Keyu Li, Ph.D

Process Systems Engineering Group
Department of Chemical Engineering
Carnegie Mellon University

Doherty Hall, Room 3203
Pittsburgh, PA 15213



Education History

2007 Ph.D., Cleveland State University, Cleveland, USA
1999 - 2003 ???????
Work History
Apr 2007 - 2009 Process Engineer, Industrial Learning Systems, Pittsburgh, PA
Jun 2001 - Jan 2002 R&D Engineer, Sino-Pec. Co., Beijing, China


Research Interests

Passivity-based Adaptive Control

Passivity theory can be introduced into process control area and a passivity-based inventory control strategy has been developed based on the idea that the manipulated variables are chosen so that the selected inventories follow their set points. The adaptive control can also be applied in a framework of passivity-based inventory control, and a feedback-feedforward control structure is built with online adaptation. Certain model parameters are estimated online to construct the adaptive feedforward controller to reject the unmeasured disturbances. This control scheme is shown in the figure below:


Bayesian State Estimation for Nonlinear/Non-Gaussian Systems

For nonlinear state estimation problems, classic methods such as extended Kalman filter (EKF) can not always work well especially when random variables are not Gaussian distributed. As an alternative, moving horizon estimation (MHE) is developed in recent years. It formulates the problem into a nonlinear programming (NLP) problem in a moving window. This method can perform better than EKF, but it is also computational demanding which raises real-time implementation concerns. Based on cell-to-cell mapping algorithm and finite Markov chain, we proposed a novel Bayesian state estimation method – cell filter (CF), which discretizes the probability distribution function (PDF) into the cell space and naturally deals with nonlinear/non-Gaussian systems.

Nonlinear Model Predictive Control in Cell Space 

Nonlinear model predictive control (NMPC) requires repeatedly solving nonlinear regulation and estimation problems online. Cell-to-cell mapping can be used in both regulation and estimation problems. In our work, nonlinear optimal control problem is solved based on simple cell mapping (SCM) algorithm, and generalized cell mapping (GCM) is used to solve estimation problem. This approach approximates the dynamic system as finite Markov chain, and finishes most online computation task offline, which significantly reduces the online work effort, and gives competitive performance for many bench-mark problems.



  • “Bayesian State Estimation of Nonlinear Systems Using Approximate Aggregate Markov Chains”, Ungarala, S., Chen, Z. Z., Li, K., Industrial & Engineering Chemistry Research, vol. 45, iss.12, pp. 4408-4421, 2006
Conference Presentations
  • Adaptive Inventory Control of Superheater Systems”, Li, K., Chan, K. H., and Ydstie, B. E., Accepted by IEEE Power Engineering Society general meeting, Pittsburgh, PA, June 2008
  • Constrained Extended Kalman Filter for Nonlinear State Estimation”, Ungarala, S., Dolence, E. and Li, K., 8th International IFAC Symposium on Dynamics and Control of Process Systems, Vol. 2, pp. 63-68, Cancun, Mexico, June 2007
  • Cell and Iterated Dynamic Programming - a Fast Optimizer for Nonlinear Model Predictive Control”, Li, K. and Ungarala, S., AIChE Annual Meeting, San Francisco, CA, Nov., 2006
  • Novel Density Based State Estimation Methods in Nonlinear Model Predictive Control”, Li, K. and Ungarala, S., AIChE Annual Meeting, Cincinnati, OH, Nov., 2005
  • Optimal Control Using Cell-to-Cell Mapping and Dynamic Programming”, Li, K. and Ungarala, S., AIChE Annual Meeting, Austin, TX, Nov., 2004