Time Optimal Control Using Gröbner Bases

Abstract: The paper presents the solution of the time optimal control with the help of Gröbner Bases theory. First the set of polynomial equations for the triple integrator system with unknowns corresponding to the switching times is constructed and later it is solved in the computer algebra system Maple using the Groebner library. In dependence of resulting switching times the control action is designed. Finally the time optimal switching surface is compared with the variety resulted from the Gröbner Bases solution.