Interpolation methods in model predictive control: an overview

References

• Bacic , M , Cannon , M , Lee , YI and Kouvaritakis , B . 2003 . General Interpolation in MPC and Its Advantages . IEEE Transactions on Automatic Control , 48 : 1092 – 1096 .
   Web of Science ®Google Scholar
• Blanchini , F . 1999 . Set Invariance in Control . Automatica , 35 : 1747 – 1767 .
   Web of Science ®Google Scholar
• Bloemen , HHJ , van den Boom , TJJ and Verbruggen , HB . 2002 . Optimizing the End-point State-weighting Matrix in Model-based Predictive Control . Automatica , 38 : 1061 – 1068 .
   Web of Science ®Google Scholar
• Camacho , EF and Bordons , C . 1999 . Model Predictive Control , Berlin : Springer-Verlag .
   Google Scholar
• Ding , Y and Rossiter , JA . 2006 . Enlarging Feasible Regions for Interpolation Methods , Berlin : IEEE International Conference on Communications .
   Google Scholar
• Ding , Y and Rossiter , JA . 2007 . “ Comparisons of Interpolation Methods for the Uncertain Case ” . In Proceedings of the American Control Conference
   Google Scholar
• Gilbert , EG and Tan. , KT . 1991 . Linear Systems with State and Control Constraints: The Theory and Application of Maximal Output Admissible Sets . IEEE Transactions on Automatic Control , 36 : 1008 – 1020 .
   Web of Science ®Google Scholar
• Imsland , L , Rossiter , JA , Pluymers , B and Suykens , J . 2008 . Robust Triple Mode MPC . International Journal of Control , 81 : 679 – 689 .
   Web of Science ®Google Scholar
• Kerrigan , E . 2000 . “ Robust Constraint Satisfaction: Invariant Sets and Predictive Control ” . In Ph.D. thesis Cambridge
   Google Scholar
• Kothare , MV , Balakrishnan , V and Morari , M . 1996 . Robust Constrained Model Predictive Control using Linear Matrix Inequalities . Automatica , 32 : 1361 – 1379 .
   Web of Science ®Google Scholar
• Kouvaritakis , B , Rossiter , JA and Cannon , M . 1998 . Linear Quadratic Feasible Predictive Control . Automatica , 34 : 1583 – 1592 .
   Web of Science ®Google Scholar
• Mendez , JA , Kouvaritakis , B and Rossiter , JA . 2000 . State Space approach to interpolation in MPC . International Journal of Robust Nonlinear Control , 10 : 27 – 38 .
   Web of Science ®Google Scholar
• Michalska , H and Mayne , D . 1993 . Robust Receding Horizon Control of Constrained Nonlinear Systems . IEEE Transactions on Automatic Control , 38 : 1623 – 1633 .
   Web of Science ®Google Scholar
• Muske , KR and Rawlings , JB . 1993 . Model Predictive Control with Linear Models . American Institute of Chemical Engineers Journal , 39 : 262 – 287 .
   Web of Science ®Google Scholar
• Pluymers , B , Roobrouck , L , Buijs , J , Suykens , JAK and De Moor , B . 2005a . Model-predictive Control with Time-varying Terminal Cost using Convex Combinations . Automatica , 41 : 831 – 837 .
   Google Scholar
• Pluymers , B , Rossiter , JA , Suykens , JAK and De Moor , B . 2005b . “ The Efficient Computation of Polyhedral Invariant Sets for Linear Systems with Polytopic Uncertainty ” . In Proceedings of the American Control Conference 804 – 809 . Portland, , USA
   Google Scholar
• Pluymers , B , Rossiter , JA , Suykens , JAK and De Moor , B . 2005c . “ Interpolation Based MPC for LTV Systems using Polyhedral Invariant Sets ” . In Proceedings of the American Control Conference 810 – 815 . Portland, , USA
   Google Scholar
• Pluymers , B , Rossiter , JA , Suykens , JAK and De Moor , B . 2005d . “ A Simple Algorithm for Robust MPC’, Accepted for publication ” . In Proceedings of the IFAC World Congress Prague, , Czech Republic
   Google Scholar
• Richalet , J . 1993 . Practique de la Commande Predictive , France : Hermes .
   Google Scholar
• Richalet , J . 2007 . ‘Industrial Application of Predictive Functional Control Plenary Talk’ , NMPC-SOFAP .
   Google Scholar
• Richalet , J , Rault , A , Testud , JL and Papon , J . 1978 . Model Predictive Heuristic Control: Applications to Industrial Processes . Automatica , 14 : 413 – 428 .
   Web of Science ®Google Scholar
• Rojas , OJ and Goodwin , GC . 2002 . A Simple Antiwindup Strategy for State Constrained Linear Control , IFAC World Congress .
   Google Scholar
• Rossiter , JA . 2003 . Model Based Predictive Control: A Practical Approach , Raton, FL : CRC Press .
   Google Scholar
• Rossiter , JA . 2006 . A Global Approach to Feasibility in Linear MPC , IEEE International Conference on Communications .
   Google Scholar
• Rossiter , JA , Ding , Y , Xi , L , Pluymers , B , Suykens , JAK and De Moor , B . 2005a . “ Interpolation Based MPC with Exact Constraint Handling: The Nominal Case ” . In Proceedings of the European Control Conference
   Google Scholar
• Rossiter , JA , Kouvaritakis , B and Bacic , M . 2004 . Interpolation Based Computationally Efficient Predictive Control . International Journal of Control , 77 : 290 – 301 .
   Web of Science ®Google Scholar
• Rossiter , JA , Kouvaritakis , B and Cannon , M . 2001 . Computationally Efficient Algorithms for Constraint Handling with Guaranteed Stability and Near Optimality . International Journal of Control , 74 : 1678 – 1689 .
   Web of Science ®Google Scholar
• Rossiter , JA , Kouvaritakis , B and Cannon , M . 2003 . “ Stability Proof for Computationally Efficient Predictive Control in the Uncertain Case ” . In Proceedings of the American Control Conference
   Google Scholar
• Rossiter , JA , Kouvaritakis , B and Cannon , M . 2005 . An Algorithm for Reducing Complexity in Parametric Predictive Control . International Journal of Control , 78 : 1511 – 1520 .
   Web of Science ®Google Scholar
• Rossiter , JA and Pluymers , B . 2005 . The Potential of Interpolation for Simplifying Predictive Control and Application to LPV Systems . Workshop on NMPC, Stuttgart ,
   Google Scholar
• Rossiter , JA , Neal , PW and Yao , L . 2002 . Applying Predictive Control to Fossil fired Power Station . Transactions of the Institute of Measurement and Control , 24 : 177 – 194 .
   Google Scholar
• Rossiter , JA , Rice , MJ and Kouvaritakis , B . 1998 . A Numerically Robust State-space Approach to Stable Predictive Control Strategies . Automatica , 34 : 65 – 73 .
   Web of Science ®Google Scholar
• Rossiter , JA and Wang , L . 2008 . “ Exploiting Laguerre Functions to Improve the Feasibility/performance Compromise in MPC ” . In Proceedings of the IEEE International Conference on Decision and Control
   Google Scholar
• Scokaert , POM and Rawlings , JB . 1998 . Constrained Linear Quadratic Regulation . IEEE Transactions on Automatic Control , 43 : 1163 – 1168 .
   Web of Science ®Google Scholar
• Sui , D and Ong , CJ . 2007 . “ Interpolated Model Predictive Controller for Linear Systems with Bounded Disturbances ” . In Proceedings of the American Control Conference
   Google Scholar
• Tan , KT and Gilbert , EG . 1992 . “ Multimode Controllers for Linear Discrete Time Systems with General State and Control Constraints ” . In Optimisation Techniques and Applications , 433 – 442 . Singapore : World Scientific .
   Google Scholar
• Wan , Z and Kothare , MV . 2002 . Robust Output Feedback Model Predictive Control Using Off-line Linear Matrix Inequalities . Journal of Process Control , 12 : 763 – 774 .
   Web of Science ®Google Scholar
• Wan , Z and Kothare , MV . 2003a . An Efficient Off-line Formulation of Robust Model Predictive Control using Linear Matrix Inequalities . Automatica , 39 : 837 – 846 .
   Web of Science ®Google Scholar
• Wan , Z and Kothare , MV . 2003b . Efficient Robust Constrained Model Predictive Control with a Time Varying Terminal Constraint Set . Systems and Control Letters , 48 : 375 – 383 .
   Web of Science ®Google Scholar
• Wang , L . 2004 . Discrete Model Predictive Control Design Using Laguerre Functions . Journal Process Control , 14 : 131 – 142 .
   Web of Science ®Google Scholar