Volume 1, Issue 1 (Journal of Control (English Edition), VOL. 01, NO. 01, 2022)
jocee 2022, 1(1): 37-47 |
Back to browse issues page
A Novel Integrated Solution Algorithm for Explicit Model Predictive Control in Embedded Applications
1- M.S. , Department of Automation and Instrumentation, Petroleum University of Technology.
2- Professor, Department of Automation and Instrumentation, Petroleum University of Technology.
2- Professor, Department of Automation and Instrumentation, Petroleum University of Technology.
Abstract: (1147 Views)
The paper addresses complexity of explicit model predictive control (MPC) in terms of online evaluation and memory requirement. Explicit MPC defines a piecewise affine (PWA) function over different regions of system state-space. An efficient approach is presented to integrate both complexity reduction schemes via 1) a separator function to remove regions defined over control actions which attain saturated values and 2) elimination of regions which have symmetry. The proposed method reduces the conventional necessity of explicit MPC, online evaluation, and storage requirement, by removing the regions corresponding to the saturated optimal control inputs using a simpler replacement function. Moreover, the method incorporates the concept of symmetries in the context of MPC quadratic programming problem to eliminate redundant symmetric regions, leading to devising a novel solution algorithm with much less complexities for embedded applications. The presented method also simplifies the symmetry identification process because the symmetry search algorithm is performed only for regions on which control action is unsaturated rather than the whole original regions. Various simulation tests are conducted to comparatively demonstrate effectiveness of the proposed algorithm for an inexpensive implementation of large-order systems in terms of the required storage and number of floating point operations.
Type of Article: Research paper |
Subject:
General
Received: 2021/09/8 | Accepted: 2022/03/14 | ePublished ahead of print: 2022/04/24 | Published: 2023/05/5
Received: 2021/09/8 | Accepted: 2022/03/14 | ePublished ahead of print: 2022/04/24 | Published: 2023/05/5
References
1. [1] M. Ławryńczuk. "Introduction to Model Predictive Control" In: Nonlinear Predictive Control Using Wiener Models. Studies in Systems, Decision and Control, 1st ed, vol 389. Springer, Cham, 2022, pp. 3-40. [DOI:10.1007/978-3-030-83815-7_1]
2. [2] R. Oberdieck, N.A. Diangelakis, EN Pistikopoulos. "Explicit model predictive control: a connected-graph approach." Automatica, vol. 76, pp. 103-112, Feb. 2017. [DOI:10.1016/j.automatica.2016.10.005]
3. [3] A. Bemporad. "A multiparametric quadratic programming algorithm with polyhedral computations based on nonnegative least squares." IEEE Transactions on Automatic Control, vol. 60, pp. 2892-2903, Mar. 2015. [DOI:10.1109/TAC.2015.2417851]
4. [4] R. Sheikhbahaei, A. Alasty, and G.Vossoughi. "Robust fault tolerant explicit model predictive control." Automatica, vol. 97, pp.248-253, Nov. 2018. [DOI:10.1016/j.automatica.2018.08.013]
5. [5] A. Bemporad, M. Morari, V. Dua, E.N. Pistikopoulos. "The explicit linear quadratic regulator for constrained systems." Automatica, vol. 38.1, pp. 3-20, Jan. 2002. [DOI:10.1016/S0005-1098(01)00174-1]
6. [6] S.W. Chen, T. Wang, N. Atanasov, V. Kumar, and M. Morari. "Large scale model predictive control with neural networks and primal active sets." Automatica, vol. 135, p.109947, Jan. 2022. [DOI:10.1016/j.automatica.2021.109947]
7. [7] Karg, Benjamin, and Sergio Lucia. "Efficient representation and approximation of model predictive control laws via deep learning." IEEE Transactions on Cybernetics 50.9 (2020): 3866-3878. [DOI:10.1109/TCYB.2020.2999556]
8. [8] A. Bemporad, A. Oliveri, T. Poggi, M. Storace. "Ultra-fast stabilizing model predictive control via canonical piecewise affine approximations." IEEE Transactions on Automatic Control, vol. 12, pp. 2883-2897, Apr. 2011. [DOI:10.1109/TAC.2011.2141410]
9. [9] A. Alessio, A. Bemporad. "A survey on explicit model predictive control." Nonlinear model predictive control. Springer Berlin Heidelberg, pp. 345-369, 2009. [DOI:10.1007/978-3-642-01094-1_29]
10. [10] M. Schwenzer, M. Ay, T. Bergs, D. Abel. "Review on model predictive control: an engineering perspective." The International Journal of Advanced Manufacturing Technology, vol. 117(5), pp. 1327-49, Nov. 2021. [DOI:10.1007/s00170-021-07682-3]
11. [11] F.J. Christophersen, M.N. Zeilinger, C. N. Jones, M. Morari. "Controller complexity reduction for piecewise affine systems through safe region elimination." Decision and Control. 46th IEEE Conference on. IEEE. 2007, pp. 4773-4778. [DOI:10.1109/CDC.2007.4434694]
12. [12] M. Kvasnica, J. Hledík, I. Rauová, M. Fikar. "Complexity reduction of explicit model predictive control via separation." Automatica, vol. 6, pp. 1776-1781, Jun. 2013. [DOI:10.1016/j.automatica.2013.02.018]
13. [13] M. Kvasnica, M. Fikar. "Clipping-based complexity reduction in explicit MPC." IEEE Transactions on Automatic Control, vol. 57.7, pp. 1878-1883, Dec. 2011. [DOI:10.1109/TAC.2011.2179428]
14. [14] C. Danielson, F. Borrelli. "Symmetric linear model predictive control." IEEE Transactions on Automatic Control, vol. 60.5, pp. 1244-1259, Nov. 2014. [DOI:10.1109/TAC.2014.2373693]
15. [15] C. Danielson. "An alternating direction method of multipliers algorithm for symmetric model predictive control." Optimal Control Applications and Methods vol. 42.1, pp. 236-260, Jan. 2021. [DOI:10.1002/oca.2672]
16. [16] D. Bremner, M.D. Sikiric, A Schürmann. "Polyhedral representation conversion up to symmetries." CRM proceedings. Vol. 48, pp. 45-72, 2009. [DOI:10.1090/crmp/048/03]
17. [17] P.T. Darga, K.A. Sakallah, I.L. Markov. "Faster symmetry discovery using sparsity of symmetries." Design Automation Conference, DAC. 45th ACM/IEEE. IEEE. 2008, pp. 149-154. [DOI:10.1145/1391469.1391509]
18. [18] T. Junttila, P. Kaski. "Engineering an efficient canonical labeling tool for large and sparse graphs." Proceedings of the Ninth Workshop on Algorithm Engineering and Experiments (ALENEX). Society for Industrial and Applied Mathematics, 2007, pp. 135-149. [DOI:10.1137/1.9781611972870.13]
19. [19] B.D. McKay. "Practical graph isomorphism." 1981, pp. 45-87.
20. [20] A. Del Rio Ruiz, and K. Basterretxea. "Towards the automatic implementation of reduced-size and high throughput mpc on fpgas," 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2019, pp. 1768-1773. [DOI:10.1109/CoDIT.2019.8820691]
21. [21] D.F. Holt, B. Eick, E.A. O'Brien. "Handbook of computational group theory (Discrete Mathematics and Its Applications)."Chapman and Hall/CRC Press, 2005.
22. [22] P. Tøndel, T.A. Johansen, A. Bemporad. "Evaluation of piecewise affine control via binary search tree." Automatica, vol. 39.5, pp. 945-950, May. 2003. [DOI:10.1016/S0005-1098(02)00308-4]
23. [23] M. Herceg, M. Kvasnica, C.N. Jones, M. Morari. "Multi-parametric toolbox 3.0." European control conference (ECC), IEEE, 2013, pp. 502-510. [DOI:10.23919/ECC.2013.6669862]
24. [24] K.V. Ling, S.P. Yue, J.M.Maciejowski. "A FPGA implementation of model predictive control." In American control conference, Minnesota Minneapolis, 2006, p. 6. [DOI:10.1109/ACC.2006.1656502]
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |