Optimum design of fuzzy controllers for nonlinear systems using multi-objective particle swarm optimization

Abstract

In this paper, a multi-objective particle swarm optimization algorithm is used to obtain the Pareto frontiers 
of the different commensurable and conflicting objective functions for fuzzy controller design. Also, the Lorenz 
dominance method is used to illustrate the equitable solutions. The nonlinear benchmarks are the inverted pendulum 
and ball-beam systems. The objective functions for the inverted pendulum system are the normalized angle error of 
the pendulum and the normalized distance error of the cart; and for the ball-beam system they are the distance error 
of the ball and the angle error of the beam, which must be minimized simultaneously. The comparison of the obtained 
results with those in the literature demonstrates the superiority of the results of this work.