Objective. To construct the graph theory model and grey correlation model of table tennis mixed doubles technology and tactics so as to provide a new research method for the analysis of table tennis mixed doubles technology and tactics. The method of graphic theory and video observation is used to study the top tactical indicators of the game, and the method of graphic theory and video observation is used to analyze the tactical data of men and women, which has a certain contribution to the world level of table tennis. The grey correlation analysis can be better applied to the technical and tactical analysis of table tennis mixed doubles. The analysis of the contribution rate of men and women in eight rounds shows that there is little difference in the net average score between male and female athletes, and female athletes are slightly higher than male athletes. The net average score of the serving round is much higher than that of the receiving round, which shows that the serving round has certain advantages for the server, and the winner is often better able to grasp the opportunity of the serving round and get higher scores. Male athletes should strengthen physical training and adapt to a higher level of confrontation.

It has been widely used in signal processing, image processing, speech recognition and synthesis, pattern recognition, machine vision, machinery fault diagnosis and monitoring, and other scientific and technological fields and has achieved great results. The application potential in nonlinear system identification is increasing. According to the theory of “overload recovery” and “functional reserve”, the mathematical model of “load-fitness state” is established to understand the adaptation characteristics and individual characteristics of athletes to sports training. The model is used to simulate the values and time required to reach the maximum fitness state for four types of precompetition reduction plans and to provide a reference for the development of precompetition training plans. The data required for parameter estimation were the actual training data of six outstanding basketball athletes (mean age 18.2 ± 0.75, mean training years 4.6 ± 0.49). And the coaches’ training plan was not intervened during the test. In order to further reduce the biaxial synchronization error of the sports platform and improve the stability of the system, the wavelet transformation capable of time-varying signal analysis and the recursive structure with dynamic capability were combined with the fuzzy neural network, and the learning ability of the neural network was used to learn and adjust the scaling and translation factors in the wavelet function, the mean and standard deviation in the fuzzy structure, and the connection weights between the layers, according to the biaxial synchronization. The simulation results show that the designed global sliding mode controller can improve the convergence speed of tracking error and ensure the single-axis tracking accuracy of the H-type motion platform compared with the traditional sliding mode controller, and the tracking accuracy and synchronization accuracy of the system can be further improved after adding the cross-coupled synchronization controller, but the improvement of synchronization control accuracy is not very satisfactory due to the fixed selection of the parameters of the cross-coupled controller. Further improvement is needed.

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