The dynamic programming paradigm provides sufficient conditions for optimality

of control laws for dynamical systems. The optimal cost-to-go function, often

referred to as the value function, provides the necessary information to

derive the control law in each state. The computation of the value function is

straightforward for discrete valued systems with a countable number of states

[1]. For systems with an infinite number of states, the value function

is approximated by parameterized function approximation architectures

[2]. A broad variety (see e.g. [3]) of different function

approximations, ranging from polynomial interpolation, over neural networks,

support vector regression to kriging models are possible candidates.

 

After assessing the applicability of the different approximation schemes to

approximate dynamic programming, this thesis should comprise a comparison with

respect to the underlying theory, computational complexity as well as features

considering the implementation. A Matlab implementation for the most promising

schemes should be carried out.