Approximate dynamic programming via penalty functions

Abstract

In this paper, we propose a novel formulation for encoding state constraints into the Linear Programming approach to Approximate Dynamic Programming via the use of penalty functions. To maintain tractability of the resulting optimization problem that needs to be solved, we suggest a penalty function that is constructed as a point-wise maximum taken over a family of low-order polynomials. Once the penalty functions are designed, no additional approximations are introduced by the proposed formulation. The effectiveness and numerical stability of the formulation is demonstrated through examples