Research on stability analysis method of dynamic system integrating mathematical modeling and data-driven algorithm

In this paper, the stability analysis method of dynamic system integrating mathematical modeling and data-driven algorithm is studied. The stability analysis of dynamic systems is of great significance in many fields, but the traditional mathematical modeling methods have many challenges in the face of complex systems, and the data-driven algorithms have problems such as poor explanatory power and insufficient generalization ability. Therefore, this study proposes a physical constraint-data compensation collaborative framework, which combines the physical prior of mathematical model with the dynamic adaptability of data-driven. The framework includes physical model, residual learner, mixed stability criterion module and other core parts, and realizes dynamic adjustment and anomaly identification through online parameter update and early warning mechanism. By constructing a mixed Lyapunov function and combining the information of model-driven and data-driven, the ability to judge the stability of complex dynamic systems is improved. Experiments are carried out in multi-machine power system and manipulator system. The results show that this fusion method is superior to traditional methods and pure data-driven methods in stability judgment accuracy, convergence speed and real-time performance, showing strong anti-noise ability and dynamic response ability, and providing an effective new method for dynamic system stability analysis.