Fast NMPC schemes for regulatory and economic NMPC – A review ☆

Abstract In this paper, NMPC schemes based on fast update methods (fast NMPC schemes) are reviewed that strive to provide a fast but typically suboptimal update of the control variables at each sampling instant with negligible computational delay. The review focuses on schemes that employ one of two subclasses of fast update methods developed for direct solution approaches, the suboptimal update methods and the sensitivity-based update methods. The connections and similarities of the fast update methods, the elements of the fast NMPC, the control architecture as well as the fast NMPC schemes as a whole are highlighted to support the assessment of the benefits and limitations of each individual scheme. In this way, this review facilitates the choice of a suitable fast NMPC scheme within the vast amount of fast NMPC schemes available in literature.

[1]  Toshiyuki Ohtsuka,et al.  A continuation/GMRES method for fast computation of nonlinear receding horizon control , 2004, Autom..

[2]  M. Diehl,et al.  Fast nonlinear model predictive control of gasoline engines , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[3]  Wolfgang Marquardt,et al.  Integration of Model Predictive Control and Optimization of Processes: Enabling Technology for Market Driven Process Operation , 2000 .

[4]  Wolfgang Marquardt,et al.  Neighboring-extremal updates for nonlinear model-predictive control and dynamic real-time optimization , 2009 .

[5]  Moritz Diehl,et al.  Efficient NMPC of unstable periodic systems using approximate infinite horizon closed loop costing , 2004, Annu. Rev. Control..

[6]  Victor M. Zavala,et al.  Computational strategies for the optimal operation of large-scale chemical processes , 2008 .

[7]  Tor Arne Johansen,et al.  Approximate explicit receding horizon control of constrained nonlinear systems , 2004, Autom..

[8]  Marti Ruben,et al.  Coordination of distributed model predictive controllers using price-driven coordination and sensitivity analysis , 2013 .

[9]  Siep Weiland,et al.  Model predictive control algorithm for nonlinear chemical processes , 2003, 2003 IEEE International Workshop on Workload Characterization (IEEE Cat. No.03EX775).

[10]  Lars Grüne,et al.  Economic receding horizon control without terminal constraints , 2013, Autom..

[11]  M. Kojima,et al.  Continuous deformation of nonlinear programs , 1984 .

[12]  Hans Bock,et al.  A Direct Multiple Shooting Method for Real-Time Optimization of Nonlinear DAE Processes , 2000 .

[13]  Mato Baotic,et al.  On the computation of linear model predictive control laws , 2010, Autom..

[14]  Victor M. Zavala,et al.  Advanced step nonlinear model predictive control for air separation units , 2009 .

[15]  Andreas Kugi,et al.  Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints , 2010, IEEE Transactions on Automatic Control.

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

[17]  Wolfgang Marquardt,et al.  Discrete first- and second-order adjoints and automatic differentiation for the sensitivity analysis of dynamic models , 2010, ICCS.

[18]  Anthony V. Fiacco,et al.  Sensitivity analysis for nonlinear programming using penalty methods , 1976, Math. Program..

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

[20]  Moritz Diehl,et al.  Real-Time Control of a Kite-Model Using an Auto-Generated Nonlinear MPC Algorithm , 2011 .

[21]  H. J. Ferreau,et al.  An online active set strategy to overcome the limitations of explicit MPC , 2008 .

[22]  D. Q. Mayne,et al.  Suboptimal model predictive control (feasibility implies stability) , 1999, IEEE Trans. Autom. Control..

[23]  Martin Mönnigmann,et al.  Accelerating online MPC with partial explicit information and linear storage complexity in the number of constraints , 2013, 2013 European Control Conference (ECC).

[24]  H. Bock,et al.  Efficient direct multiple shooting for nonlinear model predictive control on long horizons , 2012 .

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

[26]  Moritz Diehl,et al.  Aircraft control based on fast non-linear MPC & multiple-shooting , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[27]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[28]  W. C. Li,et al.  Newton-type control strategies for constrained nonlinear processes , 1989 .

[29]  H. J. Pesch.  Real-time computation of feedback controls for constrained optimal control problems. Part 2: A correction method based on multiple shooting , 1989 .

[30]  Frank Allgöwer,et al.  Computational Delay in Nonlinear Model Predictive Control , 2004 .

[31]  M. Morari,et al.  Move blocking strategies in receding horizon control , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[32]  Helen Durand,et al.  A tutorial review of economic model predictive control methods , 2014 .

[33]  Manfred Morari,et al.  Real-Time Suboptimal Model Predictive Control Using a Combination of Explicit MPC and Online Optimization , 2011, IEEE Trans. Autom. Control..

[34]  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..

[35]  H. Maurer,et al.  Sensitivity Analysis and Real-Time Optimization of Parametric Nonlinear Programming Problems , 2001 .

[36]  Wolfgang Marquardt,et al.  Sensitivity-Based Solution Updates in Closed-Loop Dynamic Optimization , 2004 .

[37]  Wolfgang Marquardt,et al.  Rigorous solution vs. fast update: Acceptable computational delay in NMPC , 2011, IEEE Conference on Decision and Control and European Control Conference.

[38]  James H. Bigelow,et al.  Implicit function theorems for mathematical programming and for systems of inequalities , 1974, Math. Program..

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

[40]  Frank Allgöwer,et al.  Sampled-Data Nonlinear Model Predictive Control for Constrained Continuous Time Systems , 2007 .

[41]  Lorenz T. Biegler.  Efficient Nonlinear Programming Algorithms for Chemical Process Control and Operations , 2007, System Modelling and Optimization.

[42]  Knut Graichen,et al.  Nichtlineare modellprädiktive Regelung basierend auf Fixpunktiterationen , 2012, Autom..

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

[44]  Andreas Kugi,et al.  Ein suboptimaler Ansatz zur schnellen modellprädiktiven Regelung nichtlinearer Systeme , 2010, Autom..

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

[46]  Wolfgang Marquardt,et al.  A hierarchical distributed economic NMPC architecture based on neighboring-extremal updates , 2012, 2012 American Control Conference (ACC).

[47]  Lars Grüne,et al.  Analysis of unconstrained NMPC schemes with incomplete optimization , 2010 .

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

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

[50]  Panagiotis D. Christofides,et al.  Real‐time economic model predictive control of nonlinear process systems , 2015 .

[51]  Wolfgang Dahmen,et al.  Introduction to Model Based Optimization of Chemical Processes on Moving Horizons , 2001 .

[52]  L. Biegler,et al.  A reduced hessian strategy for sensitivity analysis of optimal flowsheets , 1987 .

[53]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[54]  Alberto Bemporad,et al.  Model predictive control based on linear programming - the explicit solution , 2002, IEEE Transactions on Automatic Control.

[55]  Hans Bock,et al.  Fast Nonlinear Model Predictive Control with an Application in Automotive Engineering , 2009 .

[56]  Victor M. Zavala,et al.  Real-Time Nonlinear Optimization as a Generalized Equation , 2010, SIAM J. Control. Optim..

[57]  Basil Kouvaritakis,et al.  Constrained receding horizon predictive control for nonlinear systems , 2002, Autom..

[58]  Knut Graichen,et al.  A Real-Time Gradient Method for Nonlinear Model Predictive Control , 2012 .

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

[60]  Lorenz T. Biegler,et al.  Advanced-Multi-Step Nonlinear Model Predictive Control , 2013 .

[61]  Martin Guay,et al.  A new real-time perspective on non-linear model predictive control , 2006 .

[62]  Riccardo Scattolini,et al.  Architectures for distributed and hierarchical Model Predictive Control - A review , 2009 .

[63]  Mazen Alamir.  Nonlinear receding horizon sub-optimal guidance law for the minimum interception time problem , 2001 .

[64]  G. Gattu,et al.  Nonlinear Quadratic Dynamic Matrix Control with State Estimation , 1992 .

[65]  Toshiyuki Ohtsuka,et al.  A real‐time algorithm for nonlinear infinite horizon optimal control by time axis transformation method , 2013 .

[66]  Lorenz T. Biegler,et al.  An extension of Newton-type algorithms for nonlinear process control , 1995, Autom..

[67]  L. S. Pontryagin,et al.  Mathematical Theory of Optimal Processes , 1962 .

[68]  T. Ohtsuka,et al.  Nonlinear receding horizon control of an underactuated hovercraft with a multiple-shooting-based algorithm , 2003, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[69]  Hans Bock,et al.  Efficient Numerics for Nonlinear Model Predictive Control , 2010 .

[70]  Moritz Diehl,et al.  An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range , 2011, Autom..

[71]  Knut Graichen.  A fixed-point iteration scheme for real-time model predictive control , 2012, Autom..

[72]  L. Biegler,et al.  Fast economic model predictive control based on NLP-sensitivities , 2014 .

[73]  M. Diehl,et al.  Fast reduced multiple shooting methods for nonlinear model predictive control , 2007 .

[74]  R. Bellman.  Dynamic programming. , 1957, Science.

[75]  Hans Bock,et al.  Constrained Optimal Feedback Control of Systems Governed by Large Differential Algebraic Equations , 2007 .

[76]  Wolfgang Marquardt,et al.  Dynamic optimization using adaptive control vector parameterization , 2005, Comput. Chem. Eng..

[77]  Toshiyuki Ohtsuka,et al.  A real-time algorithm for nonlinear receding horizon control of descriptor systems , 2010, Proceedings of SICE Annual Conference 2010.

[78]  Jing Zhang,et al.  Economic model predictive control with triggered evaluations: State and output feedback , 2014 .

[79]  Wolfgang Marquardt,et al.  Integration of Economical Optimization and Control for Intentionally Transient Process Operation , 2007 .

[80]  Martin Guay,et al.  A Real-Time Framework for Model-Predictive Control of Continuous-Time Nonlinear Systems , 2007, IEEE Transactions on Automatic Control.

[81]  Victor M. Zavala,et al.  Optimization-based strategies for the operation of low-density polyethylene tubular reactors: nonlinear model predictive control , 2009, Comput. Chem. Eng..

[82]  L. Biegler,et al.  Nonlinear Programming Strategies for State Estimation and Model Predictive Control , 2009 .

[83]  M. Diehl,et al.  An Adjoint-based Numerical Method for Fast Nonlinear Model Predictive Control , 2008 .

[84]  Riccardo Scattolini,et al.  NONLINEAR MODEL PREDICTIVE CONTROL OF COMBINED CYCLE POWER PLANTS , 2005 .

[85]  Jie Zhao,et al.  Nonlinear Model Predictive Control of Robots Using Real-Time Optimization , 2004 .

[86]  M. Diehl,et al.  Nominal stability of real-time iteration scheme for nonlinear model predictive control , 2005 .

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

[88]  Wolfgang Marquardt,et al.  Consistent hierarchical economic NMPC for a class of hybrid systems using neighboring-extremal updates , 2014 .

[89]  Lorenz T. Biegler,et al.  Nonlinear Waves in Integrable and Nonintegrable Systems , 2018 .

[90]  Wolfgang Marquardt,et al.  A two-layer architecture for economically optimal process control and operation , 2011 .

[91]  M. Kojima.  Strongly Stable Stationary Solutions in Nonlinear Programs. , 1980 .

[92]  Wolfgang Marquardt,et al.  Structural Concepts for Optimization Based Control of Transient Processes , 2000 .

[93]  Moritz Diehl,et al.  A real‐time algorithm for nonlinear receding horizon control using multiple shooting and continuation/Krylov method , 2009 .

[94]  Wolfgang Marquardt,et al.  Infinite-Horizon Continuous-Time NMPC via Time Transformation , 2014, IEEE Transactions on Automatic Control.

[95]  A. Shapiro.  Sensitivity analysis of nonlinear programs and differentiability properties of metric projections , 1988 .

[96]  Stephen J. Wright,et al.  Partial enumeration MPC: Robust stability results and application to an unstable CSTR , 2011 .

[97]  A. Mayne.  Parametric Optimization: Singularities, Pathfollowing and Jumps , 1990 .

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

[99]  Stephen J. Wright,et al.  Fast, large-scale model predictive control by partial enumeration , 2007, Autom..

[100]  Panagiotis D. Christofides,et al.  Integrating dynamic economic optimization and model predictive control for optimal operation of nonlinear process systems , 2014 .

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

[102]  Sebastian Engell.  Feedback control for optimal process operation , 2007 .

[103]  Andrew N. Hrymak,et al.  Sensitivity analysis for chemical process optimization , 1996 .

[104]  Moritz Diehl,et al.  A Lyapunov Function for Economic Optimizing Model Predictive Control , 2011, IEEE Transactions on Automatic Control.