Continuous Time Model Uncertainty Bang-bang Control

In the modern word, there are many uncertainty. Everyday we need to face many subjective uncertain events. In order to understand them, uncertainty theory was founded by Liu[1]in 2007 and refined by Liu[2]in 2010. In the paper, we study uncertain optimal control model of multi-dimension, and the equation of optimality for uncertain optimal control problem is generalized to multi-dimension case. We make use of multi-dimension equation of optimality for the two models that the drift coefficient of the state equation is linear of decision vector and linear of state vector and decision vector. We derive the control both are uncertain bang-bang control. Two examples are given to illustrate the result obtained.