A novel order diminution of LTI systems using big bang big crunch optimization and routh approximation

Applied Mathematical Modelling

Volumn 37, Issue 16-17, 2013, Pages 8016-8028

  Desai, S R ^a   Prasad, Rajendra ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

Author keywords

Big Bang Big Crunch; Integral Square Error; Linear Time Invariant Reduced Order System; Routh Approximation; Stability

Indexed keywords

BIG CRUNCH; INTEGRAL SQUARE ERRORS; LINEAR TIME-INVARIANT SYSTEM; MULTIPLE INPUT MULTIPLE OUTPUT; REDUCED ORDER SYSTEMS; ROUTH APPROXIMATION; SINGLE INPUT SINGLE OUTPUT; STEADY-STATE CONDITION;

CONVERGENCE OF NUMERICAL METHODS; LINEAR SYSTEMS; MIMO SYSTEMS; OPTIMIZATION;

APPROXIMATION THEORY;

EID: 84881542076     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2013.02.052     Document Type: Article

References (40)

1. Antoulas A. Approximation of Large-Scale Dynamical Systems 2005, SIAM Publications, Philadelphia, PA.
2. M.S. Mahmoud, M.G. Singh, Large scale systems modelling, in: International Series on Systems and Control, vol. 3, Pergamon Press, first ed., 1981.
3. M. Jamshidi, Large Scale Systems Modelling and Control Series, New York, Amsterdam, Oxford, North Holland, vol. 9, 1983.
4. P. Benner, V. Mehrmann, D. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol. 45, Springer-Verlag, Berlin/Heidelberg, Germany, 2005.
5. R. Prasad, A.K. Mittal, S. P. Sharma, A Mixed Method for the Reduction of Multi-Variable Systems, Journal of Institution of Engineers, India, IE(I) Journal - EL, vol. 85, pp. 177-181, 2005.
6. Antonio Lepschy and Umberto Viaro, A Note on the Model Reduction Problem, IEEE Transactions on Automatic Conixol, vol. Ac-28, No. 4, 1983.
7. A.C. Antoulas, D.C. Sorensen, S. Gugercin, A survey of model reduction methods for large-scale systems, in: Structured Matrices in Operator Theory, Numerical Analysis, Control, Signal and Image Processing, Contemporary Mathematics, vol. 280, AMS publications, 2001, pp. 193-219.
8. Penzi Thilo. Algorithms for model reduction of large dynamical systems. Linear Algebra Appl. 2006, 415(2-3):322-343.
9. Teofilo Gonzalez, Handbook of Approximation Algorithms and Metaheuristics, vol. 1, Chapman and Hall/CRC Computer and Information Science Series, 2007.
10. Sivanandam S.N., Deepa S.N. A comparative study using genetic algorithm and particle swarm optimization for lower order system modelling. Int. J. Comput. Internet Manage. 2009, 17(3):1-10.
11. Panda S., Yadav J.S., Patidar N.P., Ardil C. Evolutionary techniques for model order reduction of large scale linear systems. Int. J. Comput. Math. Sci. 2009, 3(1):28-34.
12. Panda Sidhartha, Tomar S.K., Prasad R., Ardil C. Model reduction of linear systems by conventional and evolutionary techniques. Int. J. Comput. Math. Sci. 2009, 3(1):28-34.
13. Parmar G., Prasad R., Mukherjee S. Order reduction of linear dynamic systems using stability equation method and GA. Int. J. Comput. Inf. Eng. 2007, 1(1):26-32.
14. Boby Philip, Jayanta Pal, An evolutionary computation based approach for reduced order modelling of linear systems, in: IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), vol. 28-29, Coimbatore, 2010.
15. S.M. Giriraj Kumar, R. Sivasankar, T.K. Radhakrishnan, V. Dharmalingam, N. Anantharaman, Particle swarm optimization technique based design of Pi controller for a real-time non-linear process, in: Instrumentation Science and Technology, Taylor & Francis, Group, 36, 2008, pp. 525-542.
16. Hemmati Reza, Boroujeni Sayed Mojtaba Shirvani, Delafkar Hamideh, Boroujeni Amin Safarnezhad PID controller adjustment using PSO for multi area load frequency control. Aust. J. Basic Appl. Sci. 2011, 5:295-302.
17. H.M. Genc, A.K. Hocaoglu, Bearing-only target tracking based on Big Bang-Big Crunch algorithm, in: The 3rd Int. Multi-Conference on Computing in the Global Information Technology, (ICCGI 2008), 2008, 229-233.
18. T. Kumbasar, E. Yesil, I. Eksin, M. Guzelkaya, Inverse fuzzy model control with online adaptation via Big Bang-Big Crunch optimization, in: 3rd International Symposium on Communications, Control, and Signal Processing (ISCCSP), 2008, pp. 697-702.
19. T. Kumbasar, I. Eksin, M. Guzelkaya, E. Yesil, Big Bang Big Crunch optimization method based fuzzy model inversion, in: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 5317 LNAI, 2008, pp. 732-740.
20. Camp C.V. Design of space trusses using Big Bang-Big Crunch optimization. J. Struct. Eng. 2007, 133(7):999-1008.
21. Dogan M., Istefanopulos Y. Optimal nonlinear controller design for flexible robot manipUlators with adaptive internal model. IET Control Theory Appl. 2007, 1(3):770-778.
22. H.M. Gen, O.K. Erol, L. Eksi, An Application and Solution to Gate Assignment Problem for AtatOrk Airport, DECOMM 2009, 2009.
23. Pavel Y., Tabakov O. Big Bang-Big Crunch optimization method in optimum design of complex composite laminates. World Acad. Sci. Eng. Technol. 2011, 77.
24. Hakkl M. Gene, Ibrahim Eksin, Osman K. Erol, Big Bang-Big crunch optimization algorithm hybridized with local directional moves and application to target motion analysis problem, in: IEEE International Conference on Systems Man and Cybernetics (SMC), 2010, pp. 881-887.
25. Erol O.K., Eksin I. New optimization method: Big Bang-Big Crunch. Adv. Eng. Software Software 2006, 37:106-111.
26. Singh Rashmi, Verma H.K. Big Bang-Big Crunch optimization algorithm for linear phase fir digital filter design. Int. J. Electr. Commun. Comput. Eng. 2011, 3.
27. Hutton Maurice F., Friedland Bernard Routh approximations for reducing order of linear, time-invariant systems. IEEE Trans. Autom. Control 1975, AC-20(3):1-20.
28. Mukherjee S., Mishra R.N. Order reduction of linear systems using an error minimization technique. J. Franklin Inst. 1987, 323(1):23-32.
29. Chen T.C., Chang C.Y., Han K.W. Stable reduced order pade approximants using stability equation method. Electron. Lett. 1980, 16(9):345-346.
30. Pal J. Improved pade approximants using stability equation method. Electron. Lett. 1983, 19(11):426-427.
31. Parthasarathy R., Jayasimha K.N. System reduction using stability equation method and modified Cauer continued fraction. Proc. IEEE 1982, 70(10):1234-1236.
32. Davison E.J. A method for simplifying linear dynamic systems. IEEE Trans. Automat. Control 1966, AC-11:93-101.
33. Shieh L.S., Wei Y.J. A mixed method for multivariable system reduction. IEEE Trans. Automat. Control 1975, AC-20:429-432.
34. Krishnamurthy V., Seshadri V. Model reduction using the Routh stability criterion. IEEE Trans. Automat. Control 1978, AC-23(4):729-731.
35. Pal J. Stable reduced order pade approximants using the Routh Hurwitz array. Electron. Lett. 1979, 15(8):225-226.
36. Gutman P.O., Mannerfelt C.F., Molander P. Contributions to the model reduction problem. IEEE Trans. Automat. Control 1982, AC-27(2):454-455.
37. R. Prasad, J. Pal, Stable reduction of linear systems by continued fractions, in: Journal of Institution of Engineers, India, IE(I) Journal-EL, vol. 72, 1991, pp. 113-116.
38. Safonov M.G., Chiang R.Y. Model reduction for robust control: a Schur relative error method. Proc. Int. J. Adapt. Control Signal 1988, 2:259-272.
39. R. Prasad, J. Pal, Use of continued fraction expansion for stable reduction of linear multivariable systems, in: Journal of Institution of Engineers, India, IE(I) Journal - EL, 1991, vol. 72, pp. 43-47.
40. R. Prasad, J. Pal, A.K. Pant, Multivariable system approximation using polynomial derivatives, in: Journal of Institution of Engineers, India IE(J) Journal - EL, vol. 76, 1995, pp. 186-188.