Constructive model predictive control for constrained nonlinear systems

This paper develops a new model predictive control (MPC) design for stabilization of continuous‐time nonlinear systems subject to state and input constraints. The key idea is to construct an analytic form of the controller with some undetermined parameters and to calculate the parameters by minimizing online a performance index. By using the method of control Lyapunov functions (CLFs), we construct an appropriate variation on Sontag's formula, with one degree of freedom reflecting ‘decay rate’ of CLFs. Moreover, the constructed univariate control law is used to characterize the terminal region that guarantees the feasibility of the optimal control problem. Provided that the initial feasibility of the optimization problem is satisfied, the stability of the control scheme can be guaranteed. An example is given to illustrate the application of the constructive MPC design. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  E. Camacho,et al.  Nonlinear Model Predictive Control: An Introductory Review , 2007 .

[2]  Edward P. Gatzke,et al.  Nonlinear model predictive control using deterministic global optimization , 2006 .

[3]  Eric C. Kerrigan,et al.  Optimization over state feedback policies for robust control with constraints , 2006, Autom..

[4]  Panagiotis D. Christofides,et al.  Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control , 2005, Proceedings of the 2005, American Control Conference, 2005..

[5]  D. Limon,et al.  Enlarging the domain of attraction of MPC controllers , 2005, Autom..

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

[7]  Mark Cannon,et al.  Efficient nonlinear model predictive control algorithms , 2004, Annu. Rev. Control..

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

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

[10]  Basil Kouvaritakis,et al.  An interpolation strategy for discrete-time bilinear MPC problems , 2002, IEEE Trans. Autom. Control..

[11]  M. Sznaier,et al.  Suboptimal control of constrained nonlinear systems via receding horizon state dependent Riccati equations , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[12]  Murat Arcak,et al.  Constructive nonlinear control: a historical perspective , 2001, Autom..

[13]  B. Kouvaritakis,et al.  Open-loop and closed-loop optimality in interpolation MPC , 2001 .

[14]  Alex Zheng,et al.  Computationally efficient non linear predictive control algorithm for control of constrained nonlinear systems , 2001 .

[15]  Julio Solís-Daun,et al.  Global Stabilization of Nonlinear Systems with Inputs Subject to Magnitude and Rate Bounds: A Parametric Optimization Approach , 2000, SIAM J. Control. Optim..

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

[17]  John Doyle,et al.  A receding horizon generalization of pointwise min-norm controllers , 2000, IEEE Trans. Autom. Control..

[18]  P. Kokotovic,et al.  Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations , 1999 .

[19]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

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

[21]  Eduardo Sontag.  Stability and stabilization: discontinuities and the effect of disturbances , 1999, math/9902026.

[22]  Frank Allgöwer,et al.  A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability , 1997, 1997 European Control Conference (ECC).

[23]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[24]  D. Mayne,et al.  Robust receding horizon control of constrained nonlinear systems , 1993, IEEE Trans. Autom. Control..

[25]  Yuandan Lin,et al.  A universal formula for stabilization with bounded controls , 1991 .

[26]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .