Stochastic Hybrid Systems Modeling and Estimation with Applications to Air Traffic Control

Various engineering systems have become rapidly automated and intelligent as sensing, communication, and computing technologies have been increasingly advanced. The dynamical behaviors of such systems have also become complicated as they need to meet requirements on performance and safety in various operating conditions. Due to the heterogeneity in its behaviors for different operating modes, it is not appropriate to use a single dynamical model to describe its dynamics, which motivates the development of the stochastic hybrid system (SHS). The SHS is defined as a dynamical system which contains interacting time-evolving continuous state and event-driven discrete state (also called a mode) with uncertainties. Due to its flexibility and effectiveness, the SHS has been widely used for modeling complex engineering systems in many applications such as air traffic control, sensor networks, biological systems, and etc.

One of the key research areas related to the SHS is the inference or estimation of the states of the SHS, which is also known as the hybrid state estimation. This task is very challenging because both the continuous and discrete states need to be inferred from noisy measurements generated from mixed time-evolving and event-driven behavior of the SHS. This becomes even more difficult when the dynamical behavior or measurement contains nonlinearity, which is the case in many engineering systems that can be modeled as the SHS.

This research aims to 1) propose a stochastic nonlinear hybrid system model and develop novel nonlinear hybrid state estimation algorithms that can deal with the aforementioned challenges, and 2) apply them to safety-critical applications in air traffic control systems such as aircraft tracking and estimated time of arrival prediction, and unmanned aircraft system traffic management.