Development of solution for control problem based on cascade decomposition method

Abstract

Abstract The problem of simplifying solution of linear dynamic systems with preset conditions at the edges and internal points of the segment is considered. In this regard a modification technique of the existing cascade decomposition method based on obtaining a general formula for the system state and control functions is described. Coefficients of this formula are identified in a recursive way. The formula is presented to obtain the cascade decomposition method and kernel functions of the intermediate step matrices being important for the last step function. Illustratively, a practice-oriented example proves the method advantages in convenience and speed comparing with the conventional method of cascade decomposition.