Global optimality of approximate dynamic programming and its use in non-convex function minimization

摘要: Level curves of the Rosenbrock function subject to minimization and state trajectories for different initial conditions x0ź{-2, -1, 0, 1, 2}×{-2, 2}. The red plus signs denote point respective trajectory. This study investigates global optimality approximate dynamic programming (ADP) based solutions using neural networks optimal control problems with fixed final time. Issues including whether or not cost terms system dynamics need be convex functions respect their inputs are discussed sufficient result derived. Next, a new idea is presented use ADP optimization non-convex smooth functions. It shown that any guess leads direct movement toward proximity optimum function. behavior in contrast gradient methods which guided by shape local level curves. Illustrative examples provided single multi-variable demonstrate potential proposed method.