Application and Research of Differential Geometry in Control System

Differential geometry is becoming increasingly used in industrial production. It has been transformed to industrial methods concerning with its mathematical theories, and been applied in many industrial control systems. We present a comprehensive study from various domains. At first, as to the domain of chaotic system, we take Lorenz and Rossler as examples, use differential geometric method and design a controller to control these two systems. Secondly, as to the domain of decoupling control, we study tilting control on the steering vehicle body, and construct motion model of steering vehicle through symbolic operation based on differential geometry. What’s more, as to the domain of unmanned aerial vehicle (short as UAV) technology, we integrate geometrical mechanics with differential geometry and put forward a geometrical and mechanical method to model UAV. The validity and feasibility of these methods are verified through simulation experiments.