Fast Approximate Dynamic Programming for Input-Affine Dynamics

We propose two novel numerical schemes for the approximate implementation of dynamic programming (DP) operation concerned with finite-horizon optimal control discrete-time systems input-affine dynamics. The proposed algorithms involve discretization state and input spaces are based on an alternative path that solves dual problem corresponding to DP operation. provide error bounds algorithms, along a detailed analysis their computational complexity. In particular, specific class problems separable data in variables, approach can reduce typical time complexity from $\mathcal {O}(XU)$ {O}(X+U)$ , where notation="LaTeX">$X$ notation="LaTeX">$U$ denote size discrete spaces, respectively. This reduction is achieved by algorithmic transformation minimization addition via conjugation.