{'fraction_non_alphanumeric': 0.020674646354733407, 'fraction_numerical': 0.0, 'mean_word_length': 5.917293233082707, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Theoretical Difficulty in Approximate Dynamic Programming with Input Constraints

Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional constrained ADP framework, the optimal control issearched via a policy iteration algorithm, where the value under a constrainedcontrol is solved from a Hamilton-Jacobi-Bellman (HJB) equation while theconstrained control policy is improved based on the current estimated value.This concise and applicable method has been widely-used. However, the con-vergence of the existing policy iteration algorithm may possesses a theoreticaldifficulty, which might be caused by forcibly evaluating the same trajectoryeven though the control policy has already changed. This problem will beexplored in this paper.