A numerical algebraic geometry approach to nonlinear constrained optimal control

Abstract

A new method for nonlinear constrained optimal control based on numerical algebraic geometry is presented. First, the optimal control problem is formulated as a parametric optimization program. Then, certain structural information related to the optimization problem is computed off-line. Afterwards, given this information, numerical algebraic geometry techniques are used to efficiently obtain the optimal control input (i.e. optimal solution) of the original control problem in real time. By using homotopy continuation over the field of complex numbers, this approach has a probability-one guarantee of finding the global optimal solution to the problem at hand.