Computational algebraic geometry and switching surfaces in optimal control

A number of problems in control can be reduced to finding suitable real solutions of algebraic equations. In particular, such a problem arises in the context of switching surfaces in optimal control. Recently, a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Groebner bases. In this paper, we apply the Groebner basis technique to find effective solutions to the classical problem of time-optimal control.