GA-based fuzzy sliding mode controller for nonlinear systems.

*(English)*Zbl 1162.93367Summary: Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller or an adaptive fuzzy sliding mode controller capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov’s direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.

##### MSC:

93C42 | Fuzzy control/observation systems |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93C10 | Nonlinear systems in control theory |

##### Keywords:

fuzzy sliding mode controller; stability analysis; genetic algorithm; Lyapunov’s direct method##### Software:

ANFIS
PDF
BibTeX
XML
Cite

\textit{P. C. Chen} et al., Math. Probl. Eng. 2008, Article ID 325859, 16 p. (2008; Zbl 1162.93367)

**OpenURL**

##### References:

[1] | G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, Upper Saddle River, NJ, USA, 1995. · Zbl 0915.03001 |

[2] | W.-J. Wang and H.-R. Lin, “Fuzzy control design for the trajectory tracking on uncertain nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 7, no. 1, pp. 53-62, 1999. |

[3] | X.-J. Ma, Z.-Q. Sun, and Y.-Y. He, “Analysis and design of fuzzy controller and fuzzy observer,” IEEE Transactions on Fuzzy Systems, vol. 6, no. 1, pp. 41-51, 1998. |

[4] | T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116-132, 1985. · Zbl 0576.93021 |

[5] | F.-H. Hsiao, C. W. Chen, Y.-H. Wu, and W.-L. Chiang, “Fuzzy controllers for nonlinear interconnected TMD systems with external force,” Journal of the Chinese Institute of Engineers, vol. 28, no. 1, pp. 175-181, 2005. |

[6] | T.-Y. Hsieh, M. H. L. Wang, C. W. Chen, et al., “A new viewpoint of s-curve regression model and its application to construction management,” International Journal on Artificial Intelligence Tools, vol. 15, no. 2, pp. 131-142, 2006. · Zbl 05421396 |

[7] | C.-H. Tsai, C. W. Chen, W.-L. Chiang, and M.-L. Lin, “Application of geographic information system to the allocation of disaster shelters via fuzzy models,” Engineering Computations, vol. 25, no. 1, pp. 86-100, 2008. |

[8] | C. W. Chen, W.-L. Chiang, C.-H. Tsai, C.-Y. Chen, and M. H. L. Wang, “Fuzzy Lyapunov method for stability conditions of nonlinear systems,” International Journal on Artificial Intelligence Tools, vol. 15, no. 2, pp. 163-171, 2006. · Zbl 05421347 |

[9] | K. Tanaka, T. Hori, and H. O. Wang, “A multiple Lyapunov function approach to stabilization of fuzzy control systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 4, pp. 582-589, 2003. |

[10] | B. Chen, X. Liu, and S. Tong, “New delay-dependent stabilization conditions of T-S fuzzy systems with constant delay,” Fuzzy Sets and Systems, vol. 158, no. 20, pp. 2209-2224, 2007. · Zbl 1122.93048 |

[11] | C. W. Chen, C.-L. Lin, C.-H. Tsai, C.-Y. Chen, and K. Yeh, “A novel delay-dependent criterion for time-delay T-S fuzzy systems using fuzzy Lyapunov method,” International Journal on Artificial Intelligence Tools, vol. 16, no. 3, pp. 545-552, 2007. · Zbl 05421608 |

[12] | F.-H. Hsiao, J.-D. Hwang, C. W. Chen, and Z.-R. Tsai, “Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 1, pp. 152-163, 2005. · Zbl 05452572 |

[13] | K. Yeh, C.-Y. Chen, and C. W. Chen, “Robustness design of time-delay fuzzy systems using fuzzy Lyapunov method,” Applied Mathematics and Computation, vol. 205, no. 2, pp. 568-577, 2008. · Zbl 1152.93040 |

[14] | C. W. Chen, K. Yeh, W.-L. Chiang, C.-Y. Chen, and D.-J. Wu, “Modeling, H\infty control and stability analysis for structural systems using Takagi-Sugeno fuzzy model,” Journal of Vibration and Control, vol. 13, no. 11, pp. 1519-1534, 2007. · Zbl 1182.93044 |

[15] | G. Feng, C.-L. Chen, D. Sun, and Y. Zhu, “H\infty controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 1, pp. 94-103, 2005. · Zbl 05452549 |

[16] | F.-H. Hsiao, C. W. Chen, Y.-W. Liang, S.-D. Xu, and W.-L. Chiang, “T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays,” IEEE Transactions on Circuits and Systems I, vol. 52, no. 9, pp. 1883-1893, 2005. |

[17] | S. Xu and J. Lam, “Robust H\infty control for uncertain discrete-time-delay fuzzy systems via output feedback controllers,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 1, pp. 82-93, 2005. · Zbl 05452443 |

[18] | C. W. Chen, “Modeling and control for nonlinear structural systems via a NN-based approach,” Expert Systems with Applications. In press. |

[19] | C.-Y. Chen, J. R.-C. Hsu, and C. W. Chen, “Fuzzy logic derivation of neural network models with time delays in subsystems,” International Journal on Artificial Intelligence Tools, vol. 14, no. 6, pp. 967-974, 2005. · Zbl 05421351 |

[20] | P. C. Chen, C. W. Chen, and W. L. Chiang, “GA-based modified adaptive fuzzy sliding mode controller for nonlinear systems,” Expert Systems with Applications. In press. · Zbl 1162.93367 |

[21] | S. Limanond and J. Si, “Neural-network-based control design: an LMI approach,” IEEE Transactions on Neural Networks, vol. 9, no. 6, pp. 1422-1429, 1998. |

[22] | R. Palm, “Robust control by fuzzy sliding mode,” Automatica, vol. 30, no. 9, pp. 1429-1437, 1994. · Zbl 0925.93501 |

[23] | L. X. Wang, A Course in Fuzzy Systems and Control, Prentice Hall, Englewood Cliffs, NJ, USA, 1997. · Zbl 0910.93002 |

[24] | V. I. Utkin, Sliding Modes and Their Application in Variable Structure Systems, MIR Publishers, Moscow, Russia, 1978. · Zbl 0398.93003 |

[25] | J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ, USA, 1991. · Zbl 0753.93036 |

[26] | Y. Xia and Y. Jia, “Robust sliding-mode control for uncertain time-delay systems: an LMI approach,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 1086-1092, 2003. · Zbl 1364.93608 |

[27] | B. Yoo and W. Ham, “Adaptive fuzzy sliding mode control of nonlinear system,” IEEE Transactions on Fuzzy Systems, vol. 6, no. 2, pp. 315-321, 1998. |

[28] | S. Tong and H.-X. Li, “Fuzzy adaptive sliding-mode control for MIMO nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 3, pp. 354-360, 2003. |

[29] | S. Labiod, M. S. Boucherit, and T. M. Guerra, “Adaptive fuzzy control of a class of MIMO nonlinear systems,” Fuzzy Sets and Systems, vol. 151, no. 1, pp. 59-77, 2005. · Zbl 1142.93365 |

[30] | L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice Hall, Englewood Cliffs, NJ, USA, 1994. |

[31] | G. Feng, S. G. Cao, and N. W. Rees, “Stable adaptive control for fuzzy dynamic systems,” Fuzzy Sets and Systems, vol. 131, no. 2, pp. 217-224, 2002. · Zbl 1010.93517 |

[32] | D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, Reading, Mass, USA, 1989. · Zbl 0721.68056 |

[33] | S. C. Lin, Stable self-learning optimal fuzzy control system design and application, Ph.D. dissertation, Department of Electrical Engineering, National Taiwan University, Chung-li, Taiwan, 1997. |

[34] | P. C. Chen, Genetic algorithm for control of structure system, M.S. thesis, Department of Civil Engineering, Chung Yuan University, Taipei, Taiwan, 1998. |

[35] | C. C. Liu and F. C. Chen, “Adaptive control of nonlinear continuous-time systems using neural networks-general relative degree and MIMO cases,” International Journal of Control, vol. 58, no. 2, pp. 317-335, 1993. · Zbl 0781.93052 |

[36] | J.-S. R. Jang, C.-T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice-Hall, Upper Saddle River, NJ, USA, 1997. |

[37] | J.-S. R. Jang, “ANFIS: adaptive-network-based fuzzy inference system,” IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 3, pp. 665-685, 1993. |

[38] | F. J. de Souza, M. M. R. Vellasco, and M. A. C. Pacheco, “Hierarchical neuro-fuzzy quadtree models,” Fuzzy Sets and Systems, vol. 130, no. 2, pp. 189-205, 2002. · Zbl 1035.93007 |

[39] | C. W. Chen, W. L. Chiang, and F. H. Hsiao, “Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems,” Mathematics and Computers in Simulation, vol. 66, no. 6, pp. 523-537, 2004. · Zbl 1049.93556 |

[40] | C. W. Chen, “Stability conditions of fuzzy systems and its application to structural and mechanical systems,” Advances in Engineering Software, vol. 37, no. 9, pp. 624-629, 2006. · Zbl 05135632 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.