Abstract
A hybrid dynamic programming algorithm is proposed, which is based on the forward dynamic programming combined with the branch-and-bound technique. This hybrid algorithm solves nonlinear optimal control problems with complicated state and control constraints several orders faster than the conventional dynamic programming. This method overcomes the Bellman's the “curse of dimensionality”. Basically, the proposed algorithm consists of interactions similar to Darwinian evolution through the cycles of selection, multiplication through the state space quantization.
The most important idea is that this algorithm successively improves not only the optimal solution but also the accuracy of the lower bounds of the cost function which have great influence upon the number of computations as well as computation regions. To this end, the hybrid algorithm is carried out with the successive iterations under the further quantization of each state and control variable. The second idea is that this algorithm is carried out with parallel computations starting from the approximated local solutions obtained through each iteration step.
This paper assesses convergence and accuracy of the hybrid algorithm as well as the number of computations. An application of this algorithm is studied for the optimal low-thrust mission trajectory generation, in which, the Sun encounter mission is considered, and only Venus is taken as the swinged-by planet if some swingby is requested. The results show that the proposed hybrid algorithm is quite efficient for the large-scale problems with the complicated constraints such as the Sun encounter mission.
