Real-Time Iterations for Nonlinear Optimal Feedback Control

An efficient Newton-type scheme for the approximate on-line solution of optimization problems as they occur in optimal feedback control is presented. The scheme allows a fast reaction to disturbances by delivering approximations of the exact optimal feedback control which are iteratively refined during the runtime of the controlled process. The approximation errors of this real-time iteration scheme can be bounded and the solution contracts towards the optimal feedback control. The robustness and excellent real-time performance of the method is demonstrated in a numerical experiment, the control of an unstable system, namely an airborne kite that shall fly loops. This paper is a short version of an article that appeared recently in the SIAM Journal on Control and Optimization [1].

[1]  H. Bock,et al.  A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems , 1984 .

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

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

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

[5]  Hans Bock,et al.  An Efficient Algorithm for Nonlinear Model Predictive Control of Large-Scale Systems Part I: Description of the Method (Ein effizienter Algorithmus für die nichtlineare prädiktive Regelung großer Systeme Teil I: Methodenbeschreibung) , 2002 .

[6]  F. Allgower,et al.  Real-time feasibility of nonlinear predictive control for large scale processes-a case study , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[7]  H. Bock.  Numerical Treatment of Inverse Problems in Chemical Reaction Kinetics , 1981 .

[8]  Stephen J. Wright,et al.  Nonlinear Predictive Control and Moving Horizon Estimation — An Introductory Overview , 1999 .

[9]  Lorenz T. Biegler,et al.  Efficient Solution of Dynamic Optimization and NMPC Problems , 2000 .

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

[11]  Lorenz T. Biegler,et al.  Optimization approaches to nonlinear model predictive control , 1991 .

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

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

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

[15]  J. P. Schlöder,et al.  Ein effizienter Algorithmus für die nichtlineare prädiktive Regelung großer Systeme Teil II: Experimentelle Erprobung an einer Destillationskolonne (An Efficient Algorithm for Nonlinear Model Predictive Control of Large-Scale Systems Part II: Experimental Evaluation for a Distillation Column) , 2003 .

[16]  H. J. Pesch,et al.  New general guidance method in constrained optimal control, part 1: Numerical method , 1990 .

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

[18]  H. Bock,et al.  Numerical Treatment of State and Control Constraints in the Computation of Optimal Feedback Laws for Nonlinear Control Problems , 1987 .

[19]  Moritz Diehl,et al.  Real-Time Optimization for Large Scale Nonlinear Processes , 2001 .

[20]  Irene Bauer.  Numerische Verfahren zur Lösung von Anfangswertaufgaben und zur Generierung von ersten und zweiten Ableitungen mit Anwendungen bei Optimierungsaufgaben in Chemie und Verfahrenstechnik , 1999 .

[21]  Wolfgang Marquardt,et al.  Model predictive control for online optimization of semi-batch reactors , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[22]  Stephen J. Wright,et al.  Nonlinear Model Predictive Control via Feasibility-Perturbed Sequential Quadratic Programming , 2004, Comput. Optim. Appl..

[23]  K. Kunisch,et al.  Instantaneous control of backward-facing step flows , 1999 .

[24]  Hans Bock,et al.  Efficient direct multiple shooting in nonlinear model predictive control , 1999 .

[25]  R. Temam,et al.  Feedback control for unsteady flow and its application to the stochastic Burgers equation , 1993, Journal of Fluid Mechanics.

[26]  Johannes P. Schlöder,et al.  Real-Time Optimization for Large Scale Processes: Nonlinear Model Predictive Control of a High Purity Distillation Column , 2001 .

[27]  Lino de Oliveira Santos.  Multivariable predictive control of chemical processes , 2001 .