Design And Application Of Fuzzy Systems Based On Matrix Semi-Tensor Product

With the continuous development of technology,fuzzy control has become an indispensable branch in control theory.Fuzzy control has achieved fruitful results in applications such as control of complex systems and modeling.The thesis investigates fuzzy systems from several perspectives based on the matrix semi-tensor product.These perspectives include the analysis and design of multivariable fuzzy logic systems,parameter optimization of hierarchical fuzzy systems based on particle swarm optimization algorithm,and fuzzy control design based on interval intuitionistic fuzzy sets..The main work of the thesis includes:1.The thesis discusses the fundamental theoretical knowledge and current development status of fuzzy control,and introduces the research status of matrix semi-tensor product in fuzzy logic systems.2.Analysis of fuzzy logic systems and a design method are proposed in this study.For multi-variable fuzzy systems,a comprehensive investigation is conducted,and a fuzzy relation vector based on matrix semi-tensor product is proposed.It can handle the influence of interference information more effectively and simplify the inference process.Experimental comparisons with traditional methods demonstrate that using this approach to construct fuzzy systems yields superior anti-interference capabilities.3.As the dimensions of input and output variables in multivariable fuzzy control increase,the number of rules grows exponentially.While hierarchical fuzzy control can address this issue,the resulting hierarchy may not reach the optimal solution.The thesis utilizes the particle swarm optimization algorithm to optimize the parameters of the hierarchical fuzzy system.The fuzzy relation matrix is treated as a set of points in a multidimensional space,and the particle swarm algorithm iteratively adjusts the positions of these points to obtain an optimized fuzzy relation matrix.Comparative experiments with genetic algorithm optimization demonstrate that the hierarchical fuzzy system controlled by particle swarm optimization exhibits smoother control and better performance.4.In traditional multi-variable fuzzy control,fuzzy sets can only represent a specific membership value.However,interval-valued intuitionistic fuzzy sets contain membership interval and "non-membership" interval,providing higher expressive power and accuracy.In this study,based on interval-valued intuitionistic fuzzy sets and matrix semi-tensor product,a new fuzzy control method is proposed.Comparative experiments with PID algorithm and fuzzy PID algorithm for unmanned aerial vehicle control demonstrate that the proposed method yields smaller overshoot and faster response speed.5.A method for constructing fuzzy systems using data to generate interval intuitionistic fuzzy sets is proposed by constructing a new fuzzy relation hypermatrix.By introducing interval mathematics theory and hypermatrix,the reliability and accuracy of fuzzy system modeling are improved.Experimental results demonstrate that compared to RBF neural networks and traditional fuzzy control,the proposed method achieves better control accuracy and has certain error correction capabilities.