2]	L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-II. Information Sciences, vol. 8, no. 4, pp. 301-357, 1975.
[3]	L. A. Zadeh. The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences, vol. 9, no. 1, pp. 43-80, 1975.
[4]	L. A. Zadeh. Toward a generalized theory of uncertainty (GTU)-An outline. Information Sciences, vol. 172, no. 1, pp. 1-40, 2005.
[5]	L. A. Zadeh. Is there a need for fuzzy logic? Information Sciences, vol. 178, no. 13, pp. 2751-2779, 2008.
[6]	L. A. Zadeh. Toward extended fuzzy logic-A first step. Fuzzy Sets and Systems, vol. 160, no. 21, pp. 3175-3181, 2009.
[7]	B. Kuipers. Qualitative simulation. Artificial Intelligence, vol. 29, no. 3, pp. 289-338, 1986.
[8]	B. Kuipers. Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge, Cambridge, MA: The MIT Press, 1994.
[9]	B. Kuipers. Qualitative simulation as causal explanation. IEEE Transactions on Systems, Man and Cybernetics, vol. 17, no. 3, pp. 432-444, 1987.
[10]	B. J. Kuipers, C. Chiu, D. T. D. Molle, D. R. Throop. Higher-order derivative constraints in qualitative simulation. Artificial Intelligence, vol. 51, no. 1-3, pp. 343-379, 1991.
[11]	D. Berleant, B. J. Kuipers. Qualitative and quantitative simulation: Bridging the gap. Artificial Intelligence, vol. 95, no. 2, pp. 215-255, 1997.
[12]	J. L. Deng. Control problems of grey systems. Systems & Control Letters, vol. 1, no. 5, pp. 288-294, 1982.
[13]	H. V. Trivedi, J. K. Singh. Application of grey system theory in the development of a runoff prediction model. Biosystems Engineering, vol. 92, no. 4, pp. 521-526, 2005.
[14]	H. X. Li, X. H. Yuan, J. Y. Wang, Y. C. Li. The normal numbers of the fuzzy systems and their classes. Science China Information Sciences, vol. 53, no. 11, pp. 2215-2229, 2010.
[15]	H. X. Li. Probability representations of fuzzy systems. Science in China, Series F, vol. 49, no. 3, pp. 339-363, 2006.
[16]	J. L. Deng. Introduction to grey system theory. The Journal of Grey System, vol. 1, no. 1, pp. 1-24, 1989.
[17]	J. C. Helton. Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. Journal of Statistical Computation and Simulation, vol. 57, no. 1-4, pp. 3-76, 1997.
[18]	Y. L. Huang, Z. H. Chen, W. S. Gui. Grey qualitative simulation. Journal of Grey System, vol. 16, no. 1, pp. 5-20, 2004.
[19]	C. L. Chen, D. Y. Dong, Z. H. Chen, H. B. Wang. Qualitative control for mobile robot navigation based on reinforcement learning and grey system. The Mediterranean Journal of Measurement and Control, vol. 4, no. 1, pp. 1-7, 2008.
[20]	C. L. Chen, D. Y. Dong, Z. H. Chen, H. B. Wang. Grey systems for intelligent sensors and information processing. Journal of Systems Engineering and Electronics, vol. 19, no. 4, pp. 659-665, 2008.
[21]	J. S. Brown, J. De Kleer. The origin, form, and logic of qualitative physical laws. In Proceedings of International Joint Conference on Artificial Intelligence, Karlsruhe, Germany, pp. 1158-1169, 1983.

Grey Qualitative Modeling and Control Method for Subjective Uncertain Systems

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通讯作者: 陈斌, bchen63@163.com

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