James B. Rawlings Research Group


Peter K. Findeisen
M.S. Ch.E., University of Wisconsin-Madison, 1997

Publications

1
Peter K. Findeisen.
Moving horizon estimation of discrete time systems.
Master's thesis, University of Wisconsin-Madison, July 1997.

Thesis Abstract

Moving horizon state estimation of discrete time systems.

This work considers the moving horizon estimation (MHE) problem. Most of todays applied or developed control schemes assume that the state of the controlled system is know explicitly. In reality the system states often cannot be measured directly; instead, they must be estimated from available output measurements. The traditional state estimation approach for linear systems under the influence of noise is the Kalman Filter (KF). However, this approach does not allow to consider constraints on the noise terms or the states, that could improve the estimates. Also the extension to nonlinear systems is not possible without linearization or other approximations.

A class of estimation methods that seem to offer solutions to these problems is the moving horizon estimation (MHE) methods. These methods can be motivated as the dual formulation of model predictive control (MPC) for state estimation. Most of the proposed MHE schemes place special assumptions on the weights and initial values in order to guarantee stability. Often this is done to allow the use of stability results of the KF. This work tries to establish stability conditions without using the corresponding KF results, thus allowing a broader and wider variety of weighting matrices and initial values.

This work offers contributions in three different areas. It contains an extensive review of the existing moving horizon estimation concepts for linear and nonlinear systems. It shows that most stability proofs for linear MHE schemes are based on KF properties. If nonlinear systems are considered this approach is in general not possible, which explains the existence of so few NMHE algorithms with stability guarantee.

The second part derives and shows some important results and properties for linear unconstrained MHE concepts. Especially the connections between the KF, the Batch estimator and MHE are clarified. Then stability conditions for general initial weights and initial estimates for the linear unconstrained MHE are derived. These results partly coincide with dual results found for the finite horizon linear quadratic regulator. Simulations and examples are presented to clarify that the tuning of the resulting algorithms is not always intuitive. This is similar to the finite horizon LQR or the MPC without final zero endpoint constraint. Additionally some preliminary results about possible cost-functions are presented, which opens the possibility to derive more general stability results for constrained estimations problems.

As a final contribution, a toolbox allowing the easy simulation and inclusion of MHE in closed loop simulations is provided. All of the examples presented in this work where generated using this toolbox. This toolbox allows one to examine conveniently new proposed MHE algorithms and concepts.

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University of Wisconsin
Department of Chemical Engineering
Madison WI 53706