Kinetic Parameter Estimation from Spectroscopic Data for a Multi-Stage Solid-Liquid Pharmaceutical Process

Laboratory and process measurements from spectroscopic instruments are ubiquitous in pharma processes, and directly using the data can pose a number of challenges for kinetic model building. Moreover, scaling up from laboratory to industrial level requires predictive models with accurate parameter values. This means that process identification implies not only kinetic parameter estimation but also the identification of the absorbing species and estimation of variances for both the data and parameters. The recently developed, open-source toolkit KIPET (Short, M.; Schenk, C.; Thierry, D.; Rodriguez, J. S.; Biegler, L. T.; Garcı́a-Muñoz, S. Proceedings of the 9th International Conference on Foundations of Computer-Aided Process Design, 2019, 47, 299; Schenk, C.; Short, M.; Thierry, D.; Rodriguez, J. S.; Biegler, L. T.; Garcı́a-Muñoz, S.; Chen, W. Comput. Chem. Eng.2020, 134, 106716) addresses these topics and provides an alternative to standard parameter estimation packages, in particular for spectroscopic data problems. Moreover, batch processes commonly used in the chemical and pharmaceutical industries involve multiple stages to carry out synthesis operations in a step-by-step manner, often dealing with heterogeneous mixtures, wide operating temperatures, and constant additions and removals of product and waste. For such cases novel modeling approaches are required, as the structure of the kinetic model may vary with time, with model switches that are state dependent. This study presents a new modeling approach and methodology that deals with these practical issues. In developing kinetic models, it approximates the solid dissolution process and deals with multiple stages with different reactor temperatures. Moreover, variances, parameters, concentration, and absorbance profiles are estimated for the process stages using the approach presented by Chen et al. (Chen, W.; Biegler, L. T.; Garcı́a Muñoz, S. J. Chemom.2016, 30, 506). The application of these developed concepts results in realistic profiles as well as reliable kinetic parameter values. The outcomes of this work show that KIPET is a useful toolkit for dealing with pharmaceutical processes with capabilities for dealing with challenging kinetic modeling problems.Funded by Pfizer Inc

Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

A shooting algorithm for problems with singular arcs

In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system) we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated to the perturbed problem. We present numerical tests that validate our method.Comment: No. RR-7763 (2011); Journal of Optimization, Theory and Applications, published as 'Online first', January 201