Online robust tube-based MPC for time-varying systems: a practical approach

This article focuses on the design of a robust model predictive control law for constrained discrete-time time-varying systems with additive uncertainties. The proposed solution to the control problem is a tube-based MPC ensuring robustness and constraints fulfilment. Reachable sets are calculated online taking into account the system dynamics by means of an adaptive local control law and additive uncertainties. The proposed method represents a trade-off between small conservativeness and efficient real-time execution. This approach is applied to solve the trajectory tracking problem of a mobile robot. Simulation results provide a comparison between the tube-based MPC scheme and established motion control algorithms, showing the efficient execution and satisfactory behaviour of the proposed controller.

[1]  Eduardo F. Camacho,et al.  Robust tube-based MPC for tracking of constrained linear systems with additive disturbances , 2010 .

[2]  Alberto Bemporad,et al.  Robust model predictive control: A survey , 1998, Robustness in Identification and Control.

[3]  M. Berenguel,et al.  Localization and control of tracked mobile robots under slip conditions , 2009, 2009 IEEE International Conference on Mechatronics.

[4]  David Q. Mayne,et al.  Robust model predictive control using tubes , 2004, Autom..

[5]  D. Bertsekas,et al.  On the minimax reachability of target sets and target tubes , 1971 .

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

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

[8]  David Q. Mayne,et al.  Robust output feedback model predictive control of constrained linear systems: Time varying case , 2009, Autom..

[9]  David Q. Mayne,et al.  Robust output feedback model predictive control of constrained linear systems , 2006, Autom..

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

[11]  Jo Yung Wong,et al.  Theory of ground vehicles , 1978 .

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

[13]  Jay H. Lee,et al.  Model predictive control: past, present and future , 1999 .

[14]  Eduardo F. Camacho,et al.  Efficient implementation of constrained min–max model predictive control with bounded uncertainties: a vertex rejection approach , 2005 .

[15]  José Luis Guzmán,et al.  Adaptive control for a mobile robot under slip conditions using an LMI-based approach , 2009 .

[16]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[17]  E. Gilbert,et al.  Theory and computation of disturbance invariant sets for discrete-time linear systems , 1998 .

[18]  Mirko Fiacchini.  Convex Difference Inclusions for Systems Analysis and Design. Inclusiones Convexas para el Análisis y el Diseño. , 2013 .

[19]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[20]  T. Alamo,et al.  Stability analysis of systems with bounded additive uncertainties based on invariant sets: Stability and feasibility of MPC , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[21]  Paul A. Trodden,et al.  Distributed model predictive control of linear systems with persistent disturbances , 2010, Int. J. Control.

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

[23]  Eduardo F. Camacho,et al.  Min-Max MPC based on a computationally efficient upper bound of the worst case cost , 2006 .

[24]  Roland Siegwart,et al.  Introduction to Autonomous Mobile Robots , 2004 .

[25]  David Q. Mayne,et al.  Robustifying model predictive control of constrained linear systems , 2001 .

[26]  D. Limón,et al.  Robust MPC of constrained nonlinear systems based on interval arithmetic , 2005 .

[27]  Francisco Rodríguez,et al.  Robust tube-based predictive control for mobile robots in off-road conditions , 2011, Robotics Auton. Syst..

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

[29]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[30]  Carlos Canudas de Wit,et al.  Theory of Robot Control , 1996 .