Volume 15, Issue 3 (Journal of Control, V.15, N.3 Fall 2021)
JoC 2021, 15(3): 47-54 |
Back to browse issues page
Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:
Mahdi Abadi M, ghahremani N. New Approach for Accuracy Enhancement of Terminal Constraints Satisfaction in Model Predictive Control Problem. JoC 2021; 15 (3) :47-54
URL: http://joc.kntu.ac.ir/article-1-733-en.html
URL: http://joc.kntu.ac.ir/article-1-733-en.html
1- Malek Ashtar University
Abstract: (4216 Views)
In this paper, a new algorithm in order to increase the satisfaction of terminal constraints in the predictive control problem is presented. In this algorithm, by extracting mathematical relations, the terminal constraints are transferred from the final moment to the current moments. In each iteration, this transformation takes place in the optimization problem. At each moment of optimization, a new expression is obtained in terms of control inputs in each of the finite prediction control horizons. The equation of this transfer constraint is derived based on the variable discrete equations with the time of the controlled process and its execution at any moment fulfills the final constraints of the problem. This new algorithm, after extracting its mathematical relationships, is used to track the path of a robot with terminal constraints, and its performance is demonstrated using robot dynamics simulations. Also, the stability analysis of the proposed controller is performed by writing an appropriate cost function and applying Lyapunov theorem.
Keywords: Model Predictive Control, Terminal Constraints, Transformed Constraint, Real Time Computation, Stability Analysis.
Type of Article: Review paper |
Subject:
Special
Received: 2020/02/1 | Accepted: 2021/05/23 | ePublished ahead of print: 2021/06/12
Received: 2020/02/1 | Accepted: 2021/05/23 | ePublished ahead of print: 2021/06/12
References
1. [1] B. A. Conway, Spacecraft trajectory optimization. Cambridge University Press, 2010. [DOI:10.1017/CBO9780511778025]
2. [2] A. V. Rao, "Trajectory optimization: a survey," in Optimization and optimal control in automotive systems: Springer, 2014, pp. 3-21. [DOI:10.1007/978-3-319-05371-4_1]
3. [3] S. N. Ha, "A nonlinear shooting method for two-point boundary value problems," Computers & Mathematics with Applications, vol. 42, no. 10-11, pp. 1411-1420, 2001. [DOI:10.1016/S0898-1221(01)00250-4]
4. [4] R. W. Holsapple, "A modified simple shooting method for solving two-point boundary value problems", Texas Tech University, 2003.
5. [5] M. A. Patterson and A. V. Rao, "GPOPS-II: A MATLAB software for solving multiple-phase optimal control problems using hp-adaptive Gaussian quadrature collocation methods and sparse nonlinear programming," ACM Transactions on Mathematical Software (TOMS), vol. 41, no. 1, pp. 1-37, 2014, doi: 10.1145/2558904. [DOI:10.1145/2558904]
6. [6] W. Roh and Y. Kim, "Trajectory optimization for a multi-stage launch vehicle using time finite element and direct collocation methods," Engineering optimization, vol. 34, no. 1, pp. 15-32, 2002. [DOI:10.1080/03052150210912]
7. [7] F. Liu, T. Chao, S. Wang, and M. Yang, "Trajectory optimization for launch vehicle boost phase based on Gauss Pseudospectral Method," in 2016 35th Chinese Control Conference (CCC), 2016: IEEE, pp. 10910-10914. [DOI:10.1109/ChiCC.2016.7555082]
8. [8] Z. Wang and Z. Wu, "Six-DOF trajectory optimization for reusable launch vehicles via Gauss Pseudospectral method", Journal of Systems Engineering and Electronics, vol. 27, no. 2, pp. 434-441, 2016. [DOI:10.1109/JSEE.2016.00044]
9. [9] R. Padhi and M. Kothari, "Model predictive static programming: a computationally efficient technique for suboptimal control design," International journal of innovative computing, information and control, vol. 5, no. 2, pp. 399-411, 2009.
10. [10] f. Tavakkoli and A. Novinzadeh, "closed loop suboptimal guidance design for satellite launch vehicle(in Persian)," Journal of Modarres Mechanical Engineering, vol. 17, no. 9, pp. 97-106, 1396.
11. [11] G. Klančar and I. Škrjanc, "Tracking-error model-based predictive control for mobile robots in real time," Robotics and autonomous systems, vol. 55, no. 6, pp. 460-469, 2007. [DOI:10.1016/j.robot.2007.01.002]
12. [12] H. Yang, M. Guo, Y. Xia, and L. Cheng, "Trajectory tracking for wheeled mobile robots via model predictive control with softening constraints," IET Control Theory & Applications, vol. 12, no. 2, pp. 206-214, 2017. [DOI:10.1049/iet-cta.2017.0395]
13. [13] J. A. Primbs, "The analysis of optimization based controllers," Automatica, vol. 37, no. 6, pp. 933-938, 2001. [DOI:10.1016/S0005-1098(01)00036-X]
14. [14] L. Grüne, "Economic receding horizon control without terminal constraints," Automatica, vol. 49, no. 3, pp. 725-734, 2013. [DOI:10.1016/j.automatica.2012.12.003]
15. [15] H. Michalska and D. Q. Mayne, "Robust receding horizon control of constrained nonlinear systems," IEEE transactions on automatic control, vol. 38, no. 11, pp. 1623-1633, 1993. [DOI:10.1109/9.262032]
16. [16] M. Tanaskovic, L. Fagiano, R. Smith, and M. Morari, "Adaptive receding horizon control for constrained MIMO systems," Automatica, vol. 50, no. 12, pp. 3019-3029, 2014. [DOI:10.1016/j.automatica.2014.10.036]
17. [17] T. A. Johansen, "Approximate explicit receding horizon control of constrained nonlinear systems," Automatica, vol. 40, no. 2, pp. 293-300, 2004. [DOI:10.1016/j.automatica.2003.09.021]
18. [18] V. T. Minh and N. Afzulpurkar, "Robust model predictive control for input saturated and softened state constraints," Asian Journal of Control, vol. 7, no. 3, pp. 319-325, 2005. [DOI:10.1111/j.1934-6093.2005.tb00241.x]
19. [19] Y. I. Lee and B. Kouvaritakis, "Robust receding horizon predictive control for systems with uncertain dynamics and input saturation," Automatica, vol. 36, no. 10, pp. 1497-1504, 2000. [DOI:10.1016/S0005-1098(00)00064-9]
20. [20] W. H. Kwon and S. H. Han, Receding horizon control: model predictive control for state models. Springer Science & Business Media, 2006.
21. [21] N. O. Ghahramani and F. Towhidkhah, "Constrained incremental predictive controller design for a flexible joint robot," ISA transactions, vol. 48, no. 3, pp. 321-326, 2009. [DOI:10.1016/j.isatra.2009.01.010]
22. [22] R. Padhi, "Model predictive static programming: A promising technique for optimal missile guidance," To appear in Annals of Indian National Academy of Engineering (INAE), 2008.
23. [23] P. Kumar and R. Padhi, "Extension of model predictive static programming for reference command tracking," IFAC Proceedings Volumes, vol. 47, no. 1, pp. 855-861, 2014. [DOI:10.3182/20140313-3-IN-3024.00174]
24. [24] S. Blažič, "A novel trajectory-tracking control law for wheeled mobile robots," Robotics and Autonomous Systems, vol. 59, no. 11, pp. 1001-1007, 2011. [DOI:10.1016/j.robot.2011.06.005]
25. [25] F. Künhe, J. Gomes, and W. Fetter, "Mobile robot trajectory tracking using model predictive control," in II IEEE Latin-American robotics symposium, 2005, vol. 51: Citeseer.
26. [26] V. Nevistić and J. A. Primbs, "Finite receding horizon linear quadratic control: A unifying theory for stability and performance analysis," 1997.
27. [27] J. A. Primbs and V. Nevistić, "Constrained finite receding horizon linear quadratic control," in "Technical Report CIT-CDS," California Institute of Technology, 1997.
28. [28] M. Morari and J. H. Lee, "Model predictive control: past, present and future," Computers & Chemical Engineering, vol. 23, no. 4-5, pp. 667-682, 1999. [DOI:10.1016/S0098-1354(98)00301-9]
29. [29] W. Kwon and A. Pearson, "A modified quadratic cost problem and feedback stabilization of a linear system," IEEE Transactions on Automatic Control, vol. 22, no. 5, pp. 838-842, 1977. [DOI:10.1109/TAC.1977.1101619]
30. [30] J. B. Rawlings and K. R. Muske, "The stability of constrained receding horizon control," IEEE transactions on automatic control, vol. 38, no. 10, pp. 1512-1516, 1993. [DOI:10.1109/9.241565]
Send email to the article author
| Rights and permissions | |
 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. |
