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An optimal control application in power electronics using algebraic geometry

In this paper, we present an application in power electronics using an algebraic geometry approach for the optimal control of nonlinear polynomial systems. The proposed method consists of two parts, the off-line and the on-line. In the off-line part, certain generalized companion matrices are computed in relation with the optimal control problem. These are later used by the on-line part, where given the measured state of the system, the optimal control input can be efficiently calculated. Simulation results are provided for the optimal control problem of the boost dc-dc converter.