On the Computation of Switching Surfaces in Optimal Control: A Gröbner Basis Approach
Georgiou, Tryphon T.
Tannenbaum, Allen R.
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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. A powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested, namely the use of Grobner bases. We apply the Grobner basis technique to find effective solutions to the classical problem of time-optimal control.