Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 2 | 405--411
Tytuł artykułu

3-D filter SQP method for optimal control of the multistage differential-algebraic systems with inconsistent initial values

Warianty tytułu
Języki publikacji
In the article a new approach for solving complex and highly nonlinear differential-algebraic equations (DAEs) was presented. An important kind of applications of DAE systems is modeling of biotechnological processes, which can have a very different course. An efficient solving of equations describing biotechnological industrial inlets results in better optimization of the processes and has a positive impact on the environment. Some of the mentioned processes were characterized by a highly nonlinear dynamics. To obtain the trajectories of the state numerically, the backward differentiation formula was used in the presented method. As a result, a large-scale system of nonlinear algebraic equations was obtained. To solve a such system, the inexact Newton matrix-free approach was proposed. The new algorithm was tested on a mathematical model of a fed-batch fermentor for penicillin production. The numerical simulations were executed in MATLAB using Wroclaw Center for Networking and Supercomputing.(original abstract)
Opis fizyczny
  • Wrocław University of Technology
  • Wrocław University of Technology
  • Audet C., Dennis Jr J. E.. 2004. A pattern search filter method for nonlinear programming without derivatives. SIAM Journal on Optimization. 14:980-1010,
  • Banga J. R., Balsa-Canto E., Moles C. G., Alonso A. A.. 2005. Dynamic optimization of bioprocesses: Efficient and robust numerical strategies. Journal of Biotechnology. 117:407-419,
  • Betts J. T.. 2010. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Second Edition. SIAM, Philadelphia,
  • Biegler L. T.. 2010. Nonlinear Programming. Concepts, Algorithms and Applications to Chemical Processes. SIAM, Philadelphia,
  • Bielger L. T., Campbell S., Mehrmann V.. 2012. DAEs, Control, and Optimization. Control and Optimization with Differential-Algebraic Constraints. SIAM, Philadelphia,
  • Brenan K. E., Campbell S. L., Petzold L. R.. 1996. Numerical Solution of Initial- Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia,
  • Diehl M., Bock H. G., Schloder J. P., Findeisen R., Nagy Z., Allgower F.. 2002. Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations. Journal of Process Control. 12:577-585,
  • Drąg P., Styczeń K.. 2012. A Two-Step Approach for Optimal Control of Kinetic Batch Reactor with electroneutrality condition. Przegląd Elektrotechniczny. 6:176-180.
  • Fletcher R., Gould N. I. M., Leyffer S., Toint P. L., Watcher A. 2002. Global convergence of a trust region SQP-filter algorithms for general nonlinear programming. SIAM Journal on Optimization. 13:635-659,
  • Fletcher R., Leyffer S. 2002. Nonlinear programming without a penalty function. Mathematical Programming. 91:239-269,
  • Fletcher R., Leyffer S., Toint P. L. 2002. On the global convergence of a Filter-SQP algorithm. SIAM Journal on Optimization. 13:44-59,
  • Gould N. I. M., Leyffer S., Toint P. L. 2004. A multidimensional filter algorithm for nonlinear equations and nonlinear least squares. SIAM Journal on Optimization. 15:17-38,
  • Gould N. I. M., Sainvitu C., Toint P .L. 2005. A filter trust region method for unconstrained optimization. SIAM Journal on Optimization. 16:341-357,
  • Kwiatkowska M. 2012. Antimicrobial PVC composites. Processing technologies and functional properties of polymer nanomaterials for food packaging : International COST Workshop, Wroclaw, Poland, September 11-12, 2012, pp. 40-41.
  • Nocedal J, Wright S. J. 2006. Numerical Optimization. Second Edition. Springer, New York,
  • Rafajłowicz E., Styczeń K., Rafajłowicz W. 2012. A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics. Int. J. Appl. Math. Comput. Sci. 22:313-326,
  • Shen C., Xue W., Pu D. 2009. Global convergence of a tri-dimensional filter SQP algorithm based on the line search method. Applied Numerical Mathematics. '59:235-250,
  • Ulbrich M., Ulbrich S., Vicente L. N.. 2004. A globally convergent primal-dual interior filter method for nonconvex nonlinear programming. Mathematical Programming. 100:379-410,
  • Vassiliadis V. S., Sargent R. W. H., Pantelides C. C. 1994. Solution of a Class of Multistage Dynamic Optimization Problems. 1. Problems without Path Constraints. Ind. Eng. Chem. Res. 33:2111-2122,
  • Watcher A., Biegler L. T. 2005. Line search filter methods for nonlinear programming: Motivation and global convergence. SIAM Journal on Optimization. 16: 1-31,
  • Watcher A., Biegler L. T. 2005. Line search filter methods for nonlinear programming: Local convergence. SIAM Journal on Optimization. 16:32-48,
Typ dokumentu
Identyfikator YADDA

Zgłoszenie zostało wysłane

Zgłoszenie zostało wysłane

Musisz być zalogowany aby pisać komentarze.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.