Parallel Particle Swarm Optimization Optimized LDI Controller with Lyapunov Stability Criterion for Nonlinear Structural Systems

In this paper, we present a neural-network (NN) based
approach to represent a nonlinear Tagagi-Sugeno (T-S) system. A
linear differential inclusion (LDI) state-space representation is utilized
to deal with the NN models. Taking advantage of the LDI
representation, the stability conditions and controller design are
derived for a class of nonlinear structural systems. Moreover, the
concept of utilizing the Parallel Particle Swarm Optimization (PPSO)
algorithm to solve the common P matrix under the stability criteria is
given in this paper.





References:
[1] T. Takagi, and M. Sugeno, "Fuzzy identification of systems and its
applications to modeling and control,” IEEE Trans. on Systems, Man and
Cybernetics, vol. 15, no. 1, pp. 116-132, Feb. 1985.
[2] 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 Papers vol. 52, no. 9,
pp. 1883- 1893, Sep. 2005.
[3] F.H.Hsiao, C.W.Chen, Y.H. Wu, W.L. Chiang, "Fuzzy controllers for
nonlinear interconnected TMD systems with external force,”Journal of
The Chinese Institute of Engineers, vol. 28, pp. 175-181, 2005.
[4] F.H.Hsiao, W.L. Chiang, C.W.Chen, "Fuzzy Control for Nonlinear
Systems via Neural-Network-Based Approach,” International Journal
for Computational Methods in Engineering Science and Mechanics, vol.
6, pp. 145- 152, 2005.
[5] F.H.Hsiao, W.L. Chiang, C.W.Chen, S.D. Xu, and S.L. Wu, "Application
and robustness design of fuzzy controller for resonant and chaotic
systems with external disturbance,”Int. J. Uncertainty, Fuzziness and
Knowledge-Based System, vol. 13, pp. 281-295, 2005.
[6] F.H.Hsiao, J.D. Hwang, C.W.Chen, Z.R. Tsai, "Robust Stabilization of
Nonlinear Multiple Time-Delay Large-scale Systems via Decentralized
Fuzzy Control,” IEEE Trans. Fuzzy Systems, vol. 13, pp. 152- 163, 2005.
[7] 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, pp. 152-
163, 2005.
[8] S.-C. Chu, and P.-W. Tsai, "Computational Intelligence Based on the
Behavior of Cats,” International Journal of Innovative Computing,
Information and Control, vol. 3, no. 1, 2007, pp. 163-173.
[9] S.-C.Chu, P.-W.Tsai, and J.-S.Pan, "Cat Swarm Optimization,” in Proc.
9th Pacific Rim International Conference on Artificial Intelligence, LNAI
4099, 2006, pp. 854-858.
[10] J.-S. Pan, P.-W. Tsai, and B.-Y. Liao, "Fish Migration Optimization
Based on the Fishy Biology,”inProc. of 2010 4th International
Conference on Genetic and Evolutionary Computing, 2010, pp. 783-786.
[11] P.-W. Tsai,J.-S. Pan, B.-Y. Liao, M.-J. Tsai, and V. Istanda, "Bat
Algorithm Inspired Algorithm for Solving Numerical Optimization
Problems,” Applied Mechanics and Materials, vol. 148-149, 2012, pp.
134-137.
[12] T.-C. Chen, P.-W. Tsai, S.-C. Chu, and J.-S. Pan, "A Novel Optimization
Approach: Bacterial-GA Foraging,” in Proc. 2nd International Conf. on
Innovative Computing, Information and Control (ICICIC-2007), Japan.
[13] 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, 2004, pp. 523-537.
[14] C.W. Chen, W.L. Chiang, and C.H. Tsai et al., "Fuzzy Lyapunov method
for stability conditions of nonlinear systems,” International Journal on
Artificial Intelligence Tools, vol. 15, 2006, pp. 163-171.
[15] D. Dubois and H. Prade, "Fuzzy Sets and Systems: Theory and
Applications,” Academic Press, New York 1980.
[16] W. I. Lee, C. W. Chen, C. Y. Chen, and Y. C. Sui, "Application of
half-circle fuzzy numbers and development of triangular fuzzy numbers
to fuzzy control,” in Proc. 10th WSEAS International Conf. on Applied
Computer Sciences (ACS’10), Japan, 2010, pp. 335-340.
[17] J.M. Mendel, "Fuzzy logic systems for engineering: A tutorial,”in Proc.
of the IEEE, 83 March 1995.
[18] J. J. Buckley, "Fuzzy Hierarchical Analysis,”Fuzzy Sets and System, vol.
17, 1985, pp. 233-247.
[19] C.W. Chen, C.L. Lin, C.H. Tsai, C.Y. Chen, and K. Yeh, "A novel
delay-dependent criteria for time-delay T-S fuzzy systems using fuzzy
Lyapunov method,” International Journal on Artificial Intelligence
Tools, vol. 16, 2007, pp. 545-552.
[20] H. J. Zimmermann., Fuzzy Set Theory and Its Applications, (1991)
Kluwer, Dordrecht.
[21] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear Matrix
Inequalities in System and Control Theory,” Studies in Applied
Mathematics (SIAM), Philadelphia, PA, 1994.
[22] K. Tanaka and M. Sugeno, "Stability analysis and design of fuzzy control
systems,” Fuzzy Sets and Systems, vol. 45, no. 2, 1992, pp. 135-156.
[23] X.L. Luan, F. Liu, P. Shi,"Robust Finite-Time H (a) Control for
Nonlinear Jump Systems via Neural Networks,” Circuits Systems and
Signal Processing, vol. 29, pp. 481-498, 2010.
[24] J.-F. Chang, S.-C. Chu, J. F. Roddick, and J.-S. Pan, "A Parallel Particle
Swarm Optimization Algorithm with Communication Strategies,”
Journal of Information Sciences and Engineering, vol. 21, pp. 809-818,
2005.
[25] D. Abramson, and J. Abela, "A Parallel Genetic Algorithm for Solving
the School Timetabling Problem,” Technical Report, Division of
Information Technology, CSIRO, 1991.
[26] C.-H. Fang, Y.-S. Liu, S.-W. Kau, L. Hong, and C.-H. Lee, "A New
LMI-Based Approach to Relaxed Quadratic Stabilization of T-S Fuzzy
Control Systems,” IEEE Tran. on Fuzzy Systems, vol. 14, no. 3, pp.
386-397, June 2006.
[27] W.-J. Sun, "A Global Asymptotic Synchronization Problem via Internal
Model Approach,” International Journal of Control Automation and
Systems, vol. 8, pp. 1153-1158, 2010.