Input-to-state stability of discrete-time singular systems based on quasi-min–max model predictive control

This study is concerned with robust quasi-min–max model predictive control (MPC) for a class of discrete-time singular systems with persistent disturbance and input constrains. To deal with the persistent disturbance, the authors introduce the notion of input-to-state stability (ISS) of discrete-time singular system for the first time. The optimal control can be obtained by solving a quasi-min–max optimal problem of a finite horizon cost function. On the basis of the proposed dual-mode MPC approach, it can be proved that the closed-loop discrete-time singular system is ISS, regular and causal. Finally, a numerical simulation shows the feasibility and effectiveness of the proposed method.

[1]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[2]  Qingling Zhang,et al.  Brief paper - Input-to-state stability for descriptor systems with non-linear perturbations , 2011 .

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

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

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

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

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

[8]  W. P. M. H. Heemels,et al.  Predictive control of hybrid systems: Input-to-state stability results for sub-optimal solutions , 2009, Autom..

[9]  Defeng He,et al.  Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems , 2012 .

[10]  Riccardo Scattolini,et al.  Regional Input-to-State Stability for Nonlinear Model Predictive Control , 2006, IEEE Transactions on Automatic Control.

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

[12]  M. Haeri,et al.  Model predictive control of non-linear discrete time systems: a linear matrix inequality approach , 2010 .

[13]  Alan J. Laub,et al.  The linear-quadratic optimal regulator for descriptor systems , 1985, 1985 24th IEEE Conference on Decision and Control.

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

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

[16]  Defeng He,et al.  Quasi-min-max MPC for constrained nonlinear systems with guaranteed input-to-state stability , 2014, J. Frankl. Inst..

[17]  David Q. Mayne,et al.  Robust model predictive control of constrained linear systems with bounded disturbances , 2005, Autom..

[18]  Yuanqing Xia,et al.  New bounded real lemma for discrete-time singular systems , 2008, Autom..

[19]  Biao Huang,et al.  Robust model predictive control of singular systems , 2004, IEEE Trans. Autom. Control..

[20]  W. P. M. H. Heemels,et al.  On input-to-state stability of min-max nonlinear model predictive control , 2008, Syst. Control. Lett..