Combined model approximation techniques and multiparametric programming for explicit nonlinear model predictive control

Abstract This work presents a methodology to derive explicit multiparametric controllers for nonlinear systems, combining model approximation techniques and multiparametric model predictive control (mp-MPC) algorithms. Particular emphasis is given to an approach that applies a nonlinear model reduction technique, based on balancing of empirical gramians, which generates a reduced order model suitable for nonlinear mp-MPC algorithms. This approach is compared with a recently proposed method that uses a meta-modelling based model approximation technique which can be directly combined with standard multiparametric programming algorithms. The methodology is illustrated for two nonlinear models, of a distillation column and a train of CSTRs, respectively.

[1]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[2]  H. Rabitz,et al.  Practical Approaches To Construct RS-HDMR Component Functions , 2002 .

[3]  Efstratios N. Pistikopoulos,et al.  A novel approximation technique for online and multi-parametric model predictive control , 2011 .

[4]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[5]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[6]  RewieÅ ski,et al.  A trajectory piecewise-linear approach to model order reduction of nonlinear dynamical systems , 2003 .

[7]  P. Astrid,et al.  Reduction of process simulation models : a proper orthogonal decomposition approach , 2004 .

[8]  E. Pistikopoulos,et al.  A multiparametric programming approach for mixed-integer quadratic engineering problems , 2002 .

[9]  Jerrold E. Marsden,et al.  Empirical model reduction of controlled nonlinear systems , 1999, IFAC Proceedings Volumes.

[10]  Alberto Bemporad,et al.  An algorithm for multi-parametric quadratic programming and explicit MPC solutions , 2003, Autom..

[11]  Thomas F. Edgar,et al.  An improved method for nonlinear model reduction using balancing of empirical gramians , 2002 .

[12]  Constantinos Theodoropoulos,et al.  Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems , 2011, Comput. Chem. Eng..

[13]  Antonios Armaou,et al.  Equation-free gaptooth-based controller design for distributed complex/multiscale processes , 2005, Comput. Chem. Eng..

[14]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[15]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[16]  M. Morari,et al.  On-line optimization via off-line parametric optimization tools , 2000 .

[17]  T. Johansen.  On multi-parametric nonlinear programming and explicit nonlinear model predictive control , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[18]  Efstratios N. Pistikopoulos,et al.  Perspectives in Multiparametric Programming and Explicit Model Predictive Control , 2009 .

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

[20]  H. Rabitz,et al.  An efficient chemical kinetics solver using high dimensional model representation , 1999 .

[21]  Nilay Shah,et al.  Comparison of Monte Carlo and Quasi Monte Carlo Sampling Methods in High Dimensional Model Representation , 2009, 2009 First International Conference on Advances in System Simulation.

[22]  Efstratios N. Pistikopoulos,et al.  Towards the Design of Parametric Model Predictive Controllers for Non-linear Constrained Systems , 2007 .

[23]  I. Postlethwaite,et al.  Model reduction with balanced realizations , 1995 .

[24]  Victor M. Zavala,et al.  Fast implementations and rigorous models: Can both be accommodated in NMPC? , 2008 .

[25]  Efstratios N. Pistikopoulos,et al.  Recent advances in multiparametric nonlinear programming , 2010, Comput. Chem. Eng..

[26]  Diogo A. Narciso,et al.  A combined Balanced Truncation and multi-parametric programming approach for Linear Model Predictive Control , 2008 .

[27]  Efstratios N. Pistikopoulos,et al.  A Novel mp-NLP Algorithm for Explicit/Multi-parametric NMPC * , 2010 .

[28]  Efstratios N. Pistikopoulos,et al.  An Algorithm for the Solution of Multiparametric Mixed Integer Linear Programming Problems , 2000, Ann. Oper. Res..

[29]  Luis F. Domínguez,et al.  Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control , 2011 .

[30]  Anthony V. Fiacco,et al.  Introduction to Sensitivity and Stability Analysis in Nonlinear Programming , 2012 .

[31]  Efstratios N. Pistikopoulos,et al.  MPC on a chip - Recent advances on the application of multi-parametric model-based control , 2008, Comput. Chem. Eng..

[32]  Frank Allgöwer,et al.  Assessment and Future Directions of Nonlinear Model Predictive Control , 2007 .

[33]  Alberto Bemporad,et al.  A survey on explicit model predictive control , 2009 .

[34]  Dale E. Seborg,et al.  Dyanmic compartmental models for separation processes , 1986 .

[35]  P.Th.L.M. van Woerkom,et al.  MATHEMATICAL MODELS OF FLEXIBLE SPACECRAFT DYNAMICS: A SURVEY OF ORDER REDUCTION APPROACHES , 1986 .

[36]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..