Fast Nonlinear Model Predictive Control Algorithm with Neural Approximation for Embedded Systems: Preliminary Results

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1196)


This work presents preliminary results of research concerned with a fast nonlinear Model Predictive Control (MPC) algorithm implemented in an embedded system. In order to obtain a computationally efficient solution, a linear approximation of the predicted trajectory of the controlled variables is calculated for each sampling instant on-line which leads to a quadratic optimisation problem. Furthermore, the matrix of derivatives, which defines the linearised trajectory, is not determined analytically, but it is calculated (approximated) by a specially trained neural network. In order to show effectiveness of the discussed approach, a dynamic process with two inputs and two outputs is considered for which not only simulation results, but also results of real experiments performed in an embedded system based on a microcontroller are given.


Embedded systems Microcontrollers Model Predictive Control Neural networks Nonlinear control 


  1. 1.
    Chaber, P., Ławryńczuk, M.: Fast analytical model predictive controllers and their implementation for STM32 ARM microcontroller. IEEE Trans. Industr. Inf. 15, 4580–4590 (2019)CrossRefGoogle Scholar
  2. 2.
    Chaber, P., Ławryńczuk, M.: AutoMATiC: Code generation of model predictive control algorithms for microcontrollers. IEEE Trans. Industr. Inf. 16(7), 4547–4556 (2020).
  3. 3.
    Grosso, J.M., Ocampo-Martinez, C., Puig, V.: Reliability-based economic model predictive control for generalised flow-based networks including actuators’ health-aware capabilities. Int. J. Appl. Math. Comput. Sci. 26, 361–654 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Janczak, A., Korbicz, J.: Two-stage instrumental variables identification of polynomial Wiener Systems with invertible nonlinearities. Int. J. Appl. Math. Comput. Sci. 29, 571–580 (2019)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Janczak, A.: Identification of Nonlinear Systems Using Neural Networks and Polynomial Models. A Block-Oriented Approach. Lecture Notes in Control and Information Sciences, vol. 310. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  6. 6.
    Ławryńczuk, M.: Computationally Efficient Model Predictive Control Algorithms: A Neural Network Approach. Studies in Systems, Decision and Control, vol. 3. Springer, Cham (2014)Google Scholar
  7. 7.
    Ławryńczuk, M.: Explicit nonlinear predictive control algorithms with neural approximation. Neurocomputing 129, 570–584 (2014)CrossRefGoogle Scholar
  8. 8.
    Pour, F.K., Puig, V., Ocampo-Martinez, C.: Multi-layer health-aware economic predictive control of a pasteurization pilot plant. Int. J. Appl. Math. Comput. Sci. 28, 97–110 (2018)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Stellato, B., Banjac, G., Goulart, P., Bemporad, A., Boyd, S.: OSQP: an operator splitting solver for quadratic programs. arXiv e-prints (2017)
  10. 10.
    Tatjewski, P.: Advanced Control of Industrial Processes. Structures and Algorithms. Springer, London (2007)zbMATHGoogle Scholar
  11. 11.
    Wojtulewicz, A., Ławryńczuk, M.: Implementation of multiple-input multiple-output dynamic matrix control algorithm for fast processes using field programmable gate array. IFAC-PapersOnLine 51, 324–329 (2018)CrossRefGoogle Scholar
  12. 12.
    Wojtulewicz, A., Ławryńczuk, M.: Computationally efficient implementation of dynamic matrix control algorithm for very fast processes using programmable logic controller. In: 2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR), pp. 579–584 (2018)Google Scholar
  13. 13.
    Zhou, F., Peng, H., Zhang, G., Zeng, X.: A robust controller design method based on parameter variation rate of RBF-ARX model. IEEE Access 7, 160284–160294 (2019)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Control and Computation EngineeringWarsaw University of TechnologyWarsawPoland

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