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

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.