Robust model predictive control of linear systems with constraints

In this paper, disturbance observer based model predictive control of linear systems which satisfies a matching condition is proposed, where the disturbance is bounded and varying slowly. A conventional nominal model predictive control problem with tightened constraints is solved online which predicts the nominal trajectory. Two ancillary control laws are determined off-line: one drives the trajectories of the real system to the trajectories of the nominal system, the other tries to cancel out the effect of the disturbance input. Both recursive feasibility of the involved optimization problem and robust stability of systems under control are guaranteed if the optimization problem is feasible at the initial time instant. The resultant online algorithm has similar complexity to that required in conventional model predictive control.

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

[2]  Hassan K. Khalil,et al.  Nonlinear Systems Third Edition , 2008 .

[3]  Gabriele Pannocchia,et al.  Robustness of MPC and Disturbance Models for Multivariable Ill-conditioned Processes , 2001 .

[4]  Shaoyuan Li,et al.  A synthesis approach of on-line constrained robust model predictive control , 2004, Autom..

[5]  Hong Chen,et al.  Model predictive control of constrained LPV systems , 2012, Int. J. Control.

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

[7]  Jun Yang,et al.  Disturbance rejection of dead-time processes using disturbance observer and model predictive control , 2011 .

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

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

[10]  Jun Yang,et al.  Disturbance rejection of ball mill grinding circuits using DOB and MPC , 2010 .

[11]  Hong Chen,et al.  Moving horizon I control with performance adaptation for constrained linear systems , 2006, Autom..

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

[13]  Cunjia Liu,et al.  Advanced control for miniature helicopters : modelling, design and flight test , 2011 .

[14]  Defeng He,et al.  Stabilizing model predictive control of time-varying non-linear systems using linear matrix inequalities , 2016, IMA J. Math. Control. Inf..

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

[16]  Jun Yang,et al.  Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach. , 2011, ISA transactions.

[17]  Peter J. Gawthrop,et al.  A nonlinear disturbance observer for robotic manipulators , 2000, IEEE Trans. Ind. Electron..

[18]  Yu Shu,et al.  An LMI Optimization Approach for Enlarging the Terminal Region of MPC for Nonlinear Systems , 2008 .

[19]  Zhanfeng Song,et al.  Robust Model Predictive Current Control of Three-Phase Voltage Source PWM Rectifier With Online Disturbance Observation , 2012, IEEE Transactions on Industrial Informatics.

[20]  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).

[21]  F. Allgöwer,et al.  Tube MPC scheme based on robust control invariant set with application to Lipschitz nonlinear systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[22]  Alberto Bemporad,et al.  Combined Design of Disturbance Model and Observer for Offset-Free Model Predictive Control , 2007, IEEE Transactions on Automatic Control.

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

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

[25]  J. H. Leet,et al.  Worst-case formulations of model predictive control for systems with bounded parameters , 1997, Autom..