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Initialisation of Optimisation Solvers for Nonlinear Model Predictive Control: Classical vs. Hybrid Methods

Author

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  • Maciej Ławryńczuk

    (Faculty of Electronics and Information Technology, Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland)

  • Piotr M. Marusak

    (Faculty of Electronics and Information Technology, Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland)

  • Patryk Chaber

    (Faculty of Electronics and Information Technology, Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland)

  • Dawid Seredyński

    (Faculty of Electronics and Information Technology, Institute of Control and Computation Engineering, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, Poland)

Abstract

In nonlinear Model Predictive Control (MPC) algorithms, the number of cost-function evaluations and the resulting calculation time depend on the initial solution to the nonlinear optimisation task. Since calculations must be performed fast on-line, the objective is to minimise these indicators. This work discusses twelve initialisation strategies for nonlinear MPC. In general, three categories of strategies are discussed: (a) five simple strategies, including constant and random guesses as well as the one based on the previous optimal solution, (b) three strategies that utilise a neural approximator and an inverse nonlinear static model of the process and (c) four hybrid original methods developed by the authors in which an auxiliary quadratic optimisation task is solved or an explicit MPC controller is used; in both approaches, linear or successively linearised on-line models can be used. Efficiency of all methods is thoroughly discussed for a neutralisation reactor benchmark process and some of them are evaluated for a robot manipulator, which is a multivariable process. Two strategies are found to be the fastest and most robust to model imperfections and disturbances acting on the process: the hybrid strategy with an auxiliary explicit MPC controller based on a successively linearised model and the method which uses the optimal solution obtained at the previous sampling instant. Concerning the hybrid strategies, since a simplified model is used in the auxiliary controller, they perform much better than the approximation-based ones with complex neural networks. It is because the auxiliary controller has a negative feedback mechanism that allows it to compensate model errors and disturbances efficiently. Thus, when the auxiliary MPC controller based on a successively linearised model is available, it may be successfully and efficiently used for the initialisation of nonlinear MPC, whereas quite sophisticated methods based on a neural approximator are very disappointing.

Suggested Citation

  • Maciej Ławryńczuk & Piotr M. Marusak & Patryk Chaber & Dawid Seredyński, 2022. "Initialisation of Optimisation Solvers for Nonlinear Model Predictive Control: Classical vs. Hybrid Methods," Energies, MDPI, vol. 15(7), pages 1-21, March.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:7:p:2483-:d:781412
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    References listed on IDEAS

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    1. Paweł Sokólski & Tomasz A. Rutkowski & Bartosz Ceran & Daria Złotecka & Dariusz Horla, 2022. "The Influence of Cooperation on the Operation of an MPC Controller Pair in a Nuclear Power Plant Turbine Generator Set," Energies, MDPI, vol. 15(18), pages 1-19, September.
    2. David Sotelo & Antonio Favela-Contreras & Alfonso Avila & Arturo Pinto & Francisco Beltran-Carbajal & Carlos Sotelo, 2022. "A New Software-Based Optimization Technique for Embedded Latency Improvement of a Constrained MIMO MPC," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    3. Paweł Sokólski & Tomasz A. Rutkowski & Bartosz Ceran & Daria Złotecka & Dariusz Horla, 2023. "Event-Triggered Communication in Cooperative, Adaptive Model Predictive Control of a Nuclear Power Plant’s Turbo–Generator Set," Energies, MDPI, vol. 16(13), pages 1-23, June.

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