Data-based techniques to improve state estimation in model predictive control

Specifying the state estimator in model predictive control (MPC) requires separate knowledge of the disturbances entering the states and the measurements, which is usually lacking. In this dissertation, we develop the Autocovariance Least-Squares (ALS) technique which uses the correlations between routine operating data to form a least-squares problem to estimate the covariances for the disturbances. The ALS technique guarantees positive semidefinite covariance estimates by solving a semidefinite programming (SDP) problem. Many efficient algorithms for solving SDPs are available in the literature. New and simple necessary and sufficient conditions for the uniqueness of the covariance estimates are presented. We also formulate the optimal weighting to be used in the least-squares objective in the ALS technique to ensure minimum variance in the estimates. A modification to the above technique is then presented to estimate the stochastic disturbance structure and the minimum number of disturbances required to represent the data.; Simplifications to the ALS technique are presented to facilitate implementation. It is also shown that the choice of the disturbance model in MPC does not affect the closed-loop performance if appropriate covariances are used in specifying the state estimator. The ALS technique is used to estimate the appropriate covariances regardless of the plant's true unknown disturbance source and the resulting estimator gain is shown to compensate for an incorrect choice of the source of the disturbance.; The parallels between the ALS technique and the maximum likelihood estimation (MLE) technique are shown by formulating the MLE as an equivalent ALS optimization with a particular choice for the weighting in the ALS objective.; An industrial application of the ALS technique on a nonlinear blending drum model and industrial operating data is described and the results are shown to give improved state estimates as compared to rough industrial estimates for the covariances.; Moving horizon estimator (MHE) and particle filters (PF) are two common state estimators used with nonlinear models. We present a novel hybrid of the MHE with the PF to combine the advantages of both techniques. The improved performance of the hybrid MHE/PF technique is illustrated on an example.