Ralf Hannemann-Tamás

An iterative partition-based moving horizon estimator with coupled inequality constraints

We propose an iterative, partition-based moving horizon state estimator for large-scale linear systems that consist of interacting subsystems. Every subsystem estimates its own state and disturbance variables, taking into account the estimates received from neighboring subsystems. Compared to other partition-based moving horizon estimators, the proposed method has two unique features: it can handle coupled inequality constraints on the estimated variables and its state estimates come arbitrarily close to the optimal state estimates of a centralized moving horizon estimator. The applicability and performance of the proposed method are demonstrated on a numerical example and convergence and asymptotic stability are rigorously proven.

Robust dynamic optimization of batch processes under parametric uncertainty: Utilizing approaches from semi-infinite programs

Abstract The optimal solution in dynamic optimization of batch processes often exhibits active path constraints. The goal of this work is the robust satisfaction of path constraints in the presence of parametric uncertainties based on known worst-case formulations. These formulations are interpreted as semi-infinite programs (SIP). Two known SIP algorithms are extended to the dynamic case and assessed. One is a discretization approach and the other a local reduction approach. With these presented concepts, robust path constraint satisfaction is in principle guaranteed. In this work, however, local methods are used to approximate the global solution of the lower-level problem with local solvers thus allowing for (rather unlikely) constraint violations. Finally, the penicillin fermentation is introduced as a well-known case study with uncertainties, which is modified in this work by adding further dependencies. The adaptation of the SIP concepts to dynamic optimization problems are shown to be successful for this case study.

Adjoint Sensitivity Analysis for Nonsmooth Differential-Algebraic Equation Systems

An adjoint sensitivity method is presented for nonsmooth semiexplicit differential-algebraic equation systems (NDAEs) of index 1. The adjoint sensitivity system is derived for a generalization of Mayer-type functionals subject to NDAE constraints. Opposed to classical Mayer-type functionals that depend on the differential and algebraic variables evaluated only at the initial and final times, the generalization depends additionally on the evaluation at multiple interior time points. The derived adjoint sensitivity method extends and builds on the method for smooth DAEs by Cao et al. [SIAM J. Sci. Comput., 24 (2003), pp. 1076--1089] and on the method for nonsmooth ODEs by Ruban [J. Comput. Systems Sci. Internat., 36 (1997), pp. 536--542].