(368c) Nonlinear Mpc Via Novel Nonlinear Multi-Parametric Programming Techniques

Multi-parametric programming offers a very promising framework for the development of off-line based parametric controllers in the context of linear Model Predictive Control (MPC), (Pistikopoulos et al, 2007 a,b). However, while advances have been made in nonlinear multi-parametric programming, its application to nonlinear MPC has only recently started to receive some attention. A key reason for this is that the derivation of explicit parametric solutions for general non-linear optimal control problems is quite a challenging and formidable task.

In this work, we propose (i) a novel algorithm for the solution of convex nonlinear multi-parametric programming problems, and (ii) a framework for nonlinear MPC via multi-parametric programming. For (i), based on our previous work, (Dua et al, 2004), we introduce a vertex-based strategy for convex nonlinear multi-parametric programming problems, in which the parameters appear only in the RHS of the constraints. Linear approximations of both the critical regions and the parametric optimal solutions can be obtained. For (ii), we describe a framework for nonlinear MPC, which involves step (i) above coupled with a suitable model reduction step. Extensions towards handling the presence of parameters in the objective function, which requires a global optimization approach, are also discussed. An illustrative example is used throughout to highlight the key concepts and steps of the proposed approach.

References Pistikopoulos, E. N, Georgiadis, M. C., Dua, V. (2007a) Multi-Parametric Programming (Volume 1), Wiley-VCH, Weinheim. Pistikopoulos, E. N, Georgiadis, M. C., Dua, V. (2007b) Multi-Parametric Model-Based Control (Volume 2), Wiley-VCH, Weinheim. Dua, V, Papalexandri, K., Pistikopoulos, E. N, (2004), Journal of Global Optimization, 30.