Abstract
This chapter presents a modified version of \(\ell _{asso}\)-MPC that guarantees closed-loop asymptotic stability for arbitrary 1-norm input penalties. The approach is based on a new terminal cost and terminal constraint. Appropriate scalings are computed to adjust the proposed former according to the stage cost matrices. In particular, two strategies are presented to compute the required ingredients. The first one makes use of norm inequalities and linear matrix inequalities.
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References
Alessio A, Bemporad A (2009) A survey on explicit model predictive control. Nonlinear model predictive control: lecture notes in control and information sciences, vol 38, pp 345–369
Blanchini F (1994) Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions. IEEE Trans Autom Control 39:428–433
Blanchini F, Miani S (2003) Stabilisation of LPV systems: state feedback, state estimation and duality. In: Proceedings of the conference on decision and control (CDC)
Blanchini F, Miani S (2008) Set-theoretic methods in control. Birkhäuser, Boston
Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM
Cannon M, Deshmukh V, Kouvaritakis B (2003) Nonlinear model predictive control with polytopic invariant sets. Automatica 39:1487–1494
Fiacchini M, Alamo T, Camacho EF (2012) Invariant sets computation for convex difference inclusions systems. Syst Control Lett 8:819–826
Gallieri M, Maciejowski JM (2012) \(\ell _{asso}\) MPC: smart regulation of overactuated systems. In: Proceedings of the American control conference (ACC), pp 1217–1222
Gallieri M, Maciejowski J (2013a) Soft-constrained Lasso-MPC for robust LTI tracking: enlarged feasible region and an ISS gain estimate. In: Proceedings of the conference on decision and control (CDC), pp 7101–7106
Gallieri M, Maciejowski JM (2013b) Stabilising terminal cost and terminal controller for \(\ell _{asso}\)-MPC: enhanced optimality and region of attraction. In: Proceedings of the European control conference (ECC), pp 524–529
Grammatico S, Pannocchia G (2013) Achieving a large domain of attraction with short-horizon linear MPC via polyhedral Lyapunov functions. In: Proceedings of the European control conference (ECC), pp 1059–1064
Horn RA, Johnson CR (2010) Matrix analysis. Cambridge University Press, Cambridge
Kerrigan E (2000) Robust constraint satisfaction: invariant sets and predictive control. PhD thesis, University of Cambridge - St. John’s college
Kim SJ, Lusting M, Stephen Boyd, Gorinevsky D (2007b) An interior-point method for large-scale \(\ell _1\)-regularised least squares. J Sel Top Signal Process 1(4):606–617
Kothare Mayuresh V, Venkataramanan Balakrishnan, Manfred Morari (1996) Robust constrained model predictive control using linear matrix inequalities. Automatica 32(10):1361–1379
Lazar M (2010) On infinity norms as Lyapunov functions: alternative necessary and sufficient conditions. In: Proceedings of the Conference on decision and control (CDC), pp 5936–5942
Lazar M, Jokic A (2010) On infinity norms as Lyapunov functions for piecewise affine systems. In: Proceedings of the hybrid systems computation and control conference, pp 131–141
Lazar M, Heemels WPMH, Weiland S, Bemporad A (2006) Stabilizing model predictive control of hybrid systems. IEEE Trans Autom Control 51(11):1813–1818
Limon D, Alamo T, Camacho Eduardo F (2005) Enlarging the domain of attraction of MPC controllers. Automatica 41(4):629–635
Raković S, Lazar M (2012) Minkowski terminal cost functions for MPC. Automatica 48(10):2721–2725
Rawlings JB, Mayne DQ (2009) Model predictive control theory and design. Nob Hill Pub Llc, Madison
Sptvold J, Tndel P, Johansen TA (2007) Continuous selection and unique polyhedral representation of solutions to convex parametric quadratic programs. J Optim Theory Appl 134(2):177–189
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Gallieri, M. (2016). Version 2: LASSO MPC with Stabilising Terminal Cost. In: Lasso-MPC – Predictive Control with ℓ1-Regularised Least Squares. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-27963-3_5
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DOI: https://doi.org/10.1007/978-3-319-27963-3_5
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