Intelligent control of dynamic systems: innovations and optimization applications in today's world

In recent decades, control theory and dynamic systems have been recognized as a key tool in the analysis and design of complex systems in various scientific and industrial fields. This review article focuses on the fundamental and advanced concepts of optimal control of dynamic systems and examines various optimization methods and techniques. First, the concept of optimal control is explained with an emphasis on calculus of variations and fuzzy methods, and it analyzes the challenges in the design and implementation of these systems. Then the article deals with the wide applications of control theory in various fields such as engineering, medicine and economics. In the field of engineering, the results of optimization in automatic systems, robotics and control of industrial processes are investigated.In the field of medicine, how control theory is used to improve diagnostic and therapeutic systems as well as drug management is analyzed. In economics, the role of optimal control in predicting economic patterns and optimizing financial and human resources is discussed. This paper also discusses some recent innovations in the field of integration of artificial intelligence and control of dynamic systems and shows that this combination can help improve the performance of systems. Considering the growing trends in today's world, the importance and application of control theory as an effective factor in scientific and technological advances is clearly visible. The results of this review can serve as a basis for future research in the field of optimal control and its applications in different fields and provide new solutions to solve existing challenges.