Hybrid systems are dynamical systems that consist of interacting continuous states and discrete states. We research on hybrid systems theories and applications in the following areas:

1. Hybrid System Modeling
2. Hybrid Estimation Algorithms
3. Intent Inference Algorithms

 

Hybrid System Modeling

Many practical systems such as chemical plants, air transportation systems, biological systems, have with both continuous state (such as the temperature of a chemical reaction tank, or the position of an aircraft) and discrete state (such as the on/off state of a valve, the flight mode of an aircraft). The dynamics of these systems are complex because the dynamics of the continuous state and that of the discrete state are coupled, i.e. the evolution of the continuous state depends on the discrete state, and vice versa.  Furthermore, the behaviors of these systems are usually stochastic in nature due to presence of noise, uncertainties and unknown disturbances. We need an accurate mathematical model to describe such systems in order to carry out estimation, inference and predictions on the systems’ behaviors.

Hybrid systems provide a useful tool for modeling such complex systems. We develop rigorous mathematical model to accurately represent the interacting dynamics of the continuous state and discrete state. We consider both linear and nonlinear continuous state dynamics, and we model uncertainties in both the continuous state and the discrete state evolutions. We use this mathematical model to accurately describe complex dynamical systems. Based on this model, we then develop estimation, inference and prediction algorithms for various applications.

Hybrid Estimation Algorithms

Our research focuses on efficient estimation algorithms for stochastic hybrid systems whose discrete state evolutions depend on the continuous states. We study both stochastic linear hybrid systems and stochastic nonlinear hybrid systems. For stochastic linear systems, we utilize Gaussian mixture to represent the continuous state probability density function\ (pdf) and propagate the pdf by analytical methods. For stochastic nonlinear hybrid systems, we are investigating using a Parzen window method to represent the continuous state pdf, and carry out the pdf propagation by solving the Fokker-Planck equations.

We research in applications of the hybrid estimation algorithm in areas such as aircraft tracking in Air Traffic Control, aircraft trajectory predictions, and fault detections.