An investigation into the factors affecting performance of fuzzy logic systems

Fuzzy logic is a frequently used solution to control problems, especially when there are elements of human knowledge that may be incorporated into the system. Fuzzy logic comes in several varieties with the most common being based on either type-1 or type-2 fuzzy logic. Modifications to these standard varieties, termed Non-Stationary (NS) and Dual Surface (DS) are also investigated. Each variety allows a certain amount of flexibility in its expression. However, with this increased flexibility (and potentially performance) comes additional resource requirements: either during run time with higher processing and memory requirements; or at design time, with additional parameters requiring selection and optimisation. There have been several comparisons into the performance obtained from type-1 and type-2 investigating such factors as their internal configuration (such as membership functions as defined by their Footprint of Uncertainty), task difficulty and the environment in which the experiments are performed. However, no studies have been performed incorporating each of these factors with the goal of determining how they impact upon performance. The end goal of this work is the development of a methodology to understand which combination of conditions will cause type-2 control to consistently outperform type-1 based systems. This would enable the rationalisation of moving from a type-1 to a type-2 system, which is currently done without understanding if and how performance will increase with such a move. This thesis introduces a novel scheme by which several methods of comparing performance are employed to observe how the output and resulting performance levels change as factors including: controller configuration, task difficulty and environmental variability are varied. These methods are performed over three applications which gradually increase in complexity: a simple tipping example, a more developed simulation based on an autonomous sailing robots application and subsequent real-world experiments, which also involve the autonomous sailing problem. The first method of comparison studies how the rules which fire for a given input set change as the configuration of the fuzzy logic controller is increased. The second comparative technique investigates the control surfaces produced by a selection of fuzzy logic controllers to observe how they change as the internal configuration is changed. Observations such as the smoothing of the transitions between surfaces suggest that controllers with a larger FOU may give a better response. The third method for comparison is developed in which outputs from a controller operating in a simulated environment are compared to an ideal value, giving a single numeric output with which comparisons can be made. It was found that there are situations in which type-2 based fuzzy control outperforms type-1. However, these are found to be less common than expected. It is determined that this may be due to the simplicity of some of our case studies environments (especially the tipping example), where there may not be enough scope for large improvements to become apparent. These findings lay ground for future work in which (i) more developed and complex applications and (ii) a more tuned fuzzy system should be investigated to find if this will result in more obvious differences between configurations.