| Fuzziness is an important uncertainty, which plays an essential role in the real world. Fuzzy set theory has been developed very fast since it was introduced by scientist Zadeh on cybernetics in 1965. Professor Baoding Liu of Tsinghua University introduced the concepts of fuzzy process, Liu process, fuzzy differential equation. Professor Yuanguo Zhu studied a fuzzy optimal control problem and presented an equation of optimality which is called Zhu's equation of optimality. In this paper, we shall consider a fuzzy optimal control in the condition of multi-dimension. First we deal with the model of two-dimensional fuzzy optimal control problem, and then give the principle of optimality and the equation of optimality. Then we obtain the principle of optimality and equation of optimality about multidimensional fuzzy optimal control. In the last section we will solve an optimal stopping time problem and a portfolio selection problem by using the equation of optimality. |
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