Fuzzy and evolutionary modelling of nonlinear control systems

The development of a controller for a nonlinear system is still a challenging task for control engineers. This paper presents a method for the optimization of a Fuzzy Logic System (FLS) [1] for the control of nonlinear systems. A fine-grained parallel genetic algorithm has been proposed to identify the parameters of the FLS. The proposed method has been applied to control a popular set of benchmark problems, i.e., an inverse pendulum with both constant and varying shaft length and a couple of unjoined inverse pendulums fixed on a single platform. It is argued that, because of its ability to capture the imprecise information that humans can understand very easily in natural language, a fuzzy logic system provides an ideal general frame of reference for modelling any nonlinear system involving uncertainties. In this context, the evolutionary algorithms with their parallel power to search through multidimensional space are effective in estimating the parameters of the fuzzy logic system. The fine-grained parallel genetic algorithm has been executed on a PC-hosted 16-node transputer platform running under the Helios operating system. The quantitative comparison of the fuzzy-evolutionary controller to the LQR controller has been given for one example system, while for the other two systems (for which there are no analytical solutions) the value of the objective function has been provided for future reference.