Fuzzy Optimal Control Of Linear Quadratic Performance Index

Randomness, and fuzziness are two important uncertainty. Based on the credibility space, Professor Baoding Liu of Tsinghua University introduced the concepts of fuzzy process in 2008, Liu process, and etc. Based on the concept of fuzzy process, Zhu presented a fuzzy optimal control problem and gave a fundamental result called the equation of optimality in fuzzy optimal control. In this paper, we will consider a fuzzy optimal control problem of linear quadratic model. That is, we discuss the problemof maximiz-ing(minimizing) the expected value of linear quadratic objective function subject to fuzzy differential equations. First of all, we obtain necessary and sufficient conditions of fuzzy linear quadratic optimal control. Secondly, we discuss infinite time linear quadratic model and time-invariant systems.