About the object’s motion under the influence of polynomial controllibility function

Abstract

The problem of constructing state function and control function in the type of polynomials of the control problem in recent years has received much attention from authors such as Ailon A, Зубова С.П, Раецкая Е. В... The basic meaning is to facilitate the survey and evaluation of the trajectory of motion. The aim of this article is to consider the motion of object in plane with the equation of motion described by the linear dynamic system x \'(t) = Bx (t) + Du(t). With the assumption that the control function u(t) can be found in polynomial when we give input condition, the author has devised a method to prove that control function is of the degrees<=5 By adding conditions (19), we can prove that u(t) is polynomial of degrees <=2n+5