(473b) Constrained Multi-Rate State Estimation Using NLP Sensitivity-Based Moving Horizon Estimation

Constrained Multi-Rate State Estimation using NLP Sensitivity-Based Moving Horizon Estimation

Model based control schemes, such as nonlinear model predictive control, assume that the full state vector is known for feedback control. However, in reality this is not always true. Most times only a set of noisy measurements are available, and thus, the unmeasured states need to be inferred from these measurements.  Moreover, in most chemical processes, some state variables (e.g., concentrations, molecular weights, etc.) can be measured infrequently and, probably, with some time delay. The information provided by these infrequent measurements can aid the estimation process, and therefore multi-rate state estimators have been developed. Moving Horizon Estimation (MHE) provides a framework that allows to easily incorporate these infrequent observations because it uses a window of past measurements, where the slower ones can be introduced as they become available. Also, MHE is a preferred method for state estimation because it also allows the use of bounds and constraints on the state estimates that help the performance of the estimator.

Nonlinear Programming (NLP) sensitivity based MHE method has also been developed called advanced-step MHE (as-MHE). This method solves an MHE problem offline using approximated measurements, and when the new measurement becomes available a quick NLP sensitivity based correction is done to the offline solution. These sensitivity-based techniques also allow us to extract the reduced Hessian information from interior point NLP solvers that do not generally form them as part of the solution strategy. Furthermore, it is possible to show that the inverse of the reduced Hessian provides a good approximation of the covariance of the estimated states. Thus, this strategy also allows us to approximate the covariance of the state estimates at the beginning of the horizon. Therefore, it is possible to generate a fast approximation of the arrival cost covariance, as well. In this work we develop an as-MHE strategy to handle multi-rated measurements, and that takes advantage of NLP sensitivity to reduce the computational expense of the online estimation process. The proposed methodology is illustrated using benchmark examples from the literature.

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