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
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Example of a system that demonstrates poor control using linear MPC
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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.
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Structure of an MPC regulator problem
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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.
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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.
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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.
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Matthew Jeremy Tenny.
Computational Strategies for Nonlinear Model
Predictive Control.
PhD thesis, University of Wisconsin-Madison, June 2002.
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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.
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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.
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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.
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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.
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Matthew J. Tenny and James B. Rawlings.
State estimation strategies for nonlinear model predictive contrtol.
Annual AIChE Meeting, Reno, Nevada, November 2001.
University of Wisconsin
Department of Chemical Engineering
Madison WI 53706
