Searching for optimal trajectory with learning in the vicinity

An algorithm of searching for the optimal trajectory with the minimal cost of reaching the final state is presented The reduction of alternative trajectories is based on the Bellman dynamic programming principle. A similar procedure of reduction of branching alternatives was developed by the author for auto-capture of trajectories of aircrafts in the presence of noise. Learning consists in estimation of a priori unknown minimal cost W(x) of reaching the target from the initial state x and in estimating ∂W(x)/∂x on the basis of analysis of trial trajectories obtained earlier. At any moment of time, the controlling impact is chosen so as to increase the rate of decreasing of the function V(x), which characterizes the closeness of the state x to the target state x_fin, and to increase the rate of decreasing of the estimated value of W(x)