James B. Rawlings Research Group


Matt Tenny
B.S. Ch.E., Rice University
B.A. Computational & Applied Mathematics, Rice University
Ph.D., University of Wisconsin-Madison, 2002
tenny[AT]bevo[DOT]che[DOT]wisc[DOT]edu

Current Work

Example of a system that demonstrates poor control using linear MPC

Model predictive control (MPC) uses models and optimization strategies in real time to determine control actions. Because of the demand for real-time solution, the optimization methods need to be efficient. This requirement poses a challenge when the models are nonlinear.

The goal of this project is to determine which optimization strategies are best suited for MPC, and how the best optimization strategies can be tailored to the structure of the MPC problem to make it possible to solve nonlinear models in real time.

The straightforward application of MPC to systems with nonlinear models requires global solution of non-convex nonlinear optimization problems, a difficult task even with the technology available today. It is worth further exploring the MPC approach, however, because first-principles models of chemical processes are usually nonlinear, and because the MPC formulation allows constraints in the model.

In earlier work (Rao, Wright, Rawlings, 1997; Wright, 1996), we showed how an interior-point method could be tailored to the MPC problem with a linear model. In our research, we extend the reach of the interior-point approach to nonlinear models. We investigate solving the nonlinear problem by sequential quadratic programming (SQP) methods, which yield specially structured quadratic programs at each iteration.

We consider suboptimal control, which requires only that the cost function decrease with time. This method removes terminal state constraints and the need for global optimization and greatly eases the resulting optimization problems. During our investigation, we examine methods for generating feasible suboptimal control policies for real-time nonlinear implementation.

Structure of an MPC regulator problem

State estimation is another issue involved in MPC. In the case of nonlinear models, the extended Kalman filter (EKF) is often employed. However, the EKF may produce poor estimates, leading to closed-loop instability. Moving horizon estimation (MHE) is an optimization-based method that is superior to the EKF because of its ability to incorporate constraints on estimates and its proper usage of the nonlinear model. Further, MHE has a structure similar to nonlinear MPC. In our research, we apply our knowledge of the control system to MHE to develop a numerically efficient structured nonlinear estimator.

Combining these two tools, we propose to develop a prototype algorithm for the study of nonlinear control systems as well as a suite of nonlinear benchmark examples.

Publications

1
Matthew J. Tenny, James B. Rawlings, and Stephen J. Wright.
Closed-loop behavior of nonlinear model predictive control.
AIChE J., 50(9):2142-2154, September 2004.

2
Matthew J. Tenny, Stephen J. Wright, and James B. Rawlings.
Nonlinear model predictive control via feasibility-perturbed sequential quadratic programming.
Comp. Optim. Appl., 28(1):87-121, April 2004.

3
Matthew Jeremy Tenny.
Computational Strategies for Nonlinear Model Predictive Control.
PhD thesis, University of Wisconsin-Madison, June 2002.

4
Matthew J. Tenny and James B. Rawlings.
Efficient moving horizon estimation and nonlinear model predictive control.
In Proceedings of the American Control Conference, pages 4475-4480, Anchorage, Alaska, May 2002.

5
S. J. Wright and M. J. Tenny.
A feasible trust-region sequential quadratic programming algorithm.
Optimization Technical Report 02-05, University of Wisconsin-Madison, Computer Sciences Departments, August 2002.
Also Texas-Wisconsin Modeling and Control Consortium Report TWMCC-2002-01.

6
M. J. Tenny, S. J. Wright, and J. B. Rawlings.
Nonlinear model predictive control via feasibility-perturbed sequential quadratic programming.
Optimization Technical Report 02-06, University of Wisconsin-Madison, Computer Sciences Departments, August 2002.
Also Texas-Wisconsin Modeling and Control Consortium Report TWMCC-2002-02.

7
Matthew J. Tenny, James B. Rawlings, and Rahul Bindlish.
Feasible real-time nonlinear model predictive control.
In James B. Rawlings, Babatunde A. Ogunnaike, and John W. Eaton, editors, Chemical Process Control-VI: Sixth International Conference on Chemical Process Control, pages 433-437, Tucson, Arizona, January 2001. AIChE Symposium Series, Volume 98, Number 326.

8
Matthew J. Tenny and James B. Rawlings.
State estimation strategies for nonlinear model predictive contrtol.
Annual AIChE Meeting, Reno, Nevada, November 2001.

Personal Web Page: jbrwww.che.wisc.edu/~tenny

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University of Wisconsin
Department of Chemical Engineering
Madison WI 53706