Bidirectional branch and bound for controlled variable selection. Part II: Exact local method for self-optimizing control

Abstract The selection of controlled variables (CVs) from available measurements through enumeration of all possible alternatives is computationally forbidding for large-dimensional problems. In Part I of this work [Cao, Y., & Kariwala, V. (2008). Bidirectional branch and bound for controlled variable selection: Part I. Principles and minimum singular value criterion. Comput. Chem. Eng., 32 (10), 2306–2319], we proposed a bidirectional branch and bound (BAB) approach for subset selection problems and demonstrated its efficiency using the minimum singular value criterion. In this paper, the BAB approach is extended for CV selection using the exact local method for self-optimizing control. By redefining the loss expression, we show that the CV selection criterion for exact local method is bidirectionally monotonic. A number of novel determinant based criteria are proposed for fast pruning and branching purposes resulting in a computationally inexpensive BAB approach. We also establish a link between the problems of selecting a subset and combinations of measurements as CVs and present a partially bidirectional BAB method for selection of measurements, whose combinations can be used as CVs. Numerical tests using randomly generated matrices and binary distillation column case study demonstrate the computational efficiency of the proposed methods.

[1]  Yi Cao,et al.  Improved branch and bound method for control structure screening , 2005 .

[2]  S. Skogestad.  DYNAMICS AND CONTROL OF DISTILLATION COLUMNS A tutorial introduction , 1997 .

[3]  Sigurd Skogestad,et al.  Optimal Selection of Controlled Variables , 2003 .

[4]  Vidar Alstad,et al.  Studies on selection of controlled variables , 2005 .

[5]  Marc M. J. van de Wal,et al.  A review of methods for input/output selection , 2001, Autom..

[6]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[7]  Sigurd Skogestad.  Plantwide control: the search for the self-optimizing control structure , 2000 .

[8]  Vinay Kariwala,et al.  Optimal Measurement Combination for Local Self-Optimizing Control , 2007 .

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  S. Janardhanan,et al.  LOCAL SELF-OPTIMIZING CONTROL WITH AVERAGE LOSS MINIMIZATION , 2008 .

[11]  Keinosuke Fukunaga,et al.  A Branch and Bound Algorithm for Feature Subset Selection , 1977, IEEE Transactions on Computers.

[12]  Xue-wen Chen.  An improved branch and bound algorithm for feature selection , 2003, Pattern Recognit. Lett..

[13]  S. Janardhanan,et al.  OPTIMAL MEASUREMENT COMBINATIONS AS CONTROLLED VARIABLES , 2007 .

[14]  Josef Kittler,et al.  Fast branch & bound algorithms for optimal feature selection , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[15]  Sigurd Skogestad,et al.  NULL SPACE METHOD FOR SELECTING OPTIMAL MEASUREMENT COMBINATIONS AS CONTROLLED VARIABLES , 2007 .

[16]  Baozong Yuan,et al.  A more efficient branch and bound algorithm for feature selection , 1993, Pattern Recognit..

[17]  Sigurd Skogestad,et al.  Selection of Controlled Variables: Maximum Gain Rule and Combination of Measurements , 2008 .

[18]  Francesc J. Ferri,et al.  Fast Branch & Bound Algorithm in Feature Selection , 2007 .

[19]  Yi Cao,et al.  Bidirectional branch and bound for controlled variable selection: Part I. Principles and minimum singular value criterion , 2008, Comput. Chem. Eng..

[20]  D. Owens,et al.  Globally Optimal Control Structure Selection Using Branch and Bound Method 1 , 1998 .