James B. Rawlings Research Group
Matt Tenny
B.S. Ch.E., Rice University B.A. Computational & Applied Mathematics, Rice University Ph.D., University of WisconsinMadison, 2002
tenny[AT]bevo[DOT]che[DOT]wisc[DOT]edu


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
realtime 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 nonconvex nonlinear optimization
problems, a difficult task even with the technology available today.
It is worth further exploring the MPC approach, however, because
firstprinciples 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 interiorpoint method could be tailored to the MPC problem with
a linear model. In our research, we extend the reach of
the interiorpoint 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 realtime 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 closedloop
instability. Moving horizon estimation (MHE) is an optimizationbased
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.
 1

Matthew J. Tenny, James B. Rawlings, and Stephen J. Wright.
Closedloop behavior of nonlinear model predictive
control.
AIChE J., 50(9):21422154, September 2004.
 2

Matthew J. Tenny, Stephen J. Wright, and James B. Rawlings.
Nonlinear model predictive control via
feasibilityperturbed sequential quadratic
programming.
Comp. Optim. Appl., 28(1):87121, April 2004.
 3

Matthew Jeremy Tenny.
Computational Strategies for Nonlinear Model
Predictive Control.
PhD thesis, University of WisconsinMadison, 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
44754480, Anchorage, Alaska, May 2002.
 5

S. J. Wright and M. J. Tenny.
A feasible trustregion sequential quadratic programming algorithm.
Optimization Technical Report 0205, University of WisconsinMadison,
Computer Sciences Departments, August 2002.
Also TexasWisconsin Modeling and Control Consortium Report
TWMCC200201.
 6

M. J. Tenny, S. J. Wright, and J. B. Rawlings.
Nonlinear model predictive control via feasibilityperturbed
sequential quadratic programming.
Optimization Technical Report 0206, University of WisconsinMadison,
Computer Sciences Departments, August 2002.
Also TexasWisconsin Modeling and Control Consortium Report
TWMCC200202.
 7

Matthew J. Tenny, James B. Rawlings, and Rahul Bindlish.
Feasible realtime nonlinear model predictive control.
In James B. Rawlings, Babatunde A. Ogunnaike, and John W. Eaton,
editors, Chemical Process ControlVI: Sixth International Conference
on Chemical Process Control, pages 433437, 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.
University of Wisconsin
Department of Chemical Engineering
Madison WI 53706