Analysis,Design And Application Of Hierarchical Fuzzy Systems Based On Algebraic Method

Hierarchical fuzzy systems(HFSs)are an important branch of fuzzy systems,which are composed of several lower-dimensional fuzzy logic units with the serial,parallel or hybrid hierarchical structure.On one hand,based on the hierarchical structure,HFSs can alleviate the dimension explosion of fuzzy rules in the traditional fuzzy systems,and thus have been successfully applied to several research areas,such as system science,medical science and engineering.On the other hand,in terms of practical applications,hierarchical structure may affect the system performance,such as interpretability,accuracy and universal approximation.Therefore,it is of great theoretical and practical value to develop a unified mathematical framework for studying HFSs.The algebraic formulation,interpretability,universal approximation and controller design of HFSs are studied in this thesis,in which the main results are applied to the on-ramp metering of freeway.The main contents of this thesis are listed as follows:1.The interpretability and controller design of multi-input single-output(MISO)HFSs are considered.In order to improve the interpretability of considered system,a kind of interpretable HFSs formed by the interpretable fuzzy logic units is proposed,and the corresponding algebraic formulation is given.Based on the above results,the logical matrix factorization technique is proposed to design the interpretable hierarchical fuzzy controller under the scenario where the fuzzy rules are known.Moreover,the proximal policy optimization algorithm is established to discuss the case where the input-output data is incomplete.2.The algebraic formulation and controller design of multi-input multi-output(MIMO)HFSs are considered.In order to reduce the computational complexity,the parallel fuzzy relation matrix is constructed,based on which,the algebraic formulation of MIMO fuzzy systems and HFSs is given.After that,the factorization technique of parallel fuzzy relation matrix is proposed to partition the MIMO fuzzy systems into several fuzzy logic units.Based on this operation,the design algorithms of serial,parallel and hybrid hierarchical fuzzy controllers are respectively established,which need the complete fuzzy rules.3.The universal approximation and approximator design of MIMO HFSs are considered.The algebraic formulation of MISO HFSs is given,based on which,the universal approximation of considered systems is proved through the StoneWeierstrass theorem.On this premise,the design algorithm of hierarchical fuzzy approximator is developed,in which the approximation accuracy is strictly given.Furthermore,the above results of universal approximation,approximator design and approximation accuracy are extended to MIMO HFSs.4.The on-ramp metering of freeway is considered based on HFSs.According to the design methods of MISO hierarchical fuzzy controllers,a kind of hybrid hierarchical fuzzy on-ramp controller is proposed to deal with the scenario where the fuzzy rules are known,and the parallel hierarchical fuzzy on-ramp controller corresponds to the scenario where the input-output data is incomplete.The ultimate goal of the above two controllers is to maintain the maximum traffic flow,that is,to alleviate the traffic congestion.Furthermore,the simulation results show that the proposed hierarchical fuzzy on-ramp controllers can reduce the total time spent to a certain extent.The main contributions of this thesis contain three folds.(1)A new mathematical framework is established for the modeling of HFSs.This thesis gives the algebraic formulation of HFSs through the semi-tensor product method,in which the outputs of fuzzy logic units are the vector forms of fuzzy sets.Based on this characteristic,the algebraic formulation avoids the repeated defuzzification-fuzzification process of middle layer.Compared with the most existing results,the proposed mathematical framework can not only reduce the computational complexity,but also improve the interpretability and accuracy of HFSs;(2)A new research idea is proposed for the study of HFSs.This thesis explores the fundamental problems of HFSs under the proposed mathematical framework,such as interpretability,universal approximation,approximators design and controller design,which provides the theoretical basis for the follow-up research of HFSs;(3)Several feasible control methods are presented for alleviating the traffic congestion of freeway.Based on the more traffic flow information,this thesis designs the hybrid and parallel hierarchical fuzzy controllers to handle the problem of on-ramp metering.Compared with the existing results,the proposed controllers shorten the total time spent on the basis of reducing the on-ramp queue length,and thus can alleviate the traffic congestion.