(238d) Comparison of Model Approximation Methodologies for Online and Multi-Parametric/Explicit Model Predictive Control

Romain S.C. Lambert, Alexandra Krieger,  Pedro Rivotti, Efstratios N. Pistikopoulos

Model Approximation is very useful in the context of complex high fidelity modelling of systems for which it is very impractical or impossible to derive an accurate model directly from plant data. Despite powerful prediction capability, such complex models pose significant difficulties to model predictive control (MPC) applications. To address the challenge posed by complex models, a large number of model approximation techniques have been introduced [1] [4] [6]. These methods are diverse in nature and may entail very different control implementations.

In this work we attempt to establish a practical classification of model approximation as a decision tool for selection of the most appropriate strategy for online and multi-parametric model based control. Firstly we study the performance of online model approximation techniques. These model approximations techniques aim to reduce the complexity of the control problem by adaptively reducing the dynamical system online and reformulating the MPC problem. The main advantage of these approaches is the reduction in memory storage requirements. In this study we compare two approximation strategies consisting of online linearization and model order reduction. The first approach [1] consists of online linearization of the system followed by linear model order reduction. For comparison we suggest a second approach which is a combination of online linearization of the system subsequently to applying an empirical nonlinear model reduction [2]. It can be shown that the order at which linearization and dimensionality reduction are performed has an influence on the controller design.  Secondly we compare different offline approximation techniques. These approximation techniques present the advantage of being compatible with multi-parametric/explicit model predictive control (mp-MPC) algorithms [3]. The type of approximation employed implies different control strategies. We survey the use of piece-wise affine systems which entails the use of mixed integer model predictive control strategies (essentially branch and bound), trajectory piecewise linearization which can be addressed through linear mp-MPC [6], and finally nonlinear model reduction which can be combined to nonlinear mp-MPC [5]. The different combinations of approaches are compared on benchmark biomedical and chemical systems. Criteria for evaluations will consist of: Close-loop performance, cost of extraction of the approximate models, memory storage and online computation speed.

References

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[5]     Pistikopoulos, E.N., Dua, V., Bozinis, N.A., Bemporad, A., Morari, (2000) A. On-line optimization via off-line parametric optimization tools. Computers & Chemical Engineering. Volume 24, Issues 2-7, 15 July 2000, pp 183-188.

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[7]     Rivotti, P., Lambert, S.C., Dominguez, L., Pistikopoulos, E.N. (2011). 21st European symposium on computer Aided Process Engineering 

[8]     C. Seatzu, D. Corona, A. Giua, and A. Bemporad, IEEE Trans. Automatic Control, vol. 51, no. 5, pp. 726–741, 2006

[9]     Xie W., Bonis I., Theodoropoulos C. Comput. Chem. Eng. (2011) 35: 750-757.