Finite horizon model predictive control with ellipsoid mapping of uncertain linear systems

A model predictive control scheme was proposed for discrete-time uncertain linear systems subject to input constraints. The cost functional to be minimised is a finite horizon quadratic cost, which describes the performance of the corresponding nominal system. The control action is specified in terms of both feedback and open-loop components. The open-loop part of the control action steers the centre of associated ellipsoids into a set around the origin, while the feedback component forces the actual system states to remain in those ellipsoids. Both feedback and open-loop control are determined online by repeatedly solving a convex optimisation problem. The predictive control scheme guarantees recursive feasibility and robust stability if the convex optimisation problem is feasible at the initial time instant. A numerical example illustrates the effectiveness of the proposed approach.

[1]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[2]  F. Allgöwer,et al.  A quasi-infinite horizon nonlinear model predictive control scheme with guaranteed stability , 1997 .

[3]  C. Scherer,et al.  A game theoretic approach to nonlinear robust receding horizon control of constrained systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[4]  E. Yaz Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  D. Mayne,et al.  Min-max feedback model predictive control for constrained linear systems , 1998, IEEE Trans. Autom. Control..

[6]  Wook Hyun Kwon,et al.  Robust one‐step receding horizon control for constrained systems , 1999 .

[7]  Yaman Arkun,et al.  Quasi-Min-Max MPC algorithms for LPV systems , 2000, Autom..

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

[9]  Basil Kouvaritakis,et al.  Efficient robust predictive control , 2000, IEEE Trans. Autom. Control..

[10]  Luigi Chisci,et al.  Systems with persistent disturbances: predictive control with restricted constraints , 2001, Autom..

[11]  F. Fontes A General Framework to Design Stabilizing Nonlinear Model Predictive Controllers , 2001 .

[12]  Riccardo Scattolini,et al.  A stabilizing model-based predictive control algorithm for nonlinear systems , 2001, Autom..

[13]  Manfred Morari,et al.  An improved approach for constrained robust model predictive control , 2002, Autom..

[14]  Geir E. Dullerud,et al.  A nonlinear functional approach to LFT model validation , 2002, Syst. Control. Lett..

[15]  D. Limón,et al.  Input-to-state stable MPC for constrained discrete-time nonlinear systems with bounded additive uncertainties , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[16]  Frank Allgöwer,et al.  Robust model predictive control for nonlinear discrete‐time systems , 2003 .

[17]  Alberto Bemporad,et al.  Min-max control of constrained uncertain discrete-time linear systems , 2003, IEEE Trans. Autom. Control..

[18]  Lalo Magni,et al.  Special section technical notes and correspondence. Min-max model predictive control of nonlinear systems using discontinuous feedbacks , 2003, IEEE Trans. Autom. Control..

[19]  R.S. Smith,et al.  Robust model predictive control of constrained linear systems , 2004, Proceedings of the 2004 American Control Conference.

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

[21]  Luca Zaccarian,et al.  Linear LMI-based external anti-windup augmentation for stable linear systems , 2004, Autom..

[22]  Masami Saeki,et al.  Model predictive control for linear parameter varying systems using parameter dependent Lyapunov function , 2006, The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04..

[23]  Rolf Findeisen,et al.  Nonlinear model predictive control : a sampled data feedback perspective , 2005 .

[24]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[25]  Sangchul Won,et al.  Model Predictive Control for Linear Parameter Varying Systems Using a New Parameter Dependent Terminal Weighting Matrix , 2006, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[26]  Roy S. Smith Model predictive control of uncertain constrained linear systems ; LMI-based methods ∗ , 2006 .

[27]  Eduardo F. Camacho,et al.  Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties , 2006, Autom..

[28]  Toshiharu Sugie,et al.  Model predictive control for linear parameter varying constrained systems using ellipsoidal set prediction , 2007, Int. J. Control.

[29]  Hong Chen,et al.  Stabilizing model predictive control for LPV systems subject to constraints with parameter-dependent control law , 2009, 2009 American Control Conference.

[30]  Eduardo F. Camacho,et al.  Min-max Model Predictive Control of Nonlinear Systems: A Unifying Overview on Stability , 2009, Eur. J. Control.

[31]  F. Allgöwer,et al.  Robust model predictive control with disturbance invariant sets , 2010, Proceedings of the 2010 American Control Conference.

[32]  Frank Allgöwer,et al.  MPC with one free control action for constrained LPV systems , 2010, 2010 IEEE International Conference on Control Applications.