Nonlinear model predictive control for processes with complex dynamics: A parameterisation approach using Laguerre functions

Ławryńczuk, Maciej

doi:10.34768/amcs-2020-0003

Cited by 7 publications

(2 citation statements)

References 32 publications

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“…The application of Laguerre functions for representation of control input trajectories can be found mainly for state-space process models, see [16,18]. Recently, this approach has been applied in nonlinear MPC for more efficient optimization with linearized models in predictive structures of GPC type, see [5]. In this paper, the use of the Laguerre functions for the parametrization of predicted control input trajectories in the DMC algorithm will be proposed and analysed.…”

Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Tatjewski

2021

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The paper is concerned with the presentation and analysis of the Dynamic Matrix Control (DMC) model predictive control algorithm with the representation of the process input trajectories by parametrised sums of Laguerre functions. First the formulation of the DMCL (DMC with Laguerre functions) algorithm is presented. The algorithm differs from the standard DMC one in the formulation of the decision variables of the optimization problem -coefficients of approximations by the Laguerre functions instead of control input values are these variables. Then the DMCL algorithm is applied to two multivariable benchmark problems to investigate properties of the algorithm and to provide a concise comparison with the standard DMC one. The problems with difficult dynamics are selected, which usually leads to longer prediction and control horizons. Benefits from using Laguerre functions were shown, especially evident for smaller sampling intervals.

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Section: Introductionmentioning

confidence: 99%

Archives of Control Sciences

Tatjewski

2021

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“…In order to avoid the complexity of NMPC, often on-line linearization at each algorithm iteration is used (see, e.g., Boulkaibet et al, 2017;Essien et al, 2019;Ławryńczuk, 2014;2015;2020;Marusak, 2009a;2009b;Morari and Lee, 1999;Tatjewski, 2007). After a linear approximation of the nonlinear model is obtained, a prediction linear to decision variables is acquired.…”

Section: Introductionmentioning

confidence: 99%

A numerically efficient fuzzy MPC algorithm with fast generation of the control signal

Marusak¹

2021

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Model predictive control (MPC) algorithms are widely used in practical applications. They are usually formulated as optimization problems. If a model used for prediction is linear (or linearized on-line), then the optimization problem is a standard, i.e., quadratic, one. Otherwise, it is a nonlinear, in general, nonconvex optimization problem. In the latter case, numerical problems may occur during solving this problem, and the time needed to calculate control signals cannot be determined. Therefore, approaches based on linear or linearized models are preferred in practical applications. A novel, fuzzy, numerically efficient MPC algorithm is proposed in the paper. It can offer better performance than the algorithms based on linear models, and very close to that of the algorithms based on nonlinear optimization. Its main advantage is the short time needed to calculate the control value at each sampling instant compared with optimization-based numerical algorithms; it is a combination of analytical and numerical versions of MPC algorithms. The efficiency of the proposed approach is demonstrated using control systems of two nonlinear control plants: the first one is a chemical CSTR reactor with a van de Vusse reaction, and the second one is a pH reactor.

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Learning Lyapunov terminal costs from data for complexity reduction in nonlinear model predictive control

Abdufattokhov,

Zanon,

Bemporad

2024

Intl J Robust & Nonlinear

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A classic way to design a nonlinear model predictive control (NMPC) scheme with guaranteed stability is to incorporate a terminal cost and a terminal constraint into the problem formulation. While a long prediction horizon is often desirable to obtain a large domain of attraction and good closed‐loop performance, the related computational burden can hinder its real‐time deployment. In this article, we propose an NMPC scheme with prediction horizon and no terminal constraint to drastically decrease the numerical complexity without significantly impacting closed‐loop stability and performance. This is attained by constructing a suitable terminal cost from data that estimates the cost‐to‐go of a given NMPC scheme with long prediction horizon. We demonstrate the advantages of the proposed control scheme in two benchmark control problems.

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Nonlinear model predictive control for processes with complex dynamics: A parameterisation approach using Laguerre functions

Cited by 7 publications

References 32 publications

Archives of Control Sciences

Archives of Control Sciences

A numerically efficient fuzzy MPC algorithm with fast generation of the control signal

Learning Lyapunov terminal costs from data for complexity reduction in nonlinear model predictive control

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