Model order formulation of a multivariable discrete system using a modified particle swarm optimization approach

Abstract This paper proposes an algorithm for model order formulation of an absolutely stable higher order linear time invariant multivariable discrete system using a new version of evolutionary computing technique namely, Modified Particle Swarm Optimization (MPSO). A simple adjunct polynomial method has been proposed for obtaining the initial seed values of the lower order multivariable system. In the modified PSO, the movement of a particle is governed by three behaviors namely, inertia, cognitive and social. The cognitive behavior helps the particle to remember its previously visited best position. This paper proposes to split the cognitive behavior into two sections. This modification is efficiently utilized to obtain a better lower order system that reflects the characteristics of the original higher order system by minimizing the integral squared error with the steady state constraints. The results obtained are compared with the earlier techniques utilized, to validate its ease of computation. The proposed algorithm is illustrated with a numerical example from the literature.

[1]  Raymond Gorez,et al.  New reduction technique by step error minimization for multivariable systems , 1988 .

[2]  C. F. Chen,et al.  A novel approach to linear model simplification , 1968 .

[3]  Jing J. Liang,et al.  Comprehensive learning particle swarm optimizer for global optimization of multimodal functions , 2006, IEEE Transactions on Evolutionary Computation.

[4]  Uri Shaked,et al.  Discrete multivariable system approximations by minimal Pade-type stable models , 1984 .

[5]  Y. Shamash,et al.  Multivariable system reduction via modal methods and padé approximation , 1975 .

[6]  P. Gutman,et al.  Contributions to the model reduction problem , 1982 .

[7]  W. Renhart,et al.  Pareto optimality and particle swarm optimization , 2004, IEEE Transactions on Magnetics.

[8]  Cemal Ardil,et al.  Reduction of Linear Time-Invariant Systems Using Routh-Approximation and PSO , 2009 .

[9]  José Neves,et al.  The fully informed particle swarm: simpler, maybe better , 2004, IEEE Transactions on Evolutionary Computation.

[10]  Jayanta Pal,et al.  System reduction by a mixed method , 1980 .

[11]  P. J. Angeline,et al.  Using selection to improve particle swarm optimization , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[12]  Ashraf M. Abdelbar,et al.  Swarm optimization with instinct-driven particles , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[13]  Naresh K. Sinha,et al.  Control Systems , 1986 .

[14]  Yuhui Shi,et al.  Particle swarm optimization: developments, applications and resources , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[15]  The viability of analytical methods for the reduction of multivariable systems , 1981 .

[16]  Lihong Feng,et al.  Parameter independent model order reduction , 2005, Math. Comput. Simul..

[17]  E. Jury,et al.  Positivity and stability tests for multidimensional filters (discrete-continuous) , 1974 .

[18]  James Kennedy,et al.  Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[19]  Konstantinos E. Parsopoulos,et al.  UPSO: A Unified Particle Swarm Optimization Scheme , 2019, International Conference of Computational Methods in Sciences and Engineering 2004 (ICCMSE 2004).

[20]  V. Zakian,et al.  Simplification of linear time-invariant systems by moment approximants † , 1973 .

[21]  A. Selvakumar,et al.  A New Particle Swarm Optimization Solution to Nonconvex Economic Dispatch Problems , 2007, IEEE Transactions on Power Systems.

[22]  C. Therapos,et al.  A Direct Method for Model Reduction of Discrete systems , 1984 .

[23]  Kalyan Veeramachaneni,et al.  Fitness-distance-ratio based particle swarm optimization , 2003, Proceedings of the 2003 IEEE Swarm Intelligence Symposium. SIS'03 (Cat. No.03EX706).

[24]  Jacob Wolfowitz,et al.  Notes on a General Strong Converse , 1968, Inf. Control..

[25]  Sidhartha Panda,et al.  Model Reduction of Linear Systems by Conventional and Evolutionary Techniques , 2009 .

[26]  Jing J. Liang,et al.  Dynamic multi-swarm particle swarm optimizer , 2005, Proceedings 2005 IEEE Swarm Intelligence Symposium, 2005. SIS 2005..