An apologia for stabilising terminal conditions in model predictive control

This paper defends the use of a terminal cost and an explicit or implicit terminal constraint for ensuring the stability of model predictive control systems. Existing methods for ensuring stability are briefly reviewed. The necessity of a terminal constraint to satisfy certain design requirements is established. The advantages and disadvantages of employing terminal stabilising conditions are discussed.

[1]  D. Chmielewski,et al.  On constrained infinite-time linear quadratic optimal control , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[2]  Andrew R. Teel,et al.  Discrete Time Receding Horizon Optimal Control: Is the Stability Robust? , 2004 .

[3]  Michael Malisoff,et al.  Optimal Control, Stabilization and Nonsmooth Analysis , 2004 .

[4]  Stephen J. Wright,et al.  Cooperative distributed model predictive control for nonlinear systems , 2011 .

[5]  Lars Grüne,et al.  NMPC without terminal constraints , 2012 .

[6]  A. MacFarlane An Eigenvector Solution of the Optimal Linear Regulator Problem , 1963 .

[7]  M. ALAMIRf,et al.  Stability of a Truncated Infinite Constrained Receding Horizon Scheme : the General Discrete Nonlinear Case * , 2003 .

[8]  James A. Primbs,et al.  Feasibility and stability of constrained finite receding horizon control , 2000, Autom..

[9]  Andrew R. Teel,et al.  Nominally Robust Model Predictive Control With State Constraints , 2007, IEEE Transactions on Automatic Control.

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

[11]  J. J. Belletrutti,et al.  The characteristic locus design method , 1973 .

[12]  John Hauser,et al.  On the stability of receding horizon control with a general terminal cost , 2005, IEEE Transactions on Automatic Control.

[13]  Andrew R. Teel,et al.  Model predictive control: for want of a local control Lyapunov function, all is not lost , 2005, IEEE Transactions on Automatic Control.

[14]  Stephen J. Wright,et al.  Cooperative distributed model predictive control , 2010, Syst. Control. Lett..

[15]  Andrew R. Teel,et al.  Examples when nonlinear model predictive control is nonrobust , 2004, Autom..

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

[17]  J. Rawlings,et al.  Infinite Horizon Linear Quadratic Control with Constraints , 1996 .

[18]  Piernicola Bettiol,et al.  Sensitivity Interpretations of the Costate Variable for Optimal Control Problems with State Constraints , 2009, SIAM J. Control. Optim..

[19]  E. Polak,et al.  Frequency-response methods in control systems , 1981, Proceedings of the IEEE.

[20]  Lars Grne,et al.  Nonlinear Model Predictive Control: Theory and Algorithms , 2011 .

[21]  Eduardo F. Camacho,et al.  On the stability of constrained MPC without terminal constraint , 2006, IEEE Transactions on Automatic Control.

[22]  Stephen J. Wright,et al.  Conditions under which suboptimal nonlinear MPC is inherently robust , 2011, Syst. Control. Lett..

[23]  Jie Yu,et al.  Unconstrained receding-horizon control of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[24]  J. Brian Froisy,et al.  Model predictive control - Building a bridge between theory and practice , 2006, Comput. Chem. Eng..

[25]  Thomas Parisini,et al.  A receding-horizon regulator for nonlinear systems and a neural approximation , 1995, Autom..