The application of grey system theory combined with fuzzy reasoning in high order nonlinear control system

A system with partial unknown structure, parameters, and characteristics is called a grey system. Grey system theory can be employed to improve the control performance of a system without sufficient information or with highly nonlinear property. In the paper, grey system theory is introduced into sliding mode control of a high order nonlinear system and a novel grey fuzzy sliding mode controller is developed. In this controller design, a grey prediction model combined with fuzzy reasoning is proposed to obtain a sliding mode control strategy. The controller can drive the state from an arbitrary initial point of state to the origin along a sliding mode hyper plane quickly and reduce the vibration phenomenon that is caused by switching delay brought by system inertia. Grey system theory is an efficient tool in the analysis and control of nonlinear uncertain systems