Attainable Control Set Calculation Method for Over-actuated System in Which Column Vector of Efficiency Matrix is Proportional

Abstract

The control allocation method based on the attainable control set has become a hot issue in the field of control allocation, and it has been widely used in advanced satellites, airplanes, navigation, automobiles, robots and other fields. Many results have been achieved in the calculation of the attainable control set of the over-actuated system, but there is no public result for the precise calculation of the attainable control set when the column vectors of the control efficiency matrix are proportional. This paper proposes a method to determine the attainable control set of the over-actuated system when the column vectors of the control efficiency matrix are proportional. This method provides an accurate calculation method for the attainable control set of the over-actuated system when the two or more column vectors of the control efficiency matrix are proportional. The method proposed in this paper is programmed and implemented by matlab software, and an example is performed. The results show that the proposed method has high computational efficiency and accurate calculation results. The research ideas in this paper also have enlightenment for the precise calculation of the attainable control set when the third-order sub-matrix is a more general singular matrix.