An integrated perturbation analysis and Sequential Quadratic Programming approach for Model Predictive Control

Computationally efficient algorithms are critical in making Model Predictive Control (MPC) applicable to broader classes of systems with fast dynamics and limited computational resources. In this paper, we propose an integrated formulation of Perturbation Analysis and Sequential Quadratic Programming (InPA-SQP) to address the constrained optimal control problems. The proposed algorithm combines the complementary features of perturbation analysis and SQP in a single unified framework, thereby leading to improved computational efficiency and convergence property. A numerical example is reported to illustrate the proposed method and its computational effectiveness.

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

[2]  A. Zheng,et al.  A computationally efficient nonlinear MPC algorithm , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[3]  Manfred Morari,et al.  Truncated step response models for model predictive control , 1993 .

[4]  Ilya V. Kolmanovsky,et al.  Neighboring Extremal Solution for Nonlinear Discrete-Time Optimal Control Problems With State Inequality Constraints , 2009, IEEE Transactions on Automatic Control.

[5]  Torkel Glad,et al.  A Method for State and Control Constrained Linear Quadratic Control Problems , 1984 .

[6]  L. Biegler,et al.  FAST SOLVERS AND RIGOROUS MODELS: CAN BOTH BE ACCOMMODATED IN NMPC? , 2006 .

[7]  T. M. Williams Practical Methods of Optimization. Vol. 2 — Constrained Optimization , 1982 .

[8]  A. Bryson,et al.  A SUCCESSIVE SWEEP METHOD FOR SOLVING OPTIMAL PROGRAMMING PROBLEMS , 1965 .

[9]  Tor Arne Johansen,et al.  Explicit sub-optimal linear quadratic regulation with state and input constraints , 2002, Autom..

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

[11]  H. Maurer,et al.  Sensitivity analysis for parametric control problems with control-state constraints , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

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

[13]  B.W. Gordon,et al.  Uncertain Nonlinear Receding Horizon Control Systems Subject to Non-Zero Computation Time , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[15]  Richard M. Murray,et al.  Receding horizon control of vectored thrust flight experiment , 2005 .

[16]  J. Bobrow,et al.  Progress on the Algorithmic Optimization of Robot Motion , 2005 .

[17]  Pascal Dufour,et al.  On nonlinear distributed parameter model predictive control strategy: on-line calculation time reduction and application to an experimental drying process , 2003, Comput. Chem. Eng..

[18]  Lorenzo Fagiano,et al.  Set Membership approximation theory for fast implementation of Model Predictive Control laws , 2009, Autom..

[19]  T. A. Badgwell,et al.  An Overview of Industrial Model Predictive Control Technology , 1997 .

[20]  Hans Bock,et al.  An Online Active Set Strategy for Fast Parametric Quadratic Programming in MPC Applications , 2006 .

[21]  Christof Büskens,et al.  Sensitivity Analysis and Real-Time Control of Parametric Optimal Control Problems Using Nonlinear Programming Methods , 2001 .

[22]  Yasushi Hada,et al.  Constrained Model Predictive Control , 2006 .

[23]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[24]  Manuel Haro Casado,et al.  Optimization of the Course in the Ship's Movement by Input-Output Linearization , 2001 .

[25]  Richard D. Braatz,et al.  Fast model predictive control of sheet and film processes , 2000, IEEE Trans. Control. Syst. Technol..