UC Santa Cruz

Finite escape means the occurrence of an infinite value in the solution of a time-varyingdifferential equation. Finite escape can occur in the computation of either the Kalman or the Kalman-Bucy filter because the gain is time-varying. When no escape occurs it is analogous to the Heisenberg uncertainty principle [1] in atomic physics. Three noisy examples are given: a single integrator, a double integrator, and a linear oscillator. Finite escape cannot happen in the single integrator or the underdamped linear oscillator, but can happen in the double integrator and undamped linear oscillator. Therefore, finite escape can occur in the estimation of any noisy dynamic system. Except in special situations, it is impossible to achieve certainty in the determination of all state variables using neural nets, machine learning, or artificial intelligence even with an infinite amount of data. Conditions for finite escape to occur are given. Finally, practical solutions for escape are considered for the linear oscillator.