Uncertainty propagation in related control systems via the Liouville equation

Document Type



This paper studies the relationship between the evolutions of uncertain initial conditions in Φ-related control systems. It is shown that a control system abstraction can capture the time evolution of the uncertainty in the original system by an appropriate choice of control input. Φ-related control systems with stochastic initial conditions show the same behaviour as systems with deterministic initial conditions. A conservation law is applied to the probability density function (pdf) requiring that the area under it be unity. Application of the conservation law results in a partial differential equation known as the Liouville equation, for which a closed form solution is known. The solution provides the time evolution of the initial pdf which can be followed by the abstracted system.


Digital control systems; Sturm-Liouville equation; Uncertainty


Controls and Control Theory | Electrical and Computer Engineering | Engineering | Systems and Communications


Use Find in Your Library, contact the author, or interlibrary loan to garner a copy of the item. Publisher policy does not allow archiving the final published version. If a post-print (author's peer-reviewed manuscript) is allowed and available, or publisher policy changes, the item will be deposited.

UNLV article access

Search your library