A reliable modifier-adaptation strategy for real-time optimization

Abstract In model-based real-time optimization, plant-model mismatch can be handled by applying bias- and gradient-corrections to the cost and constraint functions in an iterative optimization procedure. One of the major challenges in practice is the estimation of the plant gradients from noisy measurement data, in particular for several optimization variables. In this paper we propose a new real-time optimization scheme that explores the inherent smoothness of the plant mapping to enable a reliable optimization. The idea here is to combine the quadratic approximation approach used in derivative-free optimization techniques with the iterative gradient-modification optimization scheme. The convergence of the scheme is analyzed. Simulation studies for the optimization of a ten-variable synthetic example and a reactor benchmark problem with considerable plant-model mismatch show its promising performance.

[1]  Sebastian Engell,et al.  Integration of gradient adaptation and quadratic approximation in real-time optimization , 2015, 2015 34th Chinese Control Conference (CCC).

[2]  Sebastian Engell,et al.  Handling Disturbances in Modifier Adaptation with Quadratic Approximation , 2015 .

[3]  Dominique Bonvin,et al.  Modifier-adaptation methodology for real-time optimization , 2009 .

[4]  César de Prada,et al.  Mixed Modifier-Adaptation for RTO in a Continuous Bioreactor , 2014 .

[5]  Dominique Bonvin,et al.  Use of measurements for enforcing the necessary conditions of optimality in the presence of constraints and uncertainty , 2005 .

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

[7]  Thomas E. Marlin,et al.  Model accuracy for economic optimizing controllers : the bias update case , 1994 .

[8]  Daniel Andrés,et al.  HANDLING UNCERTAINTIES IN PROCESS OPTIMIZATION , 2013 .

[9]  P. D. Roberts,et al.  An algorithm for steady-state system optimization and parameter estimation , 1979 .

[10]  B. Erik Ydstie,et al.  Adaptive extremum control using approximate process models , 1989 .

[11]  Jorge J. Moré,et al.  Recent Developments in Algorithms and Software for Trust Region Methods , 1982, ISMP.

[12]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .

[13]  Katya Scheinberg,et al.  On the convergence of derivative-free methods for unconstrained optimization , 1997 .

[14]  Sebastian Engell,et al.  Comparison of Modifier Adaptation Schemes in Real-Time Optimization , 2015 .

[15]  J. Fraser Forbes,et al.  Performance Analysis of Perturbation‐Based Methods for Real‐Time Optimization , 2008 .

[16]  Dominique Bonvin,et al.  A Dual Modifier-Adaptation Approach for Real-Time Optimization , 2010 .

[17]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[18]  Sebastian Engell,et al.  Modifier adaptation with quadratic approximation in iterative optimizing control , 2015, 2015 European Control Conference (ECC).

[19]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[20]  M. Krstić,et al.  Real-Time Optimization by Extremum-Seeking Control , 2003 .

[21]  Sebastian Engell,et al.  Iterative set-point optimization of batch chromatography , 2005, Comput. Chem. Eng..

[22]  Piotr Tatjewski,et al.  An Algorithm for Steady-State Optimizing Dual Control of Uncertain Plants , 1994 .

[23]  Katya Scheinberg,et al.  Introduction to derivative-free optimization , 2010, Math. Comput..

[24]  Peter Roberts.  Broyden Derivative Approximation in ISOPE Optimising and Optimal Control Algorithms , 2000 .

[25]  Dominique Bonvin,et al.  Use of Convex Model Approximations for Real-Time Optimization via Modifier Adaptation , 2013 .

[26]  Katya Scheinberg,et al.  Self-Correcting Geometry in Model-Based Algorithms for Derivative-Free Unconstrained Optimization , 2010, SIAM J. Optim..

[27]  I. Grossmann,et al.  An algorithm for the use of surrogate models in modular flowsheet optimization , 2008 .