**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30308

##### Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion

**Authors:**
P.-W. Tsai,
C.-Y. Chen,
C.-W. Chen

**Abstract:**

In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.

**Keywords:**
Swarm Intelligence,
adaptive fuzzy sliding mode control,
Lyapunov direct method,
evolved bat algorithm

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1093321

**References:**

[1] S. Boyd, E. Ghaoui, E. Feron, and V. Balakrishnan, "Linear Matrix Inequalities in System and Control Theory,” PA: SIAM, Philadelphia, 1994.

[2] B. S.Chen, C. H.Lee, and Y. C.Chang, "Tracking Design of Uncertain Nonlinear SISO Systems: Adaptive Fuzzy Approach,” IEEE Trans. Fuzzy Syst. 4, 1996, pp. 32-43.

[3] P. C.Chen, W. L. Chiang, C. W. Chen, and C. H. Tsai, "Adaptive fuzzy controller for nonlinear systems via genetic algorithm,” in Proc. of AEE'08 Proceedings of the 7th WSEAS International Conference on Application of Electrical Engineering, Wisconsin, USA, 2008, pp. 71-76.

[4] R.Eberhart, and J. Kennedy, "A new optimizer using particle swarm theory,” In Proc. of the 6th International Symposium on Micro Machine and Human Science, 1995, pp. 39-43.

[5] S.-C.Chu and P.-W. Tsai, "Computational Intelligence based on Behaviors of Cats,” International Journal of Innovative Computing, Information & Control, vol. 3(1), 2007, pp. 163-173.

[6] S.-C.Chu, P.-W. Tsai, and J.-S. Pan, "Cat Swarm Optimization,” In Proc. of Trends in Artificial Intelligence, 9th Pacific Rim International Conference on Artificial Intelligence, 2006, pp. 854-858, Guilin, China.

[7] G.Feng, S. G.Cao, andN. W.Rees, "Stable adaptive control of fuzzy dynamic systems,” Fuzzy Sets and Syst. 131, 2002,pp. 217-224.

[8] P.Gahinet, A.Nemirovski, A. j.Laub, and M.Chilali, "LMI Control Toolbox User’s Guide,”MA:The Math Works, Natick, 1995.

[9] D. E.Goldberg, "Genetic Algorithms in Search, Optimization, and Machine Learning,” Addison-Wesley, 1989.

[10] 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 Trans. Circuits & Systems-I:Regular Papersvol. 52, no. 9, 2005, pp. 1883- 1893.

[11] F. Y. Hsu, and L. C.Fu, "A novel adaptive fuzzy variable structure control for a class of nonlinear uncertain systems via backstepping,” Fuzzy Sets and Syst., vol. 122, 2001, pp. 83-106.

[12] D.Karaboga, "An Idea Based On Honey Bee Swarm for Numerical Optimization,” Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.

[13] D.Karaboga and B. Basturk, "On the performance of artificial bee colony (ABC) algorithm,” Applied Soft Computing, vol. 8(1), pp. 687-697, 2008.

[14] C. L.Karr, "Genetic algorithms for fuzzy controller”, AI Expert,1991,pp. 26-33.

[15] K. M.Koo, "Stable adaptive fuzzy controller with time-varying dead-zone,” Fuzzy Sets and Syst. vol. 121, 2001, pp. 161-168.

[16] C. C. Kung, and C. C.Chen, "Grey fuzzy sliding mode controller design with genetic algorithm,” in Proc.36th IEEE Conf. Decision and Control, 1997, pp. 2748-2753.

[17] S.Labiod, M. S.Boucherit, and T. M.Gurra, "Adaptive fuzzy control of a class of MIMO nonlinear systems,” Fuzzy Sets and Syst., vol. 151, 2005, pp. 59-77.

[18] S. C.Lin, "Stable Self-Learning Optimal Fuzzy Control System Design and Application,” PhD Dissertation, Department of Electrical Engineering, National Taiwan University, Taiwan, 1997.

[19] S. K.Nguang, and P.Shi, "Fuzzy Output Feedback Control Design for Nonlinear Systems: an LMI approach,” IEEE Trans. Fuzzy Syst., vol. 11, 2003, pp. 331-340.

[20] A. S.Poznyak, Y. B.Shtessel, andC. J.Gallwgos, "Min-max sliding mode control for multimodel linear time varying systems,” IEEE Trans. Automat. Contr., vol. 48,2003, pp. 2141-2150.

[21] M. C.Saaj, B.Bandyopadhyay, and H.Unbehauen, "A new algorithm for discrete-time sliding-mode control using fast output fast output sampling feedback,” IEEE Trans. Ind. Electron., vol. 49, 2002, pp. 518-523.

[22] J. J. E.Slotine and W.Li, "Applied Nonlinear Control, NJ: Prentice Hall,” Englewood Cliffs, 1991.

[23] W.-J. Sun, "A Global Asymptotic Synchronization Problem via Internal Model Approach,” International Journal of Control Automation and Systems, vol. 8, 2010, pp. 1153-1158.

[24] K. Tanaka and H. O.Wang,"Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach,” NJ: John Wiley & Sons, Inc, 2001.

[25] C. W.Tao, J, S.Taur, and M. L.Chan, "Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties,” IEEE Trans. Syst., Man, Cybern.:B, vol. 34,2004,pp. 255-262.

[26] S. Tong and H. X.Li, "Fuzzy adaptive sliding-mode control for MIMO nonlinear systems,” IEEE Trans. Fuzzy Syst., vol. 11,2003, pp. 354-360.

[27] P.-W.Tsai, J.-S. Pan, B.-Y. Liao, M.-J. Tsai, and I. Vaci, "Bat Algorithm Inspired Algorithm for Solving Numerical Optimization Problems,” Applied Mechanics and Materials, vol. 148-149, 2012, pp. 134-137.

[28] C. S. Tseng and B. S.Chen, "Decentralized Fuzzy Model Reference Tracking Control Design for Nonlinear Interconnected Systems,” IEEE Trans. Fuzzy Syst., vol. 9,2001,pp. 795-809.

[29] V. I.Utkin,"Sliding Modes and their Application in Variable Structure Systems,” MIR Publishers, Moscow, 1978.

[30] M.Vidyasagr, "Nonlinear Systems Analysis,” Prentice Hall, NJ: Englewood Cliffs, 1993.

[31] J.Wang, A. S.Rad, andP. T.Chan, "Indirect Adaptive Fuzzy SlidingMode Control: Part and Part,” Fuzzy Sets and Syst., vol. 122, 2001, pp. 21-43.

[32] L. X.Wang, "Adaptive Fuzzy Systems and Control: Design and Stability Analysis,” NJ: Prentice Hall, Englewood Cliffs, 1994.

[33] L. X.Wang, "A Course in Fuzzy Systems and Control,” NJ: Prentice Hall, Englewood Cliffs, 1997.

[34] W.Wang, J.Yi, D.Zhao, and D.Liu, "Design of a stable sliding-mode controller for a class of second-order underactuated systems,” in IEEE Proc. Control Theory Appl., vol. 151,2004, pp. 683-690.

[35] Y. Xia,and Y.Jia, "Robust sliding-mode control for uncertain time delay system: an LMI approach,” IEEE Trans. Automal. Contr., vol. 48, 2003, pp. 1086-1092.

[36] Y. Yang and C.Zhou, "Adaptive fuzzy stabilization for strict-feedback canonical nonlinear systems via backstepping and small-gain approach,” IEEE Trans. Fuzzy Syst., vol. 13,2005, pp. 104-114.

[37] B. Yooand W.Ham, "Adaptive fuzzy sliding mode control of nonlinear system,” IEEE Trans. Fuzzy Sys., vol. 6,1998, pp. 315-321.