화학공학소재연구정보센터
IEEE Transactions on Automatic Control, Vol.61, No.10, 2892-2905, 2016
Stochastic Control With Uncertain Parameters via Chance Constrained Control
Chance constrained methods handle problem uncertainty by formulating the constraints probabilistically and only guaranteeing their satisfaction up to a given violation level. This paper extends existing chance constrained methods to handle both uncertainty in the system state as well as in the constraint parameters. Due to the imperfect knowledge of the system state caused by motion, sensor and environment uncertainty, the system constraints cannot be guaranteed to be satisfied and consequently must be considered probabilistically. Prior work has primarily only dealt with uncertainty in the system state or constraint parameters but not both simultaneously, however, in many motivating applications both frequently occur. To handle this case, previous approaches either approximate the distribution leading to a nonconvex optimization program, or use sampling alone to represent the uncertainty which requires a large number of samples to accurately represent the distribution. To address these limitations, a novel hybrid method is proposed that uses both analytical functions and sampling to represent the uncertainty. It is shown that under certain conditions, the resulting optimization program using this hybrid representation is convex. To check the convexity, an efficient a priori, sufficient condition is developed. Furthermore, by using this hybrid representation, this method drastically reduces the computational complexity over previous methods, which is demonstrated through two examples. Consequently, this method has the ability to enable real-time stochastic control for the motivating applications.