## Hybrid Systems NSF

### Hybrid Systems Modeling

Hybrid system is a class of systems which incorporates both discrete dynamics and continuous dynamics. In a hybrid system, the discrete dynamics and continuous dynamics are intertwined with each other. Normally, the continuous evolution influences the discrete evolution, by the definition of guard conditions. On the other hand, the continuous evolution is ruled by different discrete states. Compared with conventional models, the hybrid system is more general and more complex. This model can be applied to model the systems with switching control law, nonlinear dynamics, time-varying parameters, etc. read more

### Hybrid Estimation

The problem of hybrid estimation involves estimating both continuous state and discrete state of a hybrid system. This problem proves to be challenging: if we do not know the discrete state transition history, the evolution of a hybrid system involves exponentially increasing computational complexity, which is often referred to as a growing hypothesis tree. This fact makes "optimal estimation" of the hybrid system computationally prohibitive. Therefore, a primary issue that most hybrid estimation algorithms are faced with is how to reduce the number of the hypotheses to an acceptable amount. read more

### Optimal Control

In this research, we propose an algorithm that generates an optimal sequence of flight modes which minimizes a given cost function while satisfying constraints. Each flight mode has its own dynamics so that the flight dynamics of an aircraft has the characteristics of a hybrid system. The control input for the hybrid system includes a mode schedule which has two components, a mode sequence and switching times, and a continuous input for each mode. read more

### Cyber Security Analysis of Cyber-Physical-Systems (CPSs)

Cyber security has emerged as one of the most important issues in the operation of CPSs due to their heavy reliance on the automation and network communications. As the first step to implement a CPS that is robust to possible cyber attacks, we have conducted a study to identify potential cyber threats and vulnerabilities inherent in the given CPS. read more

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