James B. Rawlings Research Group

Rolf H. Findeisen
M.S. Ch.E., University of Wisconsin-Madison, 1997


Rolf H. Findeisen.
Suboptimal nonlinear model predictive control.
Master's thesis, University of Wisconsin-Madison, February 1997.

Thesis Abstract

Suboptimal nonlinear model predictive control.

In this work we consider the nonlinear model predictive control problem. The success of model predictive control for constrained linear systems is largely due to the fact that the resulting on-line optimization problem is a quadratic program for which reliable solution methods exist. However, most of the existing model predictive control algorithms for nonlinear systems require the exact global solution of a non-convex nonlinear optimization problem to guarantee stability. In addition, most algorithms force the system to reach the origin after the end of the prediction horizon to guarantee a feasible solution at the next step. Even with state-of-the-art optimization algorithms, this seems to be practically impossible in finite time. Therefore it is important to modify the existing nonlinear model predictive algorithms to facilitate the solution of the resulting online optimization problem.

The first part of this thesis contains a review of the existing Model Predictive Control concepts for linear and nonlinear systems. We will see that for the nonlinear case controllers have been proposed, that overcome some of the stated problems. They permit feasible suboptimal solutions and allow the last prediction state to lie in a region instead of constraining it to zero. This can simplify the optimization problem significantly, however it is often difficult to check a priori if prerequisite assumptions are satisfied or if additional information for the algorithm must be provided.

In this thesis we propose a suboptimal model predictive control scheme for a specific class of nonlinear systems, namely systems for which the linearized system around the origin is stabilizable. This controller removes the terminal state constraint and requires only that we find solutions that are feasible and decrease the cost function. This scheme provides an asymptotically stabilizing controller while reducing the computational cost. An algorithm that uses a special optimizer that guarantees descent feasible sub steps is outlined.

In summary, this thesis reviews the state of model predictive control for nonlinear systems and proposes a new model predictive control algorithm that does not demand the global solution of a non-convex nonlinear optimization problem. This leads to a computationally more practical model predictive control algorithm.

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University of Wisconsin
Department of Chemical Engineering
Madison WI 53706