In this work we present the fundamental theoretical developments for a unified and general framework for the design of Robust Multi-Parametric Controllers (Pistikopoulos et al. 2007ab, ParOS 2007). Given a dynamic system with model uncertainties both in the right and left hand-sides (of constraints of the underlying uncertain optimisation problem), the proposed framework is realised in three steps:

1.robust reformulation of the constraints: the state/output and input constraints are reformulated to account for the worst-case model uncertainty (Ben-Tal and Nemirovski, 2001, Lim et al., 2004).

2.dynamic programming: the uncertain optimisation problem is reformulated with a dynamic programming multi-stage setting (Bellman, 2003, Faísca et al., 2008).

3.multi-parametric programming: each of the stages of the DP problem are solved as multi-parametric programming problems and the control input is obtained as an explicit function of the incumbent state (Pistikopoulos et al, 2007ab).

The above framework can guarantee the design of multi-parametric MPC (mp-MPC) controllers that can ensure constraints satisfaction for all admissible uncertainties as opposed to the previous non-robust mp-MPC design techniques (Sakizlis et al., 2004). The results are demonstrated with examples that illustrate the proposed framework.

References:

Bellman, R. (2003). Dynamic Programming. Dover Publications

Ben-Tal, A., Nemirovski, A., (2000). Math. Program 88, 411-424

Faísca, N.P., Kouramas, K.I., Saraiva, P.M., Rustem, B., Pistikopoulos, E.N., (2008). Optimization Letters 2, 267-280

Lim, X., Janak, S.L., Floudas, C.A., (2004). Comp. & Chem. Eng. 28, 1069-1085

Parametric Optimisation Solutions (ParOS) Ltd, Improved Process Control, European Patent EP1399784, 2007

Pistikopoulos, E.N., Georgiadis, M. & Dua, V., (2007). Multi-parametric Parametric Programming. Weinheim: Wiley-VCH

Pistikopoulos, E.N., Georgiadis, M. & Dua, V., (2007). Multi-parametric Parametric Model-based Control. Weinheim: Wiley-VCH

Sakizlis, V., Kakalis, N.M.P., Dua, V., Perkins, J.D., Pistikokpoulos, E.N., (2004). Automatica 40, 189-201