Structure-aware decision support system for MOO-driven control

System Analysis and Control
Authors:
Abstract:

Cyber-physical control systems must satisfy strict constrains on the magnitude of control actions and the rate of signal change, while simultaneously balancing multiple, often conflicting, control objectives. In multi-objective optimization (MOO) problems, the optimizer naturally produces a set of competing control candidates. However, in closed-loop operation, a single implementable control action must be selected at each sampling instant. In practice, this selection is typically performed through fixed scalarization rules, which can lead to performance degradation under changing operating conditions in the case of non-convex Pareto fronts or poorly scalable objectives. This work aims to improve the quality of control based on MOO through a decision support system that accounts for the structure: the proposed architecture decouples online Pareto-front construction from action selection. A heuristic multi-objective optimization algorithm based on the NSGA-II genetic algorithm generates feasible control sequences under magnitude and rate constraints, while a learned selector, denoted as Learned Pareto Filter (LPF), evaluates these candidates using structural features that account for both individual characteristics of the solutions and their interrelations within the Pareto set. The method is evaluated on two benchmark problems. First, a system with an analytically known Pareto front structure is used. Second, the approach is validated on a nonlinear boiler-turbine load-changing scenario, widely used in constrained nonlinear control studies. The results demonstrate that LPF-based selection produces smoother control actions, improved tracking performance, and greater robustness to regime changes compared to objective-based scalarization methods. The findings confirm that, in Pareto-based control, closed-loop quality depends critically on the selection mechanism rather than solely on the optimizer generating the Pareto set.

Funding:

The research was financially supported by the Ministry of Science and Higher Education of the Russian Federation within the framework of the program “World-class Research Center: Advanced Digital Technologies” (Agreement No. 075-15-2022-311 dated 20.04.2022).

  • References

    1. IEA. World Energy Outlook 2022, Available: Paris https://www.iea.org/reports/world-energy-outlook-2022 (Accessed 06.07.2026).

    2. Röth C., Milde F., Trebbels D., Schmidt J., Doppelbauer M. A Stator With Offset Segments and a Double Stator Design for the Reduction of Torque Ripple of a Switched Reluctance Motor. IEEE Transactions on Energy Conversion. 2022, Vol. 37, No. 2, Pp. 1233–1240.

    3. Wang C., Liu M., Zhao Y., Qiao Y., Chong D., Yan J. Dynamic modeling and operation optimization for the cold end system of thermal power plants during transient processes. Energy, 2018, Vol. 145, Pp. 734–746. DOI: 10.1016/j.energy.2017.12.146

    4. Ogata K. Modern control engineering, 5th ed., New Jersey: Pearson Education, Inc., 2020.

    5. Schwenzer M., Ay M., Bergs T., Abel D. Review on model predictive control: An engineering perspective. The International Journal of Advanced Manufacturing Technology, 2021, Vol. 117, No. 5, Pp. 1327–1349. DOI: 10.1007/s00170-021-07682-3

    6. Wu X., Shen J., Li Y., Lee K.Y. Stable model predictive control based on TS fuzzy model with application to boiler-turbine coordinated system. 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, Pp. 2981–2987. DOI: 10.1109/CDC.2011.6160553

    7. Wu X., Shen J., Li Y., Lee K.Y. Hierarchical optimization of boiler-turbine unit using fuzzy stable model predictive control. Control Engineering Practice, 2014, Vol. 30, Pp. 112–123. DOI: 10.1016/j.conengprac.2014.03.004

    8. Ławryńczuk M. Nonlinear predictive control of a boiler-turbine unit: A state-space approach with successive on-line model linearisation and quadratic optimization. ISA Transactions, 2017, Vol. 67, Pp. 476–495. DOI: 10.1016/j.isatra.2017.01.016

    9. Yang C., Zhang T., Zhang Z., Sun L. MLD–MPC for ultra-supercritical circulating fluidized bed boiler unit using subspace identification. Energies, 2022, Vol. 15, No. 15, Art. no. 5476. DOI: 10.3390/en15155476

    10. Banzhaf W., Machado P., Zhang M. Handbook of evolutionary machine learning, NY: Springer, 2023.

    11. Lawrence N.P., Damarla S.K., Kim J.W., Tulsyan A., Amjad F., Wang K., Chachuat B., Lee J.M., Huang B., Bhushan Gopaluni R. Machine learning for industrial sensing and control: A survey and practical perspective. Control Engineering Practice, 2024, Vol. 145, Art. no. 105841. DOI: 10.1016/j.conengprac.2024.10-5841

    12. Chuadhry M.A., M.R. G.R., Mathur A.P. Challenges in machine learning based approaches for real-time anomaly detection in industrial control systems. Proceedings of the 6th ACM on Cyber-Physical System Security Workshop, 2020, Pp. 23–29. DOI: 10.1145/3384941.340958

    13. Slowik A., Kwasnicka H. Evolutionary algorithms and their applications to engineering problems. Neu-ral Computing and Applications, 2020, Vol. 32, Pp. 12363–12379. DOI: 10.1007/s00521-020-04832-8

    14. Deeb A., Khokhlovskiy V.N., Shkodyrev V.P. Model predictive control and genetic algorithms for optimization of continuous stirred tank reactors. In: Smart electromechanical systems (eds. I.L. Tarasova, B.A. Kulik), 2024, Vol. 544, Pp. 185–191. DOI: 10.1007/978-3-031-64277-7_14

    15. Biegler L.T. A perspective on nonlinear model predictive control. Korean Journal of Chemical Engineering, 2021, Vol. 38, No. 7, Pp. 1317–1332. DOI: 10.1007/s11814-021-0791-7

    16. Jones D.F., Florentino H.O. Multi-objective optimization: Methods and applications. In: The Palgrave handbook of operations research (eds. S. Salhi, J. Boylan), 2022, Pp. 181–207. DOI: 10.1007/978-3-030-96935-6_6

    17. Deb K., Pratap A., Agarwal S., Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, Vol. 6, No. 2, Pp. 182–197. DOI: 10.1109/4235.996017

    18. Wang L., Cai Y., Ding B. Robust model predictive control with bi-level optimization for boiler-turbine system. IEEE Access, 2021, Vol. 9, Pp. 48244–48253. DOI: 10.1109/ACCESS.2021.3066371

    19. Köhler J., Soloperto R., Müller M.A., Allgöwer F. A computationally efficient robust model predictive control framework for uncertain nonlinear systems. IEEE Transactions on Automatic Control, 2020, Vol. 66, No. 2, Pp. 794–801. DOI: 10.1109/TAC.2020.2982585

    20. Wei Q., Liu Y., Lu J., Ling J., Luan Z., Chen M. A new integral critic learning for optimal tracking control with applications to boiler-turbine systems. Optimal Control: Applications and Methods, 2023, Vol. 44, No. 2, Pp. 830–845. DOI: 10.1002/oca.2792

    21. Peitz S., Dellnitz M. A survey of recent trends in multiobjective optimal control – surrogate models, feedback control and objective reduction. Mathematical and Computational Applications, 2018, Vol. 23, No. 2, Art. no. 30. DOI: 10.3390/mca23020030

    22. Bemporad A., de la Peña D.M. Multiobjective model predictive control. Automatica, 2009, Vol. 45, Pp. 2823–2830. DOI: 10.1016/j.automatica.2009.09.032

    23. Zavala V.M., Flores-Tlacuahuac A. Stability of multiobjective predictive control: A utopia-tracking approach. Automatica, 2012, Vol. 48, No. 10, Pp. 2627–2632. DOI: 10.1016/j.automatica.2012.06.066

    24. He D., Wang L., Sun J. On stability of multiobjective NMPC with objective prioritization. Automatica, 2015, Vol. 57, Pp. 189–198. DOI: 10.1016/j.automatica.2015.04.024

    25. Grüne L., Stieler M. Multiobjective model predictive control for stabilizing cost criteria. Discrete and Continuous Dynamical Systems – B, 2019, Vol. 24, No. 8, Pp. 3905–3928. DOI: 10.3934/dcdsb.2018336

    26. Xu J., Tian Y., Ma P., Rus D., Sueda S., Matusik W. Prediction-guided multi- objective reinforcement learning for continuous robot control. Proceedings of the 37th International Conference on Machine Learning, 2020, pp. 10607–10616.

    27. Deeb A., Khokhlovskiy V., Shkodyrev V. Hierarchical multi-objective control of nonlinear systems with dynamical input constraints. Artificial Intelligence and Applications, 2026, Vol 4., No. 1., Pp. 57–67. DOI: 10.47852/bonviewAIA52024314

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Previous articleNext article