Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

Kouramas, Konstantinos; Faísca, Nuno P.; Panos, Christos; Pistikopoulos, E.N.

doi:10.1016/j.automatica.2011.05.001

Cited by 65 publications

(30 citation statements)

References 17 publications

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“…The main characteristic of mp-MPC is its ability to obtain: (i) the objective and optimization variable as a function of the varying parameters, and (ii) the regions in the space of the parameters where these functions are valid (critical regions) [26,27] .This reduces the online implementation of the MPC to simple function evaluation, facilitating real time applications.…”

Section: ) Multi-parametric Strategymentioning

confidence: 99%

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Advanced Model-Based Control Studies for the Induction and Maintenance of Intravenous Anaesthesia

Nașcu

Krieger

Ionescu

et al. 2015

IEEE Trans. Biomed. Eng.

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Abstract-The paper describes strategies towards modelbased automation of intravenous anaesthesia employing advanced control techniques. In particular, based on a detailed compartmental mathematical model featuring pharmacokinetic and pharmacodynamics information two alternative model predictive control strategies are presented: a model predictive control strategy, based on online optimisation, the Extended Predictive Self Adaptive Control (EPSAC) and a multiparametric control strategy based on offline optimisation, the multi-parametric model predictive control (mp-MPC). The multi-parametric features to account for the effect of nonlinearity and the impact of estimation are also described. The control strategies are tested on a set of 12 virtually generated patient models for the regulation of the depth of anaesthesia (DOA) by means of the Bispectral Index (BIS) using Propofol as the administrated anaestetic. The simulations show fast response, suitability of dose and robustness to induce and maintain the desired BIS setpoint.

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Section: ) Multi-parametric Strategymentioning

confidence: 99%

“…Formal robust criteria can also be included [27] and this represents a topic of our ongoing research.…”

Section: B Maintenance Phasementioning

confidence: 99%

Advanced Model-Based Control Studies for the Induction and Maintenance of Intravenous Anaesthesia

Nașcu

Krieger

Ionescu

et al. 2015

IEEE Trans. Biomed. Eng.

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“…Nevertheless, parametric solutions also have their disadvantages and the literature is full of possible solutions to counter these [10]. For example: (i) in some cases the parametric solution can be difficult to compute reliably due to poor conditioning; (ii) where the parametric solution requires large numbers of regions it may not longer be computationally efficient.…”

Section: Introductionmentioning

confidence: 99%

The feasibility of parametric approaches to predictive control when using far future feed forward information

Dughman

Rossiter

2017

2017 13th IEEE International Conference on Control &Amp; Automation (ICCA)

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This is a repository copy of The feasibility of parametric approaches to predictive control when using far future feed forward information. ReuseUnless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.The feasibility of parametric approaches to predictive control when using far future feed forward information Abstract-This paper considers the tractability of parametric solvers for predictive control based optimisations, when future target information is incorporated. it is shown that the inclusion of future target information can significantly increase the implied parametric dimension to an extent that is undesirable and likely to lead to intractable problems. The paper then proposes some alternative methods for incorporating the desired target information, while minimising he implied growth in the parametric dimensions, at some possibly small cost to optimality.Index Terms-Parametric predictive control, advance knowledge, computational efficiency.

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“…The general idea is to solve the optimization problem offline and compute the vector of optimization variables, that is, optimal future control inputs, as explicit functions of the state of the system along with the corresponding regions, known as critical regions (CRs), where these functions are valid. 17,[21][22][23][24][25][26] Recently, an algorithm for explicit MPC of hybrid systems exploiting the concepts of constrained dynamical programming and multiparametric programming was proposed. 27 The authors focused on hybrid systems with linear cost function and piece-wise affine dynamics that resulted in the solution of a mp-MILP dynamic programming problem.…”

Section: Introductionmentioning

confidence: 99%

Explicit model predictive control of hybrid systems and multiparametric mixed integer polynomial programming

Charitopoulos

Dua

2016

AIChE Journal

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Hybrid systems are dynamical systems characterized by the simultaneous presence of discrete and continuous variables. Model-based control of such systems is computationally demanding. To this effect, explicit controllers which provide control inputs as a set of functions of the state variables have been derived, using multiparametric programming mainly for the linear systems. Hybrid polynomial systems are considered resulting in a Mixed Integer Polynomial Programming problem. Treating the initial state of the system as a set of bounded parameters, the problem is reformulated as a multiparametric Mixed Integer Polynomial optimization (mp-MIPOPT) problem. A novel algorithm for mp-MIPOPT problems is proposed and the exact explicit control law for polynomial hybrid systems is computed. The key idea is the computation of the analytical solution of the optimality conditions while the binary variables are treated as relaxed parameters. Finally, using symbolic calculations exact nonconvex critical regions are computed.

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Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

Cited by 65 publications

References 17 publications

Advanced Model-Based Control Studies for the Induction and Maintenance of Intravenous Anaesthesia

Advanced Model-Based Control Studies for the Induction and Maintenance of Intravenous Anaesthesia

The feasibility of parametric approaches to predictive control when using far future feed forward information

Explicit model predictive control of hybrid systems and multiparametric mixed integer polynomial programming

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