Representation formulas for solutions of linear uncertain fractional differential equations and optimal control
摘要
Within the framework of uncertainty theory, this paper investigates the optimal control problem for dynamical systems governed by a linear Caputo-type uncertain fractional differential equation. The Cauchy problem of the equation is formulated, and representation formulas for its solutions are derived using the fundamental solution matrix. Based on the informational image of the system’s position together with these formulas, the original uncertain fractional optimal control model is reduced to an auxiliary model driven by an uncertain differential equation, and solved via dynamic programming. It is further shown that the auxiliary model yields the same optimal control and optimal expected value as the original model, which ensures the validity of the proposed approach. As an application, the optimal control problem of wastewater pollutant emissions in China is investigated, and the corresponding optimal allocation of pollution control funds is derived.