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Abstract
Order diminution plays a significant role in the study of complex dynamical linear interval systems. Numerous strategies have been suggested in diverse field for order diminution of higher dimensional models. Nowadays, the optimization algorithms are commonly used for order diminution based on a specific error performance criterion known as cost or objective function. This study suggests a novel approach for order diminution of interval system using cuckoo search algorithm. The proposed technique utilises the Kharitonov’s polynomials to ensure a stable model. Typical examples have been considered to showcase the efficiency of the presented approach. Comparative study is also demonstrated with other available techniques in terms of different performance measures. The suggested approach has also been applied for order diminution of multi input multi output interval system.
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References
Al-Nadi DA, Alsmadi OM, Abo-Hammour ZS (2011) Reduced order modeling of linear MIMO systems using particle swarm optimization. In: Proceedings of 7th international conference on autonomic and autonomous systems, 15–18 February, Venice
Bai Z (2002) Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Appl Numer Math 43:9–44
Bandyopadhyay B, Ismail O, Gorez R (1994) Routh-Pade approximation for interval systems. IEEE Trans Autom Control 39(12):2454–2456
Bandyopadhyay B, Upadhye A, Ismail O (1997) γ−δ Routh approximation for interval systems. IEEE Trans Autom Control 42(8):1127–1130
Bandyopadhyay B, Sreeram V, Shingare P (2008) Stable γ−δ routh approximation for interval systems using Kharitonov polynomials. Int J Inf Syst Sci 44(3):348–361
Bansal JC, Sharma H, Arya KV (2011) Model order reduction of single input single output systems using artificial bee colony optimization algorithm. NISCO Stud Comput Intell 387:85–100
Barmish B (1994) New tools for robustness of linear systems. Macmillan Publishing Company, New York
Bartumeus F (2007) Levy processes in animal movement: an evolutionary hypothesis. Fractals 15(2):1–12
Brown CT, Liebovitch LS, Glendon R (2007) Levy flights in Dobe Ju/’hoansi foraging patterns. Hum Ecol 35(1):129–138
Chapellat H, Bhattacharyam SP (1981) Generation of Kharitonov’s theorem: robust stability of interval plants. IEEE Trans Autom Control 26(1):17–32
Desai SR, Prasad R (2013a) A new approach to order reduction using stability equation and big bang crunch optimization. J Syst Sci Control Eng 1(1):20–27
Desai SR, Prasad R (2013b) A novel order diminution of LTI systems using big bang big crunch optimization and Routh Approximation. J Appl Math Model 37:8016–8028
Dolgin Y, Zeheb E (2003) On Routh Pade model reduction of interval systems. IEEE Trans Autom Control 48(9):1610–1612
Enns D (1984) Model reduction with balanced realizations: an error bound and a frequency weighted generalization. In: Proceedings of IEEE decision and control conference, 4–7 January, Washington, DC, pp 87–91
Glover K (1984) All optimal Hankel-norm approximations of linear multivariable systems and their L∞ error bounds. Int J Control 39(6):1115–1193
Hickin J, Sinha NK (1976) New method of obtaining reduced order models for linear multivariable systems. Electron Lett 12:90–92
IonescuT C, Astolfi A (2016) Nonlinear moment matching-based model order reduction. IEEE Trans Autom Control 61(10):2837–2847
Ismail O (2004) Reduced order modeling of linear interval systems using multipoint continued fraction expansion. In: Proceedings of the international conference on information and communication technologies: from theory to applications, India
Juneja M, Nagar SK (2015) Comparative study of model order reduction using combination of PSO with conventional reduction techniques. In: International conference on industrial instrumentation and control, India, pp 58–63
Krajewski W, Lepschy A, Mian G, Viaro U (1993) On flexible model reduction by the modified factor division method. Syst Sci 19(2):23–36
Kumar M, Yadav S (2014) Model order reduction of time interval system: a survey. In: Proceedings of 3rd international conference on soft computing for problem solving, India
Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. J Comput Struct 82:781–798
Moore BC (1981) Principal component analysis in linear systems: controllability, observability and model reduction. IEEE Trans Autom Control 26(1):17–32
Parmar G, Mukherjee S, Prasad R (2007a) Reduced order modeling of linear dynamic systems using particle swarm optimized eigen spectrum analysis. Int J Comput Math Sci 1(31):45–52
Parmar G, Mukherjee S, Prasad R (2007b) System reduction using factor division algorithm and eigen spectrum analysis. Appl Math Model 31:2542–2552
Parmar G, Prasad R, Mukherjee S (2007c) Order reduction of linear dynamic systems using stability equation method and GA. Int J Comput Inf Eng 1(1):26–32
Pernebo L, Silverman LM (1981) Model reduction via balanced state space representations. IEEE Trans Autom Control 27(2):382–387
Pratheep VG, Ramesh K, Venkatachalam K (2014) Model order reduction of interval systems by pole clustering technique using GA. J Theor Appl Inf Technol 66(1):15–19
Saini DK, Prasad R (2010) Order reduction of linear interval systems using genetic Algorithm. Int J Eng Technol 2(5):316–319
Sarawathi G, Gopala Rao KA, Amarnath J (2007) A mixed method for order reduction of interval systems. In: Proceedings of international conference on intelligent and advanced systems, India
Sastry GVKR, Mallikarjuna Rao P (2003) A new method for modelling of large scale interval systems. IETE J Res 49(6):423–430
Sastry GVKR, Raja G, Rao PM (2000) Large scale interval system modeling using Routh approximants. IET J 36(8):768–769
Satakshi, Mukherjee S, Mittal RC (2005) Order reduction of linear discrete systems using a genetic algorithm. J Appl Math Model 29(6):565–578
Selvaganesan N (2007) Mixed method of model reduction for uncertain systems. Serbian J Electr Eng 4(1):1–12
Sikander A, Prasad R (2015) A novel order reduction method using cuckoo search algorithm. IETE J Res 61(2):83–90
Singh VP, Chandra D (2010) Routh-approximation based model reduction using series expansion of interval systems. In: International conference on power, control and embedded systems (ICPCES), India
Sinha AK, Pal J (1990) Simulation based reduced order modelling using a clustering technique. Comput Electr Eng 16(3):159–169
Tanwar NS, Bhatt R, Parmar G (2016) Order reduction of interval systems using Big bang Big crunch and Routh approximation. In: Proceedings of IEEE international conference on power electronics, intelligent control and energy systems (ICPEICES), July, India
Therapos CP (1983) Balanced minimal realization of SISO systems. Electron Lett 19(11):424–426
Valian E, Tavakoli S, Mohanna HA (2013) Improved cuckoo search for reliability optimization problems. Comput Ind Eng 64:459–468
Vishwakarma CB (2014) Modified Hankel matrix approach for model order reduction in time domain. Int J MathComput Sci Eng 8(2):290–296
Vishwakarma CB, Prasad R (2008) Clustering method for reducing order of linear system using Padé approximation. IETE J Res 54(5):326–330
Viswanathan GM (2010) Ecology: fish in Lévy-flight foraging. Nature 465:1018
Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Int J Math Model Numer Optim 1:330–343
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Authors and Affiliations
Department of Electronics Engineering, Rajasthan Technical University, Kota, 324 010, India
Jay Kumar & Girish Parmar
Department of Instrumentation and Control Engineering, Dr. B. R. Ambedkar National Institute of Technology, Jalandhar, 144011, India
Afzal Sikander
Department of Electrical Engineering, BBD University, Lucknow, India
Monica Mehrotra
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Correspondence toAfzal Sikander.
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Kumar, J., Sikander, A., Mehrotra, M.et al. A new soft computing approach for order diminution of interval system.Int J Syst Assur Eng Manag11, 366–373 (2020). https://doi.org/10.1007/s13198-019-00865-y
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