Computation of approximate value functions for constrained control problems

The paper discusses an iterative algorithm for computing approximations to the
optimal value function for constrained control problems. The algorithm gives an
explicit measure on the distance to the optimal value function. A major step
in the course of constructing an algorithm for these problems is to choose
an efficient parameterization. The choice has several implications.
The main obstacle in the algorithm we consider is that it involves an
infinite-dimensional optimization problem in each step, without
approximations these problems are computationally infeasible. The choice of
parameterization must thus be chosen accordingly. Multivariate polynomials
are a good candidate parameterization. To obtain a feasible algorithm, we
impose certain convexity properties and make use of recent results on
the representation of positive polynomials.