James B. Rawlings Research Group


Chris Rao
Ph.D., University of Wisconsin-Madison, 2000

Publications

1
Christopher V. Rao, James B. Rawlings, and David Q. Mayne.
Constrained state estimation for nonlinear discrete-time systems: Stability and moving horizon approximations.
IEEE Trans. Auto. Cont., 48(2):246-258, February 2003.

2
Christopher V. Rao and James B. Rawlings.
Constrained process monitoring: A moving horizon approach.
AIChE J., 48(1):97-109, January 2002.

3
Christopher V. Rao, James B. Rawlings, and Jay H. Lee.
Constrained linear state estimation - a moving horizon approach.
Automatica, 37(10):1619-1628, 2001.

4
David Q. Mayne, James B. Rawlings, Christopher V. Rao, and Pierre O. M. Scokaert.
Constrained model predictive control: Stability and optimality.
Automatica, 36(6):789-814, 2000.

5
Chritopher V. Rao and James B. Rawlings.
Linear programming and model predictive control.
J. Proc. Cont., 10:283-289, 2000.

6
Christopher V. Rao and James B. Rawlings.
Nonlinear moving horizon estimation.
In Frank Allgöwer and Alex Zheng, editors, Nonlinear Model Predictive Control, volume 26 of Progress in Systems and Control Theory, pages 45-69, Basel, 2000. Birkhäuser.

7
Christopher V. Rao.
Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems.
PhD thesis, University of Wisconsin-Madison, February 2000.

8
Christopher V. Rao and James B. Rawlings.
Steady states and constraints in model predictive control.
AIChE J., 45(6):1266-1279, June 1999.

9
Christopher V. Rao, James B. Rawlings, and Jay H. Lee.
Stability of constrained linear moving horizon estimation.
In Proceedings of American Control Conference, San Diego, CA, pages 3387-3391, June 1999.

10
Christopher V. Rao, Stephen J. Wright, and James B. Rawlings.
On the application of interior point methods to model predictive control.
J. Optim. Theory Appl., 99:723-757, 1998.

11
Christopher V. Rao, Stephen J. Wright, and James B. Rawlings.
Efficient interior point methods for model predictive control.
Preprint ANL/MCS-P644-0597, Mathematics and Computer Science Division, Argonne National Laboratory, June 1997.

12
Christopher V. Rao, John C. Campbell, James B. Rawlings, and Stephen J. Wright.
Efficient implementation of model predictive control for sheet and film forming processes.
In Proceedings of the American Control Conference, Albuquerque, NM, pages 2940-2944, 1997.

13
Christopher V. Rao and James B. Rawlings.
Constrained process monitoring: A moving horizon perspective.
Annual AIChE Meeting, Dallas, Texas, November 1999.

14
Christopher V. Rao and James B. Rawlings.
Robust model predictive control: Game theory and output feedback.
Annual AIChE Meeting, Dallas, Texas, November 1999.

15
Christopher V. Rao and James B. Rawlings.
Optimization strategies for linear model predictive control.
In Proceedings of the 1998 IFAC DYCOPS Symposium, Corfu, Greece, 1998.

16
Christopher V. Rao and James B. Rawlings.
Stability of moving horizon estimation.
Annual AIChE Meeting, Miami, Florida, November 1998.

17
Christopher V. Rao and James B. Rawlings.
Optimal experimental design for feedback systems.
Annual AIChE Meeting, Chicago, Illinois, November 1996.

Thesis Abstract

Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems

The rational design of process monitoring and control systems requires the solution of dynamic programs. With a few notable exceptions, dynamic programs are difficult, in not impossible, to solve. The difficulty arises in what Bellman called the `curse of dimensionality': the computational complexity scales exponentially in the problem dimensions. One approximate strategy that circumvents the computational difficulties associated with dynamic programming while still retaining many desirable properties is the moving horizon approximation. Moving horizon approximations are optimization based strategies that approximate the dynamic program with a series of open-loop optimal control problems. Unlike other strategies, moving horizon approximations can handle explicitly nonlinear differential algebraic equations and inequality constraints. In this dissertation, we investigate the moving horizon approximation for the constrained process monitoring (moving horizon estimation) and control (model predictive control) of nonlinear discrete-time systems. A framework is proposed for analyzing the stability properties of the moving horizon approximation. This framework allows us to derive sufficient conditions for stability and propose practical algorithms for online implementation.

In addition to the theoretical results, practical issues regarding constraints, computation, and robustness are studied. We discuss issues regarding inequality constraints in process monitoring. By incorporating prior knowledge in the form of inequality constraints, one can significantly improve the quality of state estimates for certain problems. We demonstrate how inequality constraints provide a flexible tool for complementing process knowledge and a strategy also for model simplification. For control, techniques are developed for handling inequality constraints active at steady state, a case that has not been treated in previous model predictive control theory

Computational issues are addressed. Stable suboptimal algorithms for constrained estimation and control are proposed that do not require an optimal solution: rather, a feasible solution suffices. Issues related to formulating model predictive control as a linear program are discussed. A computationally efficient interior point algorithm is developed for the model predictive control of large process systems. The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We also investigate strategies for further decomposing the problem structure in sheet and film forming processes.

The issue of output feedback and robustness are addressed by formulating MPC as a dynamic game. The game formulation allows us to obtain a separation for output feedback and prove that the closed-loop system has finite $l_2$-gain. Furthermore, the added cost associated with formulating MPC as a dynamic game is negligible; the resulting problem is a quadratic program, though the optimization problem is no longer sparse. These results are extremely conservative, however, and limitations of the proposed strategy are discussed.

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

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University of Wisconsin
Department of Chemical Engineering
Madison WI 53706