The fuzzy system based on vague partitions and its application to path tracking control for autonomous vehicles

Abstract

As significant carriers of the application of fuzzy set theories, fuzzy systems have been widely used in many fields. However, selecting fuzzifications, fuzzy reasoning engines, and defuzzifications is subjective for Mamdani fuzzy systems, and the fuzzy rule of Takagi-Sugeno-Kang fuzzy systems is less of a linguistic interpretation. Regarding these shortcomings, this paper proposes a fuzzy system based on vague partitions processing information directly from the fuzzy rule base, in which fuzzy rules have explicit semantics. Firstly, the n-dimensional vague partition of the n-dimensional universe is defined based on 1-dimensional vague partitions and the aggregation function, and its properties are discussed. Based on these, we design the new fuzzy system, and investigate its approximation properties which is the theoretical guarantee for applying the fuzzy system. As an application, we combine the fuzzy system with PID control system to deal with autonomous vehicle path tracking control problems. A series of experiments are constructed, and experimental results indicate that the fuzzy system based on vague partitions makes the fuzzy PID control system strong robustness, and has obvious advantages compared with other traditional fuzzy systems for path tracking control problems.