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Low-complexity method for hybrid MPC with local guarantees. (English) Zbl 1421.93049
93B40 Computational methods in systems theory (MSC2010)
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B28 Operator-theoretic methods
90C30 Nonlinear programming
49J52 Nonsmooth analysis
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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[1] A. Alessio and A. Bemporad, A survey on explicit model predictive control, in Nonlinear Model Predictive Control, Springer, 2009, pp. 345–369, https://doi.org/10.1007/978-3-642-01094-1_29. · Zbl 1195.93048
[2] A. Arce, A. del Real, and C. Bordons, MPC for battery/fuel cell hybrid vehicles including fuel cell dynamics and battery performance improvement, J. Process Control, 19 (2009), pp. 1289–1304, https://doi.org/10.1016/j.jprocont.2009.03.004.
[3] D. Axehill, Integer Quadratic Programming for Control and Communication, Ph.D. thesis, Linköping University, 2008.
[4] H. Bauschke and P. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, Springer, 2011, https://doi.org/10.1007/978-3-319-48311-5. · Zbl 1218.47001
[5] A. Bemporad and M. Morari, Control of systems integrating logic, dynamics, and constraints, Automatica, 35 (1999), pp. 407–427, https://doi.org/10.1016/S0005-1098(98)00178-2. · Zbl 1049.93514
[6] V. Berinde, Iterative Approximation of Fixed Points, 2nd ed., Springer, 2007, https://doi.org/10.1007/978-3-540-72234-2. · Zbl 1165.47047
[7] S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein, Distributed optimization and statistical learning via the alternating direction method of multipliers, Found. Trends Mach. Learn., 3 (2011), pp. 1–122, https://doi.org/10.1561/2200000016. · Zbl 1229.90122
[8] G. Dantzig, Linear Programming and Extensions, Princeton University Press, 1963, https://doi.org/10.7249/r366.
[9] S. Di Cairano, A. Bemporad, I. Kolmanovsky, and D. Hrovat, Model predictive control of magnetically actuated mass spring dampers for automotive applications, Int. J. Control, 80 (2007), pp. 1701–1716, https://doi.org/10.1080/00207170701379804. · Zbl 1130.93345
[10] A. Domahidi, A. Zgraggen, M. Zeilinger, M. Morari, and C. Jones, Efficient interior point methods for multistage problems arising in receding horizon control, in Proceedings of the 51st IEEE Conference on Decision and Control, Maui, HI, 2012, pp. 668–674, https://doi.org/10.1109/cdc.2012.6426855.
[11] D. Frick, Automatic Code Generation Tool, https://github.com/dafrick/codegen, 2016.
[12] D. Frick, A. Domahidi, and M. Morari, Embedded optimization for mixed logical dynamical systems, Comput. Chem. Engrg., 72 (2015), pp. 21–33, https://doi.org/10.1016/j.compchemeng.2014.06.005.
[13] T. Geyer, G. Papafotiou, R. Frasca, and M. Morari, Constrained optimal control of the step-down DC-DC converter, IEEE Trans. Power Electronics, 23 (2008), pp. 2454–2464, https://doi.org/10.1109/TPEL.2008.2002057.
[14] A. Hempel, Control of Piecewise Affine Systems through Inverse Optimization, Ph.D. thesis, Dissertation ETH No. 23222, ETH Zürich, 2016, https://doi.org/10.3929/ethz-a-010615354.
[15] R. Henrion and J. Outrata, On calculating the normal cone to a finite union of convex polyhedra, Optimization, 57 (2008), pp. 57–78, https://doi.org/10.1080/02331930701778874. · Zbl 1220.52001
[16] M. Herceg, M. Kvasnica, C. Jones, and M. Morari, Multi-parametric toolbox 3.0, in Proceedings of the European Control Conference, IEEE, 2013, pp. 502–510, https://doi.org/10.23919/ecc.2013.6669862.
[17] J.-H. Hours and C. Jones, A parametric nonconvex decomposition algorithm for real-time and distributed NMPC, IEEE Trans. Automat. Control, 61 (2016), pp. 287–302, https://doi.org/10.1109/TAC.2015.2426231. · Zbl 1359.90134
[18] B. Houska, J. Frasch, and M. Diehl, An augmented Lagrangian based algorithm for distributed nonconvex optimization, SIAM J. Optim., 26 (2016), pp. 1101–1127, https://doi.org/10.1137/140975991. · Zbl 1345.90069
[19] IBM, IBM ILOG CPLEX Optimization Studio, 2015.
[20] M. Jung, Relaxations and Approximations for Mixed-Integer Optimal Control, Ph.D. thesis, Universität Heidelberg, 2013, https://doi.org/10.11588/heidok.00016036.
[21] M. N. Jung, C. Kirches, and S. Sager, On perspective functions and vanishing constraints in mixed-integer nonlinear optimal control, in Facets of Combinatorial Optimization, Springer, 2013, pp. 387–417, https://doi.org/10.1007/978-3-642-38189-8_16. · Zbl 1320.49011
[22] R. Lang, A note on the measurability of convex sets, Arch. Math. (Basel), 47 (1986), pp. 90–92, https://doi.org/10.1007/BF01202504. · Zbl 0607.28003
[23] S. Leyffer, MacMPEC: AMPL Collection of MPECs, Argonne National Laboratory, https://wiki.mcs.anl.gov/leyffer/index.php/MacMPEC, 2009.
[24] G. Li and T. Pong, Global convergence of splitting methods for nonconvex composite optimization, SIAM J. Optim., 25 (2015), pp. 2434–2460, https://doi.org/10.1137/140998135. · Zbl 1330.90087
[25] A. Liniger, A. Domahidi, and M. Morari, Optimization-based autonomous racing of 1:43 scale RC cars, Optimal Control Appl. Methods, 36 (2015), pp. 628–647, https://doi.org/10.1002/oca.2123. · Zbl 1330.93094
[26] J. Löfberg, YALMIP: A toolbox for modeling and optimization in MATLAB, in Proceedings of the IEEE International Conference on Robotics and Automation, New Orleans, LA, 2004, pp. 284–289, https://doi.org/10.1109/CACSD.2004.1393890.
[27] S. Magnússon, P. C. Weeraddana, M. G. Rabbat, and C. Fischione, On the convergence of alternating direction Lagrangian methods for nonconvex structured optimization problems, IEEE Trans. Control Network Syst., 3 (2016), pp. 296–309, https://doi.org/10.1109/TCNS.2015.2476198. · Zbl 1370.90196
[28] M. Morari and J. Lee, Model predictive control: Past, present and future, Comput. Chem. Engrg., 23 (1999), pp. 667–682, https://doi.org/10.1016/S0098-1354(98)00301-9.
[29] J. Nocedal and S. Wright, Numerical Optimization, 2nd ed., Springer Science+Business Media, 2006, https://doi.org/10.1007/978-0-387-40065-5.
[30] R. A. Poliquin, R. T. Rockafellar, and L. Thibault, Local differentiability of distance functions, Trans. Amer. Math. Soc., 352 (2000), pp. 5231–5249, https://www.jstor.org/stable/221932. · Zbl 0960.49018
[31] R. Rockafellar and R. Wets, Variational Analysis, Springer, 1998, https://doi.org/10.1007/978-3-642-02431-3.
[32] A. Ruszczyński, Nonlinear Optimization, Princeton University Press, 2006, https://doi.org/10.2307/j.ctvcm4hcj.
[33] R. Takapoui, N. Moehle, S. Boyd, and A. Bemporad, A simple effective heuristic for embedded mixed-integer quadratic programming, Int. J. Control, (2017), pp. 1–11, https://doi.org/10.1080/00207179.2017.1316016.
[34] J. Vielma, Mixed integer linear programming formulation techniques, SIAM Rev., 57 (2015), pp. 3–57, https://doi.org/10.1137/130915303. · Zbl 1338.90277
[35] J. J. Ye, Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints, SIAM J. Optim., 10 (2000), pp. 943–962, https://doi.org/10.1137/S105262349834847X. · Zbl 1005.49019
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