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Pre-computing in Polynomial MPC


Ph. Rostalski

Presentation at ABB Corporate Research, Baden-Dättwil, Switzerland

Some recently developed techniques for constrained polynomial optimal control problems are reviewed. Assuming a system modeled by a polynomial vector field, a polynomial cost function and semi-algebraic constraints, the optimal control problem is stated as a parametric optimization problem (mpPP). Utilizing latest developments in the area of algebraic geometry, real algebraic geometry and numerical algebraic geometry, we will describe different methods to solve such problems. Particular in model predictive control, where such a parametric optimization problem has to be solved repeatedly for changing parameter values, pre-computation might prove beneficial for a fast evaluation of the cost function and the optimizer.


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