Optimal control by dynamic programming using systematic reduction in grid size

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Abstract
The use of dynamic programming to solve non-linear optimal control problems resistant to other methods is investigated. The proposed method utilizing a relatively coarse grid followed by systematic reduction in the grid size is shown to converge to the optimal solution in a reasonable number of iterations. The method is easy to program and the likelihood of obtaining the global optimum is very high if the initial grid is chosen to be sufficiently large. Computational results are presented for three systems to show that dynamic programming provides an attractive procedure when fast computers are available.