Uncertainty Propagation in Related Control Systems Via the Liouville Equation
International Journal of Modelling, Identification and Control
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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
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Uncertainty Propagation in Related Control Systems Via the Liouville Equation.
International Journal of Modelling, Identification and Control, 9(4),