بهینگی جهانی برنامه نویسی پویای تقریبی و استفاده از آن در به حداقل رساندن تابع غیر محدب

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