复杂系统的宏观行为与分形结构的研究

This project has systematically studied similar structures and macro-behavior of complex systems. A fundamental framework of similarity theory has been set up. The intersection of subsystems and its influence on dynamic behavior of composite complex systems have been thoroughly studied. Interconnection terms are no longer treated as disturbances as in traditional methods. The project exploits many modern techniques such as differential geometry, Lyapunov functions, varying structure control,neural network and LMIs. A number theoretical results and design methodologies of complex systems are obtained concerning controllability,observability, stability, and robust control, adaptive control,decentralized control, hybrid control and holographic control..These results reveal inherent laws between the structure and the motion.of complex systems. The research shows that similar structures simplify.a lot the analysis and design for complex systems. Local constitutions.contain global information and subsystems reflect properties of large.scale systems, which is called a holographic feature and is characterized by systems with similarity. The study of the project provides some new concepts, ideas and methodologies for the study of complexity science

本项目指出生物、社会、管理等复杂系统实际呈现的宏观结构，即局部与总体相似的自相似结构，或分形结构。并研究这类结构与系统宏观行为、功能间的关系。其中含适应外界环境、实现特定性能，发展提高等。自适应性是复杂系统的结构形成及发展的内因，将予充分关注。由于这类结构现实存在且有较普遍代表性，故此项研究有重要意义且有我国特色。