33 KJEMI 2 2026 Faculty of Natural Sciences, NTNU, 18. februar 2026 Navn: Simen Bjorvand Veiledere: Main supervisor: Professor Johannes Jäschke - Co-supervisor: Dr. Caroline Satye Nakama Opponenter: First opponent: Professor Moritz Diehl, University of Freiburg, Germany Second opponent: Associate Professor Mario Zanon, IMT School for Advanced Studies Lucca, Italy Chair of the committee: Professor Sebastien Gros, NTNU Tittel på prøveforelesning: Learning value functions and their sensitivities from data — The AI / Reinforcement Learning perspective Tittel på avhandling: Development and Applications of Sensitivity based methods in Process Systems Engineering Sammendrag: In this thesis concepts from sensitivity theory is applied to research problems within process systems engineering. Using parametric nonlinear programming sensitivity theory, a novel approach for calculating the Arrival Cost in Moving Horizon Estimation is presented. Algorithms for solving the robust Multistage Model Predictive Control problem efficiently through primal decomposition is proposed, using concepts from parametric nonlinear programming sensitivity theory, generalized sensitivity theory and nonsmooth equation solving. Moving Horizon Estimation (MHE) refers to an optimization-based state estimation approach where a fixed time horizon of past states are estimated using a horizon of past measurements. The strengths of the MHE is that nonlinear model equations can be incorporated without approximations and that physical insight can easily be implemented as inequality constraints. When a new measurement becomes available the oldest measurement in the horizon is discarded to make room for the new one. To account for discarded measurements a term known as the Arrival Cost is included in MHE optimization problem. This term can be thought of as summarizing all "forgotten" measurements and is represented as prior of the oldest state in the horizon. In this thesis a novel method for calculating the Arrival Cost is presented. By interpreting the MHE as an approximation of the Full Information (FI) problem where no measurements are discarded, the FI problem can be split into two problems, the MHE problem and an Ideal Arrival Cost problem. This Ideal Arrival Cost problem is a parametric Nonlinear Program, and thus by applying parametric nonlinear programming sensitivities it can be approximated. Multistage Model Predictive Control (msMPC) is a robust control formulation that accounts for parametric uncertainty by constructing a set of scenarios for different parameter realizations. The resulting msMPC optimization problem quickly becomes large and expensive to solve. Thus, to allow for real-time implementations the computational time must be kept manageably low. One such approach to reduce computational time are decomposition methods where the problem is divided into smaller subproblems that can be solved simultaneous in parallel. In these algorithms the subproblems are repeatedly resolved while a coordinator algorithm attempts to recover the solution of the original problem. The main computational expense of these algorithms comes from; 1) the coordinator algorithm requiring many iterations to converge resulting in several resolves and 2) the computational time to solve the subproblems. In this thesis these two issues are addressed for a msMPC primal decomposition algorithm. Using parametric Nonlinear Programming sensitivity and nonsmooth equation solving the efficiency of the coordinator algorithm is addressed, and using generalized sensitivity theory and nonsmooth equation solving the computational time of solving the subproblems are addressed. In addition to applying sensitivity concepts to MHE and msMPC, new sensitivity theory which can be applied to researches problems in Process Systems Engineering as well as other fields of applied Mathematics is developed. In the final contribution of the thesis generalized sensitivity theory for nonsmooth discrete-time systems is established. This is done by using a generalized sensitivity tool known as the Lexicographical Directional derivative. With this new theory first order (generalized) derivative information in the form of Lexicographical derivatives can be obtained, that describes the behavior of nonsmooth discrete-time system solutions with respect to parameters.
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