{'fraction_non_alphanumeric': 0.017276422764227643, 'fraction_numerical': 0.0, 'mean_word_length': 5.480263157894737, '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}}
Optimal control and zero-sum differential game for Hurwicz model considering singular systems with multifactor and uncertainty

Uncertainty theory is a new branch of mathematics concerned with the analysis of subjective indeterminacy. Based on the concept of uncertain theory, this paper considers optimal control and zero-sum differential game for multi-factor uncertain continuous-time singular systems with Hurwicz criterion, where dynamic systems are modelled by a type of uncertain differential equation driven by canonical Liu process. Using the approach of dynamic programming, the principle of optimality is proposed and then the equation of optimality is derived to resolve an uncertain control model. A two-player zero-sum uncertain differential game is further investigated based on the optimality equation above, and an equilibrium equation is presented to locate a saddle-point in the game. Finally, an example is discussed to illuminate the effectiveness of the results.