Abstract
This paper introduces a novel neural network model predictive controller based on Archimedes optimization algorithm to control constrained nonlinear systems, namely robot manipulators. Neural network models of a simple structure are used to accurately predict the system’s future outputs. The new Archimedes optimization algorithm is utilized to solve the optimization problem of model predictive control and compute the optimal control action; this algorithm was widely used in different engineering fields due to its good accuracy and convergence speed. The performances of the suggested control algorithm are investigated by simulating a two-degrees-of-freedom robot manipulator. The obtained results are compared with those of various techniques, namely the PID controller, the computed torque controller, and the neural network-based model predictive control using the teaching–learning-based optimization and the particle swarm optimization. To complete the study, the developed controller is implemented on a DSP board and used to control a three-degrees-of-freedom robot manipulator; its results are compared to the neural network-based model predictive control based on the teaching–learning-based optimization and the particle swarm optimization. The simulation and the experimental results demonstrate that the proposed controller provides satisfactory robustness and accuracy, can handle constraints, and can be used to control systems with fast dynamics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Afram, A., Janabi-Sharifi, F., Fung, A. S., et al. (2017). Artificial neural network (ANN) based model predictive control (MPC) and optimization of HVAC systems: A state of the art review and case study of a residential HVAC system. Energy and Buildings, 141, 96–113. https://doi.org/10.1016/j.enbuild.2017.02.012
Bakarac, P., Holaza, J., Kaluz, M., et al. (2018). Explicit MPC based on Approximate Dynamic Programming. in 2018 European Control Conference, ECC 2018 pp 1172–1177. https://doi.org/10.23919/ECC.2018.8550567
Banga, JR., Moles, CG., Alonso, AA. (2004). Global Optimization of Bioprocesses using Stochastic and Hybrid Methods. In: Frontiers in global optimization. Springer, pp 45–70, https://doi.org/10.1007/978-1-4613-0251-3_3
Bemporad, A., Borrelli, F., & Morari, M. (2000). Piecewise linear optimal controllers for hybrid systems. Proceedings of the American Control Conference, 2, 1190–1194. https://doi.org/10.1109/acc.2000.876688
Bemporad, A., Morari, M., Dua, V., et al. (2002). The explicit linear quadratic regulator for constrained systems. Automatica, 38(1), 3–20. https://doi.org/10.1016/S0005-1098(01)00174-1
Benrabah, M., Kara, K., AitSahed, O., et al. (2021). Constrained Nonlinear Predictive Control Using Neural Networks and Teaching-Learning-Based Optimization. Journal of Control, Automation and Electrical Systems, 32(5), 1228–1243. https://doi.org/10.1007/s40313-021-00755-4
Berberich, J., Kohler, J., Muller, M. A., et al. (2021). Data-driven model predictive control with stability and robustness guarantees. IEEE Transactions on Automatic Control, 66(4), 1702–1717. https://doi.org/10.1109/TAC.2020.3000182
Bongard, J., Berberich, J., Koehler, J., et al. (2022). Robust stability analysis of a simple data-driven model predictive control approach. IEEE Transactions on Automatic Control. https://doi.org/10.1109/TAC.2022.3163110
Boulkaibet, I., Belarbi, K., Bououden, S., et al. (2017). A new T-S fuzzy model predictive control for nonlinear processes. Expert Systems with Applications, 88, 132–151. https://doi.org/10.1016/j.eswa.2017.06.039
Chowdhri, N., Ferranti, L., Iribarren, F. S., et al. (2021). Integrated nonlinear model predictive control for automated driving. Control Engineering Practice. https://doi.org/10.1016/j.conengprac.2020.104654
Clarke, D. W., Mohtadi, C., & Tuffs, P. S. (1987). Generalized predictive control-Part I. The basic algorithm. Automatica, 23(2), 137–148. https://doi.org/10.1016/0005-1098(87)90087-2
Clarke, D. W., Mohtadi, C., & Tuffs, P. S. (1987). Generalized Predictive Control-Part II Extensions and interpretations. Automatica, 23(2), 149–160. https://doi.org/10.1016/0005-1098(87)90088-4
Coelho, J. P., De Moura Oliveira, P. B., & Cunha, J. B. (2005). Greenhouse air temperature predictive control using the particle swarm optimisation algorithm. Computers and Electronics in Agriculture, 49(3), 330–344. https://doi.org/10.1016/j.compag.2005.08.003
Coello, C. A. C. (2002). Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art. Computer Methods in Applied Mechanics and Engineering, 191(11–12), 1245–1287. https://doi.org/10.1016/S0045-7825(01)00323-1
Coello, C. A. C. (2022). Constraint-handling techniques used with evolutionary algorithms. Proceedings of the Genetic and Evolutionary Computation Conference Companion doi, 10(1145/3520304), 3533640.
Cutler, C. R., & Ramaker, B. L. (1980). Dynamic matrix control??A computer control algorithm. Joint Automatic Control Conference, 17, 72. https://doi.org/10.1109/JACC.1980.4232009
De Keyser, R. M., & Van Cauwenberghe, A. R. (1985). Extended prediction self-adaptive control. IFAC Proceedings Series, 7, 1255–1260. https://doi.org/10.1016/s1474-6670(17)60736-5
De Nicolao, G., Magni, L., Scattolini, R. (2000). Stability and Robustness of Nonlinear Receding Horizon Control. In: Nonlinear Model Predictive Control, pp 3–22, https://doi.org/10.1007/978-3-0348-8407-5_1
Diehl, M., Ferreau, H. J., & Haverbeke, N. (2009). Efficient numerical methods for nonlinear MPC and moving horizon estimation (pp. 391–417). Springer. https://doi.org/10.1007/978-3-642-01094-1_32
Ding, Y., Wang, L., Li, Y., et al. (2018). Model predictive control and its application in agriculture: A review. Computers and Electronics in Agriculture, 151, 104–117. https://doi.org/10.1016/j.compag.2018.06.004
Ding, Y., Pandala, A., Li, C., et al. (2021). Representation-Free Model Predictive Control for Dynamic Motions in Quadrupeds. IEEE Transactions on Robotics, 37(4), 1154–1171. https://doi.org/10.1109/TRO.2020.3046415
Eid, A., El-Kishky, H. (2021). Multi-objective Archimedes Optimization Algorithm for Optimal Allocation of Renewable Energy Sources in Distribution Networks. Lecture Notes in Networks and Systems 211 LNNS:65–75. https://doi.org/10.1007/978-3-030-73882-2_7
Farina, M., Giulioni, L., & Scattolini, R. (2016). Stochastic linear Model Predictive Control with chance constraints - A review. Journal of Process Control, 44, 53–67. https://doi.org/10.1016/j.jprocont.2016.03.005
Fathy, A., Alharbi, A. G., Alshammari, S., et al. (2022). Archimedes optimization algorithm based maximum power point tracker for wind energy generation system. Ain Shams Engineering Journal. https://doi.org/10.1016/j.asej.2021.06.032
Grüne, L., & Pannek, J. (2017). Nonlinear Model Predictive Control (pp. 45–69). Springer. https://doi.org/10.1007/978-3-319-46024-6_3
Hashim, F. A., Hussain, K., Houssein, E. H., et al. (2021). Archimedes optimization algorithm: a new metaheuristic algorithm for solving optimization problems. Applied Intelligence, 51(3), 1531–1551. https://doi.org/10.1007/s10489-020-01893-z
Houssein, E. H., din Helmy, B. E., & Rezk, H. (2021). An enhanced Archimedes optimization algorithm based on Local escaping operator and Orthogonal learning for PEM fuel cell parameter identification. Engineering Applications of Artificial Intelligence. https://doi.org/10.1016/j.engappai.2021.104309
Hu, J., Shan, Y., Guerrero, J. M., et al. (2021). Model predictive control of microgrids - An overview. Renewable and Sustainable Energy Reviews. https://doi.org/10.1016/j.rser.2020.110422
Huang, Y., Wang, H., Khajepour, A., et al. (2017). Model predictive control power management strategies for HEVs: A review. Journal of Power Sources, 341, 91–106. https://doi.org/10.1016/j.jpowsour.2016.11.106
Kerrigan, EC., Maciejowski, JM. (2002). Designing model predictive controllers with prioritised constraints and objectives. 2002 IEEE International Symposium on Computer Aided Control System Design, CACSD 2002 - Proceedings pp 33–38. https://doi.org/10.1109/CACSD.2002.1036925
Kouvaritakis, B., & Cannon, M. (2001). Non-linear Predictive Control: theory and practice. Iet. https://doi.org/10.1049/pbce061e
Li, B., & Wang, Y. (2022). An Enhanced Model Predictive Controller for Quadrotor Attitude Quick Adjustment with Input Constraints and Disturbances. International Journal of Control, Automation and Systems, 20(2), 648–659. https://doi.org/10.1007/s12555-020-0815-9
Li, J., Wang, J., Wang, S., et al. (2021). Neural Approximation-based Model Predictive Tracking Control of Non-holonomic Wheel-legged Robots. International Journal of Control, Automation and Systems, 19(1), 372–381. https://doi.org/10.1007/s12555-019-0927-2
Li, Y., Shen, J., Lee, K. Y., et al. (2012). Offset-free fuzzy model predictive control of a boiler-turbine system based on genetic algorithm. Simulation Modelling Practice and Theory, 26, 77–95. https://doi.org/10.1016/j.simpat.2012.04.002
Li, Y., Zhu, H., Wang, D., et al. (2021b). Comprehensive optimization of distributed generation considering network reconstruction based on Archimedes optimization algorithm. IOP Conference Series: Earth and Environmental Science 647(1). https://doi.org/10.1088/1755-1315/647/1/012031
Li, Z., & Wang, G. (2017). Generalized predictive control of linear time-varying systems. Journal of the Franklin Institute, 354(4), 1819–1832. https://doi.org/10.1016/j.jfranklin.2016.10.021
Lin, F. (2007). Robust control design: an optimal control approach. John Wiley & Sons.
Mercieca, J., Fabri, SG. (2011). Particle swarm optimization for nonlinear model predictive control. Proc ADVCOMP pp 88–93
Mesbah, A. (2016). Stochastic model predictive control: An overview and perspectives for future research. IEEE Control Systems, 36(6), 30–44. https://doi.org/10.1109/MCS.2016.2602087
Michalewicz, Z. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4(1), 1–32. https://doi.org/10.1162/evco.1996.4.1.1
Mollov, S., Babuška, R., Abonyi, J., et al. (2004). Effective optimization for fuzzy model predictive control. IEEE Transactions on Fuzzy Systems, 12(5), 661–675. https://doi.org/10.1109/TFUZZ.2004.834812
Muñoz De La Peña, D., Alamo, T., Bemporad, A., et al. (2004). A dynamic programming approach for determining the explicit solution of linear MPC controllers. Proceedings of the IEEE Conference on Decision and Control, 3, 2479–2484. https://doi.org/10.1109/CDC.2004.1428785
Muske, K. R., & Rawlings, J. B. (1993). Model predictive control with linear models. AIChE Journal, 39(2), 262–287. https://doi.org/10.1002/aic.690390208
Richalet, J., Rault, A., Testud, J. L., et al. (1978). Model predictive heuristic control. Applications to industrial processes. Automatica, 14(5), 413–428. https://doi.org/10.1016/0005-1098(78)90001-8
Rossiter, J. A. (2017). Model-based predictive control : a practical approach. CRC Press.
Sahed, O. A., Kara, K., & Benyoucef, A. (2015). Artificial bee colony-based predictive control for non-linear systems. Transactions of the Institute of Measurement and Control, 37(6), 780–792. https://doi.org/10.1177/0142331214546796
Sahed, O. A., Kara, K., Benyoucef, A., et al. (2016). An efficient artificial bee colony algorithm with application to nonlinear predictive control. International Journal of General Systems, 45(4), 393–417. https://doi.org/10.1080/03081079.2015.1086344
Sarimveis, H., & Bafas, G. (2003). Fuzzy model predictive control of non-linear processes using genetic algorithms. Fuzzy Sets and Systems, 139(1), 59–80. https://doi.org/10.1016/S0165-0114(02)00506-7
Soeterboek, A., Verbruggen, H., & van den Bosch, P. (1991). On the Design of the Unified Predictive Controller. IFAC Proceedings Volumes, 24, 351–356. https://doi.org/10.1016/S1474-6670(17)51344-0
Spielberg, N. A., Brown, M., & Gerdes, J. C. (2021). Neural Network Model Predictive Motion Control Applied to Automated Driving With Unknown Friction. IEEE Transactions on Control Systems Technology. https://doi.org/10.1109/TCST.2021.3130225
Ydstie, B. E. (1985). Extended horizon adaptive control. IFAC Proceedings Series. https://doi.org/10.1016/s1474-6670(17)61089-9
Zhixiang, H., Hui, C., Heqing, L. (2008). Neural networks predictive control using AEPSO. Proceedings of the 27th Chinese Control Conference, CCC pp 180–183. https://doi.org/10.1109/CHICC.2008.4605861
Zimmer, A., Schmidt, A., Ostfeld, A., et al. (2015). Evolutionary algorithm enhancement for model predictive control and real-time decision support. Environmental Modelling and Software, 69, 330–341. https://doi.org/10.1016/j.envsoft.2015.03.005
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Aouaichia, A., Kara, K., Benrabah, M. et al. Constrained Neural Network Model Predictive Controller Based on Archimedes Optimization Algorithm with Application to Robot Manipulators. J Control Autom Electr Syst 34, 1159–1178 (2023). https://doi.org/10.1007/s40313-023-01033-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40313-023-01033-1