Explicit improved vertex control for uncertain, time‐varying linear discrete‐time systems with state and control constraints

Summary A technique is presented to compute an explicit state feedback solution to the regulation problem for uncertain and/or time-varying linear discrete-time systems with state and control constraints. A piecewise affine control law is provided that not only guarantees recursive feasibility and robust asymptotic stability but is also optimal for a region of the state space containing the origin. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  Morten Hovd,et al.  Implicit improved vertex control for uncertain, time-varying linear discrete-time systems with state and control constraints , 2013, Autom..

[2]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[3]  Per-olof Gutman,et al.  Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states , 1984, The 23rd IEEE Conference on Decision and Control.

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

[5]  Morten Hovd,et al.  On feasible sets for MPC and their approximations , 2011, Autom..

[6]  M. Morari,et al.  Optimal complexity reduction of piecewise affine models based on hyperplane arrangements , 2004, Proceedings of the 2004 American Control Conference.

[7]  Morten Hovd,et al.  Control with constraints for linear stationary systems: An interpolation approach , 2014, Autom. Remote. Control..

[8]  M. Hovd,et al.  Improved vertex control for time-varying and uncertain linear discrete-time systems with control and state constraints , 2011, Proceedings of the 2011 American Control Conference.

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

[10]  Franco Blanchini,et al.  Minimum-time control for uncertain discrete-time linear systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[11]  Per-Olof Gutman,et al.  Explicit constraint control based on interpolation techniques for time-varying and uncertain linear discrete-time systems , 2011 .

[12]  Jun Zhang,et al.  Improved model prediction and RMPC design for LPV systems with bounded parameter changes , 2013, Autom..

[13]  Edoardo Mosca,et al.  An ellipsoidal off-line MPC scheme for uncertain polytopic discrete-time systems , 2008, Autom..

[14]  Alberto Bemporad,et al.  Model predictive control based on linear programming - the explicit solution , 2002, IEEE Transactions on Automatic Control.

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

[16]  Tor Arne Johansen,et al.  Computation, approximation and stability of explicit feedback min-max nonlinear model predictive control , 2009, Autom..

[17]  Zhenghong Yu,et al.  Worst-case formulations of model predictive control for systems with bounded parameters , 1997, Autom..

[18]  Mathieu Desbrun,et al.  Barycentric coordinates for convex sets , 2007, Adv. Comput. Math..

[19]  Mayuresh V. Kothare,et al.  An e!cient o"-line formulation of robust model predictive control using linear matrix inequalities (cid:1) , 2003 .

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