Robust region elimination for piecewise affine control laws. (English) Zbl 1406.93120
Summary: This paper is concerned with uncertain linear discrete-time systems controlled by a piecewise affine feedback law defined on a polyhedral domain. Assuming the initial state is contained in a given set, a novel algorithm is proposed to identify regions of the polyhedral partition which are guaranteed not to be visited during real-time operation. By dispensing with the need to store the aforementioned regions and associated control functions, the proposed method enables a reduction in both storage and online computational demands.
MSC:
| 93B40 | Computational methods in systems theory (MSC2010) |
| 93C41 | Control/observation systems with incomplete information |
| 93C55 | Discrete-time control/observation systems |
| 93C05 | Linear systems in control theory |
| 93B52 | Feedback control |
| 93-04 | Software, source code, etc. for problems pertaining to systems and control theory |
Keywords:
piecewise affine system; explicit model predictive control; region elimination; computational complexitySoftware:
MPTReferences:
| [1] | Airan, A.; Bhushan, M.; Bhartiya, S., Linear machine solution to point location problem, IEEE Transactions on Automatic Control, 62, 3, 1403-1410 (2017) · Zbl 1366.90127 |
| [2] | Alessandro, A.; Bemporad, A., A survey on explicit model predictive control, (Nonlinear model predictive control, vol. 384 (2009), Springer: Springer Berlin/Heidelberg, Germany), 345-369 · Zbl 1195.93048 |
| [3] | Bemporad, A.; Borrelli, F.; Morari, M., Model predictive control based on linear programming - the explicit solution, IEEE Transactions on Automatic Control, 47, 12, 1974-1985 (2002) · Zbl 1364.93697 |
| [4] | Bemporad, A.; Borrelli, F.; Morari, M., Min-max control of constrained uncertain discrete-time linear systems, IEEE Transactions on Automatic Control, 48, 9, 1600-1606 (2003) · Zbl 1364.93181 |
| [5] | Bemporad, A.; Filippi, C., Suboptimal explicit receding horizon control via approximate multiparametric quadratic programming, Journal of Optimization Theory and Applications, 117, 1, 9-38 (2003) · Zbl 1044.90080 |
| [6] | Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N., The explicit linear quadratic regulator for constrained systems, Automatica, 38, 1, 3-20 (2002) · Zbl 0999.93018 |
| [7] | Bemporad, A.; Oliveri, A.; Poggi, T.; Storace, M., Ultra-fast stabilizing model predictive control via canonical piecewise affine approximations, IEEE Transactions on Automatic Control, 56, 12, 2883-2897 (2011) · Zbl 1368.93356 |
| [8] | Borrelli, F.; Bemporad, A.; Morari, M., Predictive control for linear and hybrid systems (2015), Cambridge University Press |
| [9] | Christophersen, F. J.; Zeilinger, M. N.; Jones, C. N.; Morari, M., Controller complexity reduction for piecewise affine systems through safe region elimination, (Proc. Conference on decision and control (2007)), 4773-4778 |
| [10] | Gao, Y.; Sun, L. N., Explicit solution of min-max model predictive control for uncertain systems, IET Control Theory & Applications, 10, 4, 461-468 (2016) |
| [11] | Genuit, B. A.G.; Lu, L.; Heemels, W. P.M. H., Approximation of explicit model predictive control using regular piecewise affine functions: an input-to-state stability approach, IET Control Theory & Applications, 6, 8, 1015-1028 (2012) |
| [12] | Geyer, T.; Torrisi, F. D.; Morari, M., Optimal complexity reduction of polyhedral piecewise affine systems, Automatica, 44, 7, 1728-1740 (2008) · Zbl 1149.93303 |
| [13] | Grancharova, A.; Johansen, T. A., Approximate explicit model predictive control incorporating heuristics, (Proc. International symposium on computer aided control system design (2002)), 92-97 |
| [14] | Herceg, M.; Kvasnica, M.; Jones, C.; Morari, M., Multi-parametric toolbox 3.0, (Proc. European control conference (2013)), 502-510 |
| [15] | Johansen, T. A.; Grancharova, A., Approximate explicit constrained linear model predictive control via orthogonal search tree, IEEE Transactions on Automatic Control, 48, 5, 810-815 (2003) · Zbl 1364.93396 |
| [16] | Johansen, T. A.; Jackson, W.; Schreiber, R.; Tondel, P., Hardware synthesis of explicit model predictive controllers, IEEE Transactions on Control Systems Technology, 15, 1, 191-197 (2007) |
| [17] | Jones, C. N.; Grieder, P.; Rakovic, S. V., A logarithmic-time solution to the point location problem for parametric linear programming, Automatica, 42, 12, 2215-2218 (2006) · Zbl 1120.90029 |
| [18] | Jones, C. N.; Morari, M., The double description method for the approximation of explicit MPC Control Laws, (Proc. Conference on decision and control (2008)), 4724-4730 |
| [19] | Jones, C. N.; Morari, M., Polytopic approximation of explicit model predictive controllers, IEEE Transactions on Automatic Control, 55, 11, 2292-2297 (2010) · Zbl 1368.93172 |
| [20] | Kvasnica, M.; Fikar, M., Clipping-Based complexity reduction in explicit MPC, IEEE Transactions on Automatic Control, 57, 7, 1878-1883 (2012) · Zbl 1369.93344 |
| [21] | Kvasnica, M.; Löfberg, J.; Fikar, M., Stabilizing polynomial approximation of explicit MPC, Automatica, 47, 10, 2542-2553 (2011) |
| [22] | Kvasnica, M.; Takács, B.; Holaza, J.; Ingole, D., Reachability analysis and control synthesis for uncertain linear systems in MPT, IFAC-PapersOnLine, 48, 14, 302-307 (2015) |
| [23] | Martínez-Rodríguez, M. C.; Brox, P.; Baturone, I., Digital VLSI implementation of piecewise-affine controllers based on lattice approach, IEEE Transactions on Control Systems Technology, 23, 3, 842-854 (2015) |
| [24] | Meiser, S., Point location in arrangements of hyperplanes, Information and Computation, 106, 2, 286-303 (1993) · Zbl 0781.68121 |
| [25] | Nguyen, H. N.; Olaru, S.; Hovd, M., A patchy approximation of explicit model predictive control, International Journal of Control, 85, 12, 1929-1941 (2012) · Zbl 1253.93043 |
| [26] | Nguyen, N. A.; Olaru, S.; Rodriguez-Ayerbe, P.; Kvasnica, M., Convex liftings-based robust control design, Automatica, 77, 206-213 (2017) · Zbl 1355.93143 |
| [27] | Raković, S.; Grieder, P.; Kvasnica, M.; Mayne, D.; Morari, M., Computation of invariant sets for piecewise affine discrete time systems subject to bounded disturbances, (Proc. Conference on decision and control (2004)), 1418-1423 |
| [28] | Rawlings, J. B.; Mayne, D. Q., Model predictive control: Theory and design (2015), Nob Hill Pub |
| [29] | Rossiter, J.; Grieder, P., Using interpolation to improve efficiency of multiparametric predictive control, Automatica, 41, 4, 637-643 (2005) · Zbl 1061.93047 |
| [30] | Summers, S.; Jones, C. N.; Lygeros, J.; Morari, M., A multiresolution approximation method for fast explicit model predictive control, IEEE Transactions on Automatic Control, 56, 11, 2530-2541 (2011) · Zbl 1368.93416 |
| [31] | Tøndel, P.; Johansen, T. A.; Bemporad, A., Evaluation of piecewise affine control via binary search tree, Automatica, 39, 5, 945-950 (2003) · Zbl 1031.93069 |
| [32] | Wang, Y.; Jones, C.; Maciejowski, J., Efficient point location via subdivision walking with application to explicit MPC, (Proc. European control conference (2007)), 447-453 |
| [33] | Wena, C.; Mab, X.; Ydstie, B. E., Analytical expression of explicit MPC solution via lattice piecewise-affine function, Automatica, 45, 4, 910-917 (2009) · Zbl 1162.93358 |
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