Computation of approximate value functions for constrained control problems

Abstract

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