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Weiyi Liu



Strongly motivated by the theoretical interests and practical problems, my research interests lie in the complex cyber-physical systems that can be accurately modeled as hybrid systems with both physical and logical elements such as aircraft/spacecraft, unmanned aerial vehicles (UAVs), networked robotics and air traffic control. Defined on the hybrid state space, hybrid systems exhibit interacting continuous and discrete dynamics, usually represented by differential equations and finite state machines, respectively. While the hybrid system has many modeling advantages, its complex dynamics has posed many challenges to control engineering.
My study on hybrid systems has primarily focused on two important fields: hybrid system state estimation (hybrid estimation) and cooperative control of multi-vehicle systems. On the one hand, estimation enables controllers to keep track of the state of dynamical systems with the information from sensor observations. Due to the hybrid dynamics of many aerospace systems and the decentralized allocations of the sensors, my study on the hybrid estimation methodologies and the corresponding sensor scheduling strategies are highly desired.  On the other hand, in multi-vehicle systems, the motions of the vehicles have to be coordinated in such a way that the vehicles can achieve their goals without conflict between them. My research in this area is focused on the optimal coordination of multiple vehicles using stochastic approaches. Specifically, three stages are involved in the study: multi-vehicle probabilistic trajectory prediction, conflict detection and stochastic optimal confl ict res olution. My research on multi-vehicle systems has various applications such as formation flight of aircraft/spacecraft, control of multiple UAVs, and air traffic control. Specifically, I have developed a set of tools for air traffic control, which can potentially improve the efficiency and safety of the current system.


*Journal Articles:

W. Liu and I. Hwang, Probabilistic Aircraft Mid-Air Conflict Resolution Using Stochastic Optimal Control, IEEE Transactions on Intelligent Transportation Systems. 2011. Submitted.

W. Liu and I. Hwang, On Hybrid State Estimation for Stochastic Hybrid Systems, IEEE Transactions on Automatic Control, 2011. Under review.

W. Liu, J. Wei, M. Liang, Y. Cao and I. Hwang, Multi-sensor Data Fusion and Fault Detection for Aircraft Tracking in Air Traffic Control, IEEE Transactions on Aerospace and Electronic Systems, 2011. Under review.

W. Liu and I. Hwang, Stochastic Hybrid System Model with Applications to Aircraft Trajectory Prediction and Conflict Detection, AIAA Journal on Guidance, Dynamics and Control. vol. 34, no. 6, November, 2011.

W. Liu and I. Hwang, Estimation, Fault Detection and Isolation for Stochastic Linear Hybrid Systems with Unknown Fault Input, IET Journal on Control Theory and Applications. vol.5, no.12, pp.1353-1368, August, 2011.

*Conferences and Proceedings:

W. Liu, and I. Hwang, Dynamical Filtering Equations for Stochastic Hybrid System State Estimation. Submitted to the 51th IEEE Conference on Decision and Control, Maui, HI, Dec. 2012.

W. Liu, C. Kwon, I. Aljanabi and I. Hwang, Cyber Security Analysis of Aircraft State Estimators Using an Optimization Approach. Submitted to the 2012 AIAA Guidance Navigation and Control (GNC) Conference, Minneapolis, MN.

J. Goppert, W. Liu, A. Shull, V. Sciandra and I. Hwang, Numerical Analysis of Cyber Attacks on Unmanned Aerial Vehicles. Accepted by the 2012 AIAA InfoTech Conference, Garden Grove, CA.

W. Liu and I. Hwang, Stochastic Hybrid System State Estimation with Applications to Aircraft Tracking for Air Traffic Control, Accepted by the 2012 American Control Conference, Montreal, Canada.

W. Liu and I. Hwang, Probabilistic Aircraft Conflict Resolution: a Stochastic Optimal Control Approach, Accepted by the 2012 American Control Conference, Montreal, Canada.

W. Liu and I. Hwang, Stochastic Approximation with Applications to Event Driven Filtering, In Proceedings of the 50th IEEE Conference on Decision and Control, Orlando, FL, Dec. 2011.

W. Liu and I. Hwang, Optimal Sensor Scheduling Algorithm for Hybrid Estimation, In Proceedings of the 2011 American Control Conference, San Francisco, CA, Jul. 2011.

W. Liu and I. Hwang, Intent-Based Probabilistic Trajectory Prediction and Conflict Detection for Air Traffic Control, In Proceedings of the 49th IEEE Conference on Decision and Control, Atlanta, GA, Dec. 2010. 

W. Liu and I. Hwang, Robust Estimation Algorithm for A Class of Hybrid Systems with Unknown Continuous Fault Inputs, In Proceedings of the 2010 American Control Conference, Baltimore, MD, USA, Jun. 2010.

W. Liu, C.-E.Seah and I. Hwang, Estimation Algorithm for Stochastic Linear Hybrid Systems with Quadratic Guard Conditions, In Proceedings of the 48th IEEE Conference on Decision and Control, Shanghai, China, Dec. 2009.

Z. Fu, M. Yuan, D. Sun and W. Liu, Research on Piezoelectric Sensor Array in Structural Health Monitoring, In Proceedings of the 7th Symposium on Instrumentation and Control Technology, Beijing, China, 2008.


  • Purdue University, West Lafayette, IN Ph.D. in Aeronautics and Astronautics Major 2008.8 - present
  • Research topic: Estimation, optimization and control for hybrid systems with applications to air traffic surveillance and management.
  • M.S. in Applied Mathematics Minor 2010.1 - 2012.5 Research topic: Mathematical statistics, probability theory, stochastic processes and stochastic differential equations with applications to computational finance.
  • Beijing University of Aeronautics and Astronautics (BUAA), Beijing, China
  • B.S. in Electrical Engineering (graduated with distinction) 2003.9 - 2007.6


Graduate student, School of Aeronautics and Astronautics, Purdue University


Office: ARMS 3132

Personal webpage:

Useful Links

The art of hybrid systems:


Convex optimization:

An intro to SDE:

An intro to Bayesian analysis:

Stochastic process:

Estimation with application to tracking and navigation:

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