Model Abstraction in Dynamical Systems: Application to Mobile Robot Control
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This work also studies the relationship between the evolution of uncertain initial conditions in abstracted 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. Abstracted control systems with stochastic initial conditions show the same behavior 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 convservation 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.
- Doctoral Dissertations