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2012 | 22 | 2 | 313-326
Tytuł artykułu

A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.
Rocznik
Tom
22
Numer
2
Strony
313-326
Opis fizyczny
Daty
wydano
2012
otrzymano
2011-03-28
poprawiono
2011-08-19
Twórcy
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
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  • Betts, J.T. (2010). Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd Edn., Society for Industrial and Applied Mathematics, Philadelphia, PA.
  • Biegler, L.T. (2010). Nonlinear Programming. Concepts, Algorithms, and Applications to Chemical Processes, SIAM, Philadelphia, PA.
  • Burger, J. and Pogu, M. (1991). Functional and numerical solution of a control problem originating from heat transfer, Journal of Optimization Theory and Applications 68(1): 49-73.
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  • Chin, C.M. and Fletcher, R. (2003). On the global convergence of an SLP-filter algorithm that takes EQP steps, Mathematical Programming 96(1): 161-177.
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  • Christofides, P.D. (2001). Nonlinear and Robust Control of PDE Systems: Methods and Applications to Transport-Reaction Processes, Birkhauser, Boston, MA.
  • Conn, A.R., Gould, N. I. and Toint, P.L. (2000). Trust-Region Methods, MPS-SIAM Series on Optimization, SIAM, Philadelphia, PA.
  • Demetriou, M.A. and Kazantzis, N. (2004). A new actuator activation policy for performance enhancement of controlled diffusion processes, Automatica 40(3): 415-421.
  • El-Farra, N.E., Armaou, A. and Christofides, P.D. (2003). Analysis and control of parabolic PDE systems with input constraints, Automatica 39(3): 715-725.
  • Fattorini, H.O. (1999). Infinite Dimensional Optimization and Control Theory, Cambridge University Press, Cambridge.
  • Fletcher R. and Leyffer, S. (2002). Nonlinear programming without a penalty function, Mathematical Programming, Series A 91(2): 239-269.
  • Fletcher, R., Leyffer, and Toint, P.L. (2002a). On the global convergence of a filter-SQP algorithm, SIAM Journal on Optimization 13(1): 44-59.
  • Fletcher R., Gould, N.I.M., Leyffer, S., Toint, Ph.L. and Wachter, A. (2002b). Global convergence of trust-region SQP-filter algorithms for general nonlinear programming, SIAM Journal on Optimization 13(3): 635-659.
  • Fletcher, R. (2010). The sequential quadratic programming method, in G. Di Pillo and F. Schoen (Eds.), Nonlinear Optimization, Lecture Notes in Mathematics, Vol. 1989, Springer-Verlag, Berlin/Heidelberg.
  • Han, J. and Papalambros, P.Y. (2010). An SLP Filter algorithm for probabilistic analytical target cascading, Structural and Multidisciplinary Optimization 41(5): 935-945.
  • Hinze, M., Pinnau, R., Ulbrich, M. and Ulbrich S. (2009). Optimization with PDE Constraints, Springer, Berlin/Heidelberg.
  • Lasiecka, I. and Triggiani, R. (2000). Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Vol. I: Abstract Parabolic Systems, Vol. II: Abstract Hyperbolic-Like Systems over a Finite Time Horizon, Encyclopedia of Mathematics and Its Applications, Vol. 74, Cambridge University Press, Cambridge.
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  • Lasiecka, I. and Chueshow I. (2008). Long-time Behavior of Second Order Evolution Equations with Nonlinear Damping, Memoirs of the American Mathematical Society, Philadephia, PA.
  • Li, D. (2006). A new SQP-filter method for solving nonlinear programming problems, Journal of Computational Mathematics 24(5): 609-634.
  • Nie, P. and Ma, C. (2006). A trust-region filter method for general non-linear programming, Applied Mathematics and Computation 172(2): 1000-1017.
  • Nettaanmaki P. and Tiba, D. (1994). Optimal Control of Nonlinear Parabolic Systems, Marcel Dekker, New York, NY.
  • Nocedal J. and Wright, S.J. (2006). Numerical Optimization, Springer, Berlin/Heidelberg.
  • Perona, P. and Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7): 629-639.
  • Rafajłowicz, E. (2008). Testing homogeneity of coefficients in distributed systems with application to quality monitoring, IEEE Transactions on Control Systems Technology 16: 314-321.
  • Rafajłowicz, E. and Rafajłowicz, W. (2010). Testing (non-)linearity of distributed-parameter systems from a video sequence, Asian Journal of Control 12(2): 453-461.
  • Schittkowski, K. (2002). Numerical Data Fitting in Dynamical Systems; A Practical Introduction with Applications and Software, Applied Optimization, Vol. 77, Kluwer Academic Publishers, Dordrecht.
  • Schittkowski, K. (2009). An active set strategy for solving optimization problems with up to 200,000,000 nonlinear constraints, Applied Numerical Mathematics 59(12): 2999-3007.
  • Shen, C., Xue, W. and Pu, D. (2009). Global convergence of a tridimensional filter SQP algorithm based on the line search method, Applied Numerical Mathematics 59(2): 235-250.
  • Shen, C., Xue, W. and Chen, X. (2010). Global convergence of a robust filter SQP algorithm, European Journal of Operational Research 206(1): 34-45.
  • Skowron, M. and Styczeń, K., (2009). Evolutionary search for globally optimal stable multicycles in complex systems with inventory couplings, International Journal of Chemical Engineering, Article ID 137483, DOI:10.1155/2009/137483.
  • Su, K. and Che, J. (2007). A modified SQP-filter method and its global convergence, Applied Mathematics and Computation 194(1): 92-101.
  • Su, K. and Yu, Z. (2009). A modified SQP method with nonmonotone technique and its global convergence, Computers and Mathematics with Applications 57(2): 240-247.
  • Troltzsch, F. (2010). Optimal Control of Partial Differential Equations. Theory, Methods and Applications, American Mathematical Society Press, Providence, RI.
  • Turco, A. (2010). Adaptive filter SQP, in C. Blum and R. Battiti (Eds.), Learning and Intelligent Optimization, Lecture Notes in Computer Science, Vol. 6073, Springer-Verlag, Berlin/Heidelberg, pp. 68-81.
  • Uciński, D. (2005). Optimal Measurement Methods for Distributed Parameter System Identification, CRC Press, London/New York, NY.
  • Ulbrich, S. (2004). On the superlinear local convergence of a filter-SQP method, Mathematical Programming, Series B 100(1): 217-245.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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