Particle Swarm Optimization of fuzzy models for Anti-Lock Braking Systems

This paper suggests a Particle Swarm Optimization (PSO) approach to the optimal tuning of fuzzy models for Anti-lock Braking Systems (ABSs). A set of ten local state-space models of the ABS is first obtained by the linearization of the nonlinear state-space model of the ABS process at ten operating points. The initial Takagi-Sugeno (T-S) fuzzy models are next obtained by the modal equivalence principle, namely by placing the local state-space models of the process in the rule consequents. The optimization problem targets the minimization of the objective function (OF) expressed as the mean squared modeling error, and the vector variable of the OF consists of the feet of the triangular input membership functions. A PSO algorithm solves the optimization problem and gives the optimal T-S fuzzy models. A set of real-time experimental results is included to validate the PSO approach and the optimal T-S fuzzy models for real-world ABS laboratory equipment.