Switching surfaces and Groebner bases

A number of problems in control can be reduced to finding suitable real sol utions 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 note, we ap ply the Groebner basis technique to find effective solutions to the classic al problem of time-optimal control.