Multi-dimension Uncertain Linear Quadratic Optimal Control

Optimal control has been studied by many researchers since1950s. Now the optimal control theory has been applied to many areas. Liu founded the uncertainty theory in2007, and then many scholars pay great attention to the uncertain optimal control. Engineers working on automatic control usually consider practical problems as linear quadratic models. Based on the uncertain theory, we discuss uncertain optimal control problems of multi-dimension about linear quadratic models in this paper.First, we introduce the knowledge of uncertainty theory, including uncertain mea-sure, uncertain variable, uncertain distribution and uncertain differential equation. And then, we give the multi-dimensional uncertain linear quadratic optimal control model. Based on multi-dimensional uncertain equation of optimality, we obtain a nec-essary and sufficient condition of uncertain optimal control. On the one hand, we discuss the multi-dimensional uncertain linear quadratic optimal control model with fi-nite time. On the other hand, we prove the nature of convergence in mean of uncertain variable sequence. And then, we study the model with infinity time.