Showing papers by "Hans Georg Bock published in 2009"

Optimal experimental design for parameter estimation of a cell signaling model.

Abstract: Differential equation models that describe the dynamic changes of biochemical signaling states are important tools to understand cellular behavior. An essential task in building such representations is to infer the affinities, rate constants, and other parameters of a model from actual measurement data. However, intuitive measurement protocols often fail to generate data that restrict the range of possible parameter values. Here we utilized a numerical method to iteratively design optimal live-cell fluorescence microscopy experiments in order to reveal pharmacological and kinetic parameters of a phosphatidylinositol 3,4,5-trisphosphate (PIP3) second messenger signaling process that is deregulated in many tumors. The experimental approach included the activation of endogenous phosphoinositide 3-kinase (PI3K) by chemically induced recruitment of a regulatory peptide, reversible inhibition of PI3K using a kinase inhibitor, and monitoring of the PI3K-mediated production of PIP3 lipids using the pleckstrin homology (PH) domain of Akt. We found that an intuitively planned and established experimental protocol did not yield data from which relevant parameters could be inferred. Starting from a set of poorly defined model parameters derived from the intuitively planned experiment, we calculated concentration-time profiles for both the inducing and the inhibitory compound that would minimize the predicted uncertainty of parameter estimates. Two cycles of optimization and experimentation were sufficient to narrowly confine the model parameters, with the mean variance of estimates dropping more than sixty-fold. Thus, optimal experimental design proved to be a powerful strategy to minimize the number of experiments needed to infer biological parameters from a cell signaling assay.

Direct methods with maximal lower bound for mixed-integer optimal control problems

Abstract: Many practical optimal control problems include discrete decisions These may be either time-independent parameters or time-dependent control functions as gears or valves that can only take discrete values at any given time While great progress has been achieved in the solution of optimization problems involving integer variables, in particular mixed-integer linear programs, as well as in continuous optimal control problems, the combination of the two is yet an open field of research We consider the question of lower bounds that can be obtained by a relaxation of the integer requirements For general nonlinear mixed-integer programs such lower bounds typically suffer from a huge integer gap We convexify (with respect to binary controls) and relax the original problem and prove that the optimal solution of this continuous control problem yields the best lower bound for the nonlinear integer problem Building on this theoretical result we present a novel algorithm to solve mixed-integer optimal control problems, with a focus on discrete-valued control functions Our algorithm is based on the direct multiple shooting method, an adaptive refinement of the underlying control discretization grid and tailored heuristic integer methods Its applicability is shown by a challenging application, the energy optimal control of a subway train with discrete gears and velocity limits

Fast Nonlinear Model Predictive Control with an Application in Automotive Engineering

Abstract: Although nonlinear model predictive control has become a well-established control approach, its application to time-critical systems requiring fast feedback is still a major computational challenge. In this article we investigate a new multi-level iteration scheme based on theory and algorithmic ideas from [2], and extending the idea of real-time iterations as presented in [4]. This novel approach takes into account the natural hierarchy of different time scales inherent in the dynamic model. Applications from aerodynamics and chemical engineering have been successfully treated. In this contribution we apply the investigated multi-level iteration scheme to fast optimal control of a vehicle and discuss the computational performance of the scheme.

A minima tracking variant of semi-infinite programming for the treatment of path constraints within direct solution of optimal control problems

Abstract: We present an extension of the direct multiple shooting method for the solution of optimal control problems with path constraints. The extension allows for fully automatic and accurate treatment of path constraints in case of relatively coarse discretizations of the control while maintaining a prescribed resolution of the system dynamics. It is based on a reduction principle from classical theory of semi-infinite programming. On the basis of these theoretical foundations the minima tracking algorithm is designed. We theoretically and numerically compare this method with a sampling technique. The numerical test case is a well-known, difficult space shuttle reentry benchmark problem.

Vorausschauend Planen, Gezielt Handeln — Über Die Regelung Und Steuerung Technischer Prozesse

Abstract: Seit Beginn der industriellen Revolution nimmt die Steuerungs- und Regelungstechnik eine Schlusselstellung in vielen technischen Bereichen ein. James Watts Fliehkraftregler fur Dampfmaschinen ist eines der fruhen Beispiele eines extrem erfolgreichen Reglerkonzepts, von dem Ende der 1860er Jahre geschatzte 75000 Exemplare allein in England im Einsatz waren [2, S. 24]. Etwa um diese Zeit begannen Ingenieure, motiviert durch die immer hohere Komplexitat der zu regelnden Maschinen, sich systematisch mit theoretischen Grundlagen der Regelung zu beschaftigen. Dies fuhrte unausweichlich zu der Einsicht, dass das dynamische Verhalten der geregelten Systeme nur mit Hilfe der Mathematikverstanden und weiterentwickelt werden konnte, oder wie Werner von Siemens, ein weiterer technischer Pionier in diesem Bereich es formulierte: „Ohne Mathematik tappt man doch immer im Dunkeln.“

Real-Time Moving Horizon State and Parameter Estimation for SMB Processes

Abstract: Advances in numerical algorithms have rendered the application of advanced process control schemes feasible for complex chemical processes that are described by high-order first-principles models. Applying real-time iteration schemes reduces the CPU requirement such that rigorous models can be applied that enable a precise forecast of the system behaviour. In this paper, a moving horizon state and parameter estimation scheme for chromatographic simulated moving bed SMB processes is presented. The simultaneous state and parameter estimation is based on a high-order nonlinear SMB model which incorporates rigorous models of the chromatographic columns and the discrete shifting of the inlet and outlet ports. The estimation is performed using sparse measurement information: the concentrations of the components are only measured at the two outlet ports (which are periodically switched) and at one fixed location between two columns. The goal is to reconstruct the full state of the system, i.e. the concentration profiles along all columns, and to identify model parameters reliably. The state estimation scheme assumes a deterministic model within the prediction horizon, state noise is only present in the state and in the parameters prior to and at the beginning of the horizon. The scheme can be applied online. The advantage of this estimation scheme is that it is applicable to all process scenarios encountered during the real operation of an SMB plant, e.g. start up, transition periods, varying flows and switching times, since no model simplification nor a state reduction scheme are applied. Numerical simulations (start up of the SMP process) of a validated model for a separation problem with nonlinear isotherms of the Langmuir type demonstrate the efficiency of the algorithm.