A new soft computing approach for order diminution of interval system

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.

[1]  B. Moore Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[2]  Girish Parmar,et al.  Order reduction of interval systems using Big bang Big crunch and Routh approximation , 2016, 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES).

[3]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010 .

[4]  Clifford T. Brown,et al.  Lévy Flights in Dobe Ju/’hoansi Foraging Patterns , 2007 .

[5]  C. Therapos Balanced minimal realisation of SISO systems , 1983 .

[6]  S. Mukherjee,et al.  Order Reduction of Linear Dynamic Systems using Stability Equation Method and GA , 2007 .

[7]  C. Vishwakarma Modified Hankel Matrix Approach for Model Order Reduction in Time Domain , 2014 .

[8]  Ezra Zeheb,et al.  On Routh-Pade model reduction of interval systems , 2003, IEEE Trans. Autom. Control..

[9]  Frederic Bartumeus,et al.  LÉVY PROCESSES IN ANIMAL MOVEMENT: AN EVOLUTIONARY HYPOTHESIS , 2007 .

[10]  J. Amarnath,et al.  A mixed method for order reduction of interval systems , 2007, 2007 International Conference on Intelligent and Advanced Systems.

[11]  Z. Bai Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems , 2002 .

[12]  G. Parmar,et al.  Reduced Order Modelling of Linear Dynamic Systems using Particle Swarm Optimized Eigen Spectrum Analysis , 2007 .

[13]  S. R. Desai,et al.  A new approach to order reduction using stability equation and big bang big crunch optimization , 2013 .

[14]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[15]  B. Bandyopadhyay,et al.  γ-δ Routh approximation for interval systems , 1997, IEEE Trans. Autom. Control..

[16]  Dia I. Abu-Al-Nadi,et al.  Reduced Order Modeling of Linear MIMO Systems Using Particle Swarm Optimization , 2011 .

[17]  N. Selvaganesan,et al.  Mixed Method of Model Reduction for Uncertain Systems , 2007 .

[18]  Vinay Pratap Singh,et al.  Routh-approximation based model reduction using series expansion of interval systems , 2010, 2010 International Conference on Power, Control and Embedded Systems.

[19]  Afzal Sikander,et al.  A Novel Order Reduction Method Using Cuckoo Search Algorithm , 2015 .

[20]  B. Ross Barmish,et al.  New Tools for Robustness of Linear Systems , 1993 .

[21]  K. Glover All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[22]  J. Hickin,et al.  Erratum: New method of obtaining reduced-order models for linear multivariable systems , 1976 .

[23]  P. Mallikarjuna Rao,et al.  A New Method for Modelling of Large Scale Interval Systems , 2003 .

[24]  Devender Kumar Saini,et al.  Order Reduction of Linear Interval Systems Using Genetic Algorithm , 2010 .

[25]  J. B. Stankovic,et al.  FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES , 2007 .

[26]  Gandhimohan M. Viswanathan,et al.  Ecology: Fish in Lévy-flight foraging , 2010, Nature.

[27]  Saeed Tavakoli,et al.  Improved cuckoo search for reliability optimization problems , 2013, Comput. Ind. Eng..

[28]  C. Vishwakarma,et al.  Clustering Method for Reducing Order of Linear System using Pade Approximation , 2008 .

[29]  S. R. Desai,et al.  A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh Approximation , 2013 .

[30]  Harish Sharma,et al.  Model Order Reduction of Single Input Single Output Systems Using Artificial Bee Colony Optimization Algorithm , 2011, NICSO.

[31]  Mahendra Kumar,et al.  Model Order Reduction of Time Interval System: A Survey , 2013, SocProS.

[32]  Jayanta Pal,et al.  Simulation based reduced order modeling using a clustering technique , 1990 .

[33]  G. Parmar,et al.  System reduction using factor division algorithm and eigen spectrum analysis , 2007 .

[34]  S. K. Nagar,et al.  Comparative study of Model Order Reduction using combination of PSO with conventional reduction techniques , 2015, 2015 International Conference on Industrial Instrumentation and Control (ICIC).

[35]  Satakshi,et al.  Order reduction of linear discrete systems using a genetic algorithm , 2005 .

[36]  R. Gorez,et al.  Routh-Pade approximation for interval systems , 1994, IEEE Trans. Autom. Control..

[37]  L. Silverman,et al.  Model reduction via balanced state space representations , 1982 .

[38]  D. Enns Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[39]  Alessandro Astolfi,et al.  Nonlinear Moment Matching-Based Model Order Reduction , 2016, IEEE Transactions on Automatic Control.