40 3.3.2 Construction based on the vertex representation, p.45 ,
On ultimate boundedness control of uncertain systems in the absence of matching assumptions. Automatic Control, IEEE Transactions on, vol.27, issue.1, pp.153-158, 1982. ,
The explicit linear quadratic regulator for constrained systems, Automatica, vol.38, issue.1, pp.3-20, 2002. ,
DOI : 10.1016/S0005-1098(01)00174-1
Min-max control of constrained uncertain discrete-time linear systems, IEEE Transactions on Automatic Control, vol.48, issue.9, pp.1600-1606, 2003. ,
DOI : 10.1109/TAC.2003.816984
Model Predictive Control ??? Numerical Methods for the Invariant Sets Approximation, Numerical Analysis and Its Applications, pp.192-199, 2009. ,
DOI : 10.1109/TAC.2005.843854
URL : https://hal.archives-ouvertes.fr/hal-00431013
On the construction of invariant sets for piecewise affine systems using the transition graph, 2009 IEEE International Conference on Control and Automation, pp.122-127, 2009. ,
DOI : 10.1109/ICCA.2009.5410557
URL : https://hal.archives-ouvertes.fr/hal-00418327
On the positive invariance of polyhedral sets for discrete-time systems, Systems & Control Letters, vol.11, issue.3, pp.243-248, 1988. ,
DOI : 10.1016/0167-6911(88)90065-5
Positively invariant polyhedral sets of discrete-time linear systems, International Journal of Control, vol.82, issue.6, pp.1713-1726, 1988. ,
DOI : 10.1080/00207178808906132
Constrained regulation of linear systems, Automatica, vol.31, issue.2, pp.223-227, 1995. ,
DOI : 10.1016/0005-1098(94)E0053-K
Ultimate boundedness control for uncertain discrete-time systems via set-induced lyapunov functions. Automatic Control, IEEE Transactions on, vol.39, issue.2, pp.428-433, 1994. ,
Set invariance in control, Automatica, vol.35, issue.11, pp.1747-1767, 1999. ,
DOI : 10.1016/S0005-1098(99)00113-2
Set-theoretic methods in control, 2008. ,
DOI : 10.1007/978-3-319-17933-9
Convex optimization, 2004. ,
Linear matrix inequalities in system and control theory, SIAM, vol.15, 1994. ,
DOI : 10.1137/1.9781611970777
Rank revealing QR factorizations, Linear Algebra and its Applications, vol.88, issue.89, pp.67-82, 1987. ,
DOI : 10.1016/0024-3795(87)90103-0
On constrained infinite-time linear quadratic optimal control, Decision and Control Proceedings of the 35th IEEE Conference on, pp.1319-1324, 1996. ,
Plane self stresses and projected polyhedra 1: the basic pattern, Structural Topology, vol.19, pp.55-73, 1993. ,
Spaces of stresses, projections and parallel drawings for spherical polyhedra. Contributions to Algebra and Geometry, pp.259-281, 1994. ,
Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties, Systems & Control Letters, vol.43, issue.5, pp.355-359, 2001. ,
DOI : 10.1016/S0167-6911(01)00118-9
Triangulations. structures for algorithms and applications, Algorithms and Computation in Mathematics, vol.25, 2010. ,
Non-fragile controller design: an overview, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), pp.2829-2831, 1998. ,
DOI : 10.1109/ACC.1998.688371
Voronoi diagrams and arrangements, Discrete Comput. Geom, 1986. ,
An improved algorithm for combinatorial multi-parametric quadratic programming, Automatica, vol.49, issue.5, pp.1370-1376, 2013. ,
DOI : 10.1016/j.automatica.2013.02.022
URL : https://hal.archives-ouvertes.fr/hal-00827224
Inverse Optimality in Robust Stabilization, SIAM Journal on Control and Optimization, vol.34, issue.4, pp.1365-1391, 1996. ,
DOI : 10.1137/S0363012993258732
cdd/cdd+ reference manual. Institute for Operations Research, 1997. ,
Postoptimal analyses, parametric programming and related topics, 1995. ,
DOI : 10.1515/9783110871203
Fourier-motzkin elimination and its dual, Journal of Combinatorial Theory, Series A, vol.14, issue.3, pp.288-297, 1973. ,
Linear systems with state and control constraints: the theory and application of maximal output admissible sets, IEEE Transactions on Automatic Control, vol.36, issue.9, pp.1008-1020, 1991. ,
DOI : 10.1109/9.83532
Explicit Nonlinear Model Predictive Control, 2012. ,
DOI : 10.1007/978-3-642-28780-0
Convex polytopes, 1967. ,
Implications of Inverse Parametric Optimization in Model Predictive Control, Developments in Model- Based Optimization and Control, 2015. ,
DOI : 10.1007/978-3-319-26687-9_3
URL : https://hal.archives-ouvertes.fr/hal-01259959
Admissible sets and feedback control for discretetime linear dynamical systems with bounded controls and states. Automatic Control, IEEE Transactions on, vol.31, issue.4, pp.373-376, 1986. ,
An algorithm to find maximal state constraint sets for discrete-time linear dynamical systems with bounded controls and states. Automatic Control, IEEE Transactions on, vol.32, issue.3, pp.251-254, 1987. ,
Recognizing Voronoi Diagrams with Linear Programming, ORSA Journal on Computing, vol.4, issue.4, 1992. ,
DOI : 10.1287/ijoc.4.4.369
Equivalence of hybrid dynamical models, Automatica, vol.37, issue.7, pp.1085-1091, 2001. ,
DOI : 10.1016/S0005-1098(01)00059-0
Inverse Parametric Optimization With an Application to Hybrid System Control, IEEE Transactions on Automatic Control, vol.60, issue.4, pp.1064-1069, 2015. ,
DOI : 10.1109/TAC.2014.2336992
Discrete Time Constrained Linear Systems, Control and Dynamic Systems, vol.71, pp.157-213, 1995. ,
DOI : 10.1016/S0090-5267(06)80018-6
Multi-Parametric Toolbox 3.0, Proc. of the European Control Conference, pp.502-510, 2013. ,
Relaxing PWQ Lyapunov stability criteria for PWA systems, Automatica, vol.49, issue.2, 2012. ,
DOI : 10.1016/j.automatica.2012.10.013
URL : https://hal.archives-ouvertes.fr/hal-00794374
Piecewise quadratic lyapunov functions for stability verification of approximate explicit mpc. Modeling, Identification and Control, pp.45-53, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00524537
On multi-parametric nonlinear programming and explicit nonlinear model predictive control, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., pp.2768-2773, 2002. ,
DOI : 10.1109/CDC.2002.1184260
Approximate explicit receding horizon control of constrained nonlinear systems, Automatica, vol.40, issue.2, pp.293-300, 2004. ,
DOI : 10.1016/j.automatica.2003.09.021
When Is a Linear Control System Optimal?, Journal of Basic Engineering, vol.86, issue.1, pp.51-60, 1964. ,
DOI : 10.1115/1.3653115
Robust, fragile, or optimal? Transactions on Automatic Control, pp.1098-1105, 1997. ,
Robust constraint satisfaction: Invariant sets and predictive control, 2001. ,
Nonlinear systems, p.323, 2002. ,
A systematic method to obtain ultimate bounds for perturbed systems, International Journal of Control, vol.18, issue.2, pp.167-178, 2007. ,
DOI : 10.1109/9.763226
Theory and computation of disturbance invariant sets for discrete-time linear systems, Mathematical Problems in Engineering, vol.4, issue.4, pp.317-367, 1998. ,
DOI : 10.1155/S1024123X98000866
A revisit to inverse optimality of linear systems, International Journal of Control, vol.5, issue.10, pp.1506-1514, 2012. ,
DOI : 10.1049/iet-cta.2007.0371
Robust constrained model predictive control using linear matrix inequalities, Automatica, vol.32, issue.10, pp.1361-1379, 1996. ,
DOI : 10.1016/0005-1098(96)00063-5
Inverse optimal design of input-to-state stabilizing nonlinear controllers, IEEE Transactions on Automatic Control, vol.43, issue.3, pp.336-350, 1998. ,
DOI : 10.1109/9.661589
Inverse optimal stabilization of a rigid spacecraft Automatic Control, IEEE Transactions on, vol.44, issue.5, pp.1042-1049, 1999. ,
Real-time model predictive control via multi-parametric programming: theory and tools, 2009. ,
Clipping-based complexity reduction in explicit mpc Automatic Control, IEEE Transactions on, vol.57, issue.7, pp.1878-1883, 2012. ,
Complexity reduction of explicit model predictive control via separation, Automatica, vol.49, issue.6, pp.1776-1781, 2013. ,
DOI : 10.1016/j.automatica.2013.02.018
About the inverse problem of optimal control, 2003. ,
P.L.-Spheres, convex polytopes, and stress, Discrete & Computational Geometry, vol.16, issue.4, 1996. ,
DOI : 10.1007/BF02711516
URL : https://hal.archives-ouvertes.fr/jpa-00224550
YALMIP : a toolbox for modeling and optimization in MATLAB, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508), pp.284-289, 2004. ,
DOI : 10.1109/CACSD.2004.1393890
Inverse minimax optimality of model predictive control policies, Systems & Control Letters, vol.58, issue.1, pp.31-38, 2009. ,
DOI : 10.1016/j.sysconle.2008.07.005
On reciprocal diagrams and diagrams of forces. Philosophical Magazine, ser. 4, pp.250-261 ,
Constrained Control of Uncertain, Time-Varying, Discrete-Time Systems: An Interpolation-Based Approach, Lecture Notes in Control and Information Sciences, vol.451, 2014. ,
DOI : 10.1007/978-3-319-02827-9
Explicit constraint control based on interpolation techniques for time-varying and uncertain linear discrete-time systems, World Congress, pp.5741-5746, 2011. ,
DOI : 10.3182/20110828-6-IT-1002.03517
URL : https://hal.archives-ouvertes.fr/hal-00592340
Constructive solution of inverse parametric linear/quadratic programming problems . a. URL https ,
URL : https://hal.archives-ouvertes.fr/hal-01207234
Convex liftingsbased robust control design ,
URL : https://hal.archives-ouvertes.fr/hal-01509316
Explicit fragility margins for PWA control laws of discrete-time linear systems, 2014 European Control Conference (ECC), 2014. ,
DOI : 10.1109/ECC.2014.6862538
URL : https://hal.archives-ouvertes.fr/hal-01087256
An inverse optimality argument to improve robustness in constrained control, IFAC World Congress, pp.1631-1636, 2014. ,
DOI : 10.3182/20140824-6-ZA-1003.02586
URL : https://hal.archives-ouvertes.fr/hal-01086391
On the lifting problems and their connections with piecewise affine control law design, 2014 European Control Conference (ECC), 2014. ,
DOI : 10.1109/ECC.2014.6862605
URL : https://hal.archives-ouvertes.fr/hal-01087243
Inverse parametric convex programming problems via convex liftings, 19th IFAC World Congress, 2014. ,
DOI : 10.3182/20140824-6-ZA-1003.02364
URL : https://hal.archives-ouvertes.fr/hal-01086492
Explicit robustness and fragility margins for linear discrete systems with piecewise affine control law, Automatica, vol.68, 2015. ,
DOI : 10.1016/j.automatica.2015.10.048
URL : https://hal.archives-ouvertes.fr/hal-01408554
Any discontinuous PWA function is optimal solution to a parametric linear programming problem, 2015 54th IEEE Conference on Decision and Control (CDC), 2015. ,
DOI : 10.1109/CDC.2015.7403151
URL : https://hal.archives-ouvertes.fr/hal-01259879
Inverse parametric linear/quadratic programming problem for continuous PWA functions defined on polyhedral partitions of polyhedra, 2015 54th IEEE Conference on Decision and Control (CDC), 2015. ,
DOI : 10.1109/CDC.2015.7403150
URL : https://hal.archives-ouvertes.fr/hal-01259895
Recognition of additively weighted Voronoi diagrams and weighted Delaunay decompositions, 2015 European Control Conference (ECC), 2015. ,
DOI : 10.1109/ECC.2015.7330565
URL : https://hal.archives-ouvertes.fr/hal-01259935
On the complexity of the convex liftings-based solution to inverse parametric convex programming problems, 2015 European Control Conference (ECC), 2015. ,
DOI : 10.1109/ECC.2015.7331064
URL : https://hal.archives-ouvertes.fr/hal-01140609
Robust control design based on convex liftings, the 8th IFAC Symposium on Robust Control Design, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01159892
Hovd, and I. Necoara. Fully inverse parametric linear/quadratic programming problems via convex liftings ,
A parameterized polyhedra approach for explicit constrained predictive control, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), pp.1580-1585, 2004. ,
DOI : 10.1109/CDC.2004.1430269
Avoiding constraints redundancy in predictive control optimization routines. Automatic Control, IEEE Transactions on, vol.50, issue.9, pp.1459-1465, 2005. ,
On the continuity and complexity of control laws based on multiparametric linear programs, Proceedings of the 45th IEEE Conference on Decision and Control, pp.5465-5470, 2006. ,
DOI : 10.1109/CDC.2006.377330
URL : https://hal.archives-ouvertes.fr/hal-00261371
Positive invariant sets for fault tolerant multisensor control schemes, International Journal of Control, vol.40, issue.12, pp.2622-2640, 2010. ,
DOI : 10.1016/j.automatica.2004.01.014
URL : https://hal.archives-ouvertes.fr/hal-00293927
Explicit robustness margins for discrete-time linear systems with PWA control, 2013 17th International Conference on System Theory, Control and Computing (ICSTCC), 2013. ,
DOI : 10.1109/ICSTCC.2013.6688989
URL : https://hal.archives-ouvertes.fr/hal-00917917
Mono-and Multivariable Control and Estimation: Linear, Quadratic and LMI Methods, 2011. ,
DOI : 10.1007/978-3-642-13734-1
Multi-parametric programming, 2007. ,
DOI : 10.1002/9783527631216
The Minkowski???Lyapunov equation for linear dynamics: Theoretical foundations, Automatica, vol.50, issue.8, pp.2015-2024, 2014. ,
DOI : 10.1016/j.automatica.2014.05.023
Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), pp.1418-1423, 2004. ,
DOI : 10.1109/CDC.2004.1430242
Invariant approximations of the minimal robust positively invariant set. Automatic Control, IEEE Transactions on, vol.50, issue.3, pp.406-410, 2005. ,
Reachability analysis of discrete-time systems with disturbances. Automatic Control, IEEE Transactions on, vol.51, issue.4, pp.546-561, 2006. ,
Model predictive heuristic control, Automatica, vol.14, issue.5, pp.413-428, 1978. ,
DOI : 10.1016/0005-1098(78)90001-8
Convex analysis. Number 28, 1970. ,
Tuning mpc using h ? loop shaping, American Control Conference Proceedings of the 2000, pp.1332-1336, 2000. ,
Research on gain scheduling, Automatica, vol.36, issue.10, pp.1401-1425, 2000. ,
DOI : 10.1016/S0005-1098(00)00058-3
Polyhedral Partitions and Stresses, 1999. ,
Convex bodies: the Brunn?Minkowski theory, 2013. ,
DOI : 10.1017/CBO9780511526282
Theory of linear and integer programming, 1998. ,
Lifting Planar Graphs to Realize Integral 3-Polytopes and Topics in Pseudo-Triangulations, 2008. ,
Approximate explicit linear mpc via delaunay tessellation, Control Conference (ECC), pp.2833-2838, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00418337
Characterisation Of Receding Horizon Control For Constrained Linear Systems, Asian Journal of Control, vol.6, issue.6, pp.271-286, 2003. ,
DOI : 10.1111/j.1934-6093.2003.tb00118.x
On the facet-to-facet property of solutions to convex parametric quadratic programs, Automatica, vol.42, issue.12, pp.422209-2214, 2006. ,
DOI : 10.1016/j.automatica.2006.06.026
Set-theoretic Fault-tolerant Control in Multisensor Systems, 2013. ,
DOI : 10.1002/9781118649428
URL : https://hal.archives-ouvertes.fr/hal-00826961
Robust explicit MPC design under finite precision arithmetic, Proceedings of the 19th World Congress The International Federation of Automatic Control, 2014. ,
DOI : 10.3182/20140824-6-ZA-1003.01033
Suboptimal control of linear systems with state and control inequality constraints, 26th IEEE Conference on Decision and Control, 1987. ,
DOI : 10.1109/CDC.1987.272491
Robust Positively Invariant Sets for Linear Systems subject to model-uncertainty and disturbances, Nonlinear Model Predictive Control, pp.213-217, 2012. ,
DOI : 10.3182/20120823-5-NL-3013.00032
An algorithm for multi-parametric quadratic programming and explicit MPC solutions, Automatica, vol.39, issue.3, pp.489-497, 2003. ,
DOI : 10.1016/S0005-1098(02)00250-9
Constrained regulation of linear continuous-time dynamical systems, Systems & Control Letters, vol.13, issue.3, pp.247-252, 1989. ,
DOI : 10.1016/0167-6911(89)90071-6
Feedback control of linear discrete-time systems under state and control constraints, International Journal of Control, vol.13, issue.6, pp.1727-1735, 1988. ,
DOI : 10.1109/TAC.1985.1103785
Fast Model Predictive Control Using Online Optimization, IEEE Transactions on Control Systems Technology, vol.18, issue.2, pp.267-278, 2010. ,
DOI : 10.1109/TCST.2009.2017934
Lectures on polytopes, 1995. ,
DOI : 10.1007/978-1-4613-8431-1