On the role of the necessary conditions of optimality in structuring dynamic real-time optimization schemes

Abstract In dynamic optimization problems, the optimal input profiles are typically obtained using models that predict the system behavior. In practice, however, process models are often inaccurate, and on-line model adaptation is required for appropriate prediction and re-optimization. In most dynamic real-time optimization schemes, the available measurements are used to update the plant model, with uncertainty being lumped into selected uncertain plant parameters; furthermore, a piecewise-constant parameterization is used for the input profiles. This paper argues that the knowledge of the necessary conditions of optimality (NCO) can help devise more efficient and more robust real-time optimization schemes. Ideally, the structuring decisions involve the NCO as follows: (i) one measures or estimates the plant NCO, (ii) a NCO-based input parameterization is used, and (iii) model adaptation is performed to meet the plant NCO. The benefit of using the NCO in dynamic real-time optimization is illustrated in simulation through the comparison of various schemes for solving a final-time optimal control problem in the presence of uncertainty.

[1]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[2]  Ignacio E. Grossmann,et al.  A note on approximation techniques used for process optimization , 1985 .

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

[4]  Lorenz T. Biegler,et al.  Fast nonlinear model predictive control: Formulation and industrial process applications , 2013, Comput. Chem. Eng..

[5]  Alex Simpkins,et al.  System Identification: Theory for the User, 2nd Edition (Ljung, L.; 1999) [On the Shelf] , 2012, IEEE Robotics & Automation Magazine.

[6]  Lorenz T. Biegler,et al.  Technology Advances for Dynamic Real-Time Optimization , 2009 .

[7]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[8]  Wolfgang Marquardt,et al.  Adaptive switching structure detection for the solution of dynamic optimization problems , 2006 .

[9]  Dominique Bonvin,et al.  Dynamic optimization of batch processes: I. Characterization of the nominal solution , 2003, Comput. Chem. Eng..

[10]  Stephen P. Boyd,et al.  Fast Model Predictive Control Using Online Optimization , 2010, IEEE Transactions on Control Systems Technology.

[11]  Victor M. Zavala,et al.  The advanced-step NMPC controller: Optimality, stability and robustness , 2009, Autom..

[12]  Mukul Agarwal,et al.  Batch unit optimization with imperfect modelling: a survey , 1994 .

[13]  MORITZ DIEHL,et al.  A Real-Time Iteration Scheme for Nonlinear Optimization in Optimal Feedback Control , 2005, SIAM J. Control. Optim..

[14]  Michel Gevers,et al.  Identification for Control: Achievements and Open Problems 1 , 2004 .

[15]  M. Diehl,et al.  Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations , 2000 .

[16]  L. Grüne,et al.  Nonlinear Model Predictive Control : Theory and Algorithms. 2nd Edition , 2011 .

[17]  L. T. Biegler,et al.  FAST NONLINEAR MODEL PREDICTIVE CONTROL : OPTIMIZATION STRATEGY AND INDUSTRIAL PROCESS APPLICATIONS , 2011 .

[18]  J. Rawlings,et al.  Feedback control of chemical processes using on-line optimization techniques , 1990 .

[19]  Manfred Morari,et al.  Real-time suboptimal model predictive control using a combination of explicit MPC and online optimization , 2008, 2008 47th IEEE Conference on Decision and Control.

[20]  Thomas E. Marlin,et al.  Design cost: a systematic approach to technology selection for model-based real-time optimization systems , 1996 .

[21]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[22]  G. Box.  Robustness in the Strategy of Scientific Model Building. , 1979 .

[23]  Thomas E. Marlin,et al.  Model adequacy requirements for optimizing plant operations , 1994 .

[24]  Dominique Bonvin,et al.  Real-Time Optimization of Batch Processes by Tracking the Necessary Conditions of Optimality , 2007 .

[25]  Karl Johan Åström,et al.  Matching Criteria for Control and Identification , 1993 .

[26]  Manfred Morari,et al.  Towards computational complexity certification for constrained MPC based on Lagrange Relaxation and the fast gradient method , 2011, IEEE Conference on Decision and Control and European Control Conference.

[27]  Babu Joseph,et al.  On-line optimization using a two-phase approach: an application study , 1987 .

[28]  Ian David Lockhart Bogle,et al.  Computers and Chemical Engineering , 2008 .

[29]  Bala Srinivasan,et al.  Interplay between identification and optimization in run-to-run optimization schemes , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[30]  M. Diehl,et al.  Real-time optimization and nonlinear model predictive control of processes governed by differential-algebraic equations , 2000 .

[31]  James B. Rawlings,et al.  Optimizing Process Economic Performance Using Model Predictive Control , 2009 .

[32]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[33]  Hans Joachim Ferreau,et al.  Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation , 2009 .

[34]  Wolfgang Marquardt,et al.  Detection and exploitation of the control switching structure in the solution of dynamic optimization problems , 2006 .

[35]  Efstratios N. Pistikopoulos,et al.  Multi-parametric model-based control : theory and applications , 2007 .

[36]  Dominique Bonvin,et al.  Adaptation strategies for real-time optimization , 2009, Comput. Chem. Eng..

[37]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[38]  Dominique Bonvin,et al.  Dynamic optimization of batch processes: II. Role of measurements in handling uncertainty , 2003, Comput. Chem. Eng..

[39]  Dominique Bonvin,et al.  Batch process optimization via run-to-run constraints adaptation , 2007, 2007 European Control Conference (ECC).

[40]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[41]  Panagiotis D. Christofides,et al.  Economic model predictive control of nonlinear process systems using Lyapunov techniques , 2012 .

[42]  Michel Gevers,et al.  Identification for Control: Achievements and Open Problems 1 , 2004 .