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462353 On the Robust Explicit Model Predictive Control of Hybrid Discrete-Time Linear Systems

*now*’ such that there will exist a ‘

*future*’, feasible control action. While such robust approaches have been applied extensively to the case of discrete-time continuous systems, only few approaches have been proposed regarding hybrid systems, i.e. systems featuring both continuous and discrete components [5].

In this work, we consider the development of novel closed-loop robust explicit MPC strategies for hybrid discrete-time linear systems. It extends our results for continuous systems [6], which is based on the following components: (i) a robust counterpart formulation for the special case of box-constrained uncertainty, guaranteeing constraint satisfaction, (ii) a multi-parametric linear programming (mp-LP) problem for each stage (starting from the final stage in a dynamic programming setting), and (iii) the recursive solution of the mp-LP problem yielding the initial set of states for which robust constraint satisfaction can be guaranteed. For the case of hybrid systems, we show that (i) a similar type of robust counterpart formulation can be derived under mild assumptions, (ii) this robust counterpart results in a multi-parametric mixed-integer linear programming (mp-MILP) problem which can be formulated for each stage, and (iii) using state-of-the-art methods the mp-MILP problem can be solved recursively. This then enables the formulation of the robust explicit hybrid MPC problem as a multi-parametric mixed-integer quadratic programming problem, for which the authors recently proposed the first exact solution algorithm [7]. Using a series of example problems, the applicability and scalability of this novel approach will be highlighted.

**References**

[1] Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O. M. (2000) Constrained model predictive control: Stability and optimality. Automatica, 36(6), 789 – 814.

[2] Kerrigan, E. C.; Maciejowski, J. M. (2004) Feedback min-max model predictive control using a single linear program: robust stability and the explicit solution. International Journal of Robust and Nonlinear Control, 14(4), 395 – 413.

[3] Wan, Z.; Kothare, M. V. (2003) An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica, 39(5), 837 – 846.

[4] Bemporad, A.; Borrelli, F.; Morari, M. (2003) Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control, 48(9), 1600 – 1606.

[5] Nascu, I.; Oberdieck, R.; Pistikopoulos, E. N. (2015) Offset-free Explicit Hybrid Model Predictive Control of Intravenous Anaesthesia. In Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (SMC), 2475 – 2480.

[6] Oberdieck, R.; Misener, R.; Pistikopoulos, E. N. (2016) Robust explicit/multi-parametric control. AIChE Journal, in revision.

[7] Oberdieck, R.; Pistikopoulos, E. N. (2015) Explicit hybrid model-predictive control: The exact solution. Automatica, 58, 152 – 159.

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