Extension of Iterative Dynamic Programming to High-Dimensional Systems by Using Randomly Chosen Values for Control

Iterative dynamic programming employing region contraction and randomly generated admissible values for control is examined for high-dimensional optimal control problems. The use of randomly generated control values becomes necessary when the number of control variables is very large. Choosing control values at random is especially useful to keep the number of points reasonably small when the number of control variables is very large. In the numerical example where there are twenty state variables and twenty control variables, convergence to the optimum was fast even when only one hundred randomly chosen control values were used at each grid point.