Volume 16, Issue 3 (Journal of Control, V.16, N.3 Fall 2022)                   JoC 2022, 16(3): 11-24 | Back to browse issues page

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Nejabat E, Homaeinezhad M R. A class of multi-agent discrete hybrid non linearizable systems: Optimal controller design based on quasi-Newton algorithm for a class of sign-undefinite hessian cost functions. JoC 2022; 16 (3) :11-24
URL: http://joc.kntu.ac.ir/article-1-909-en.html
1- Faculty of Mechanical Engineering, K. N. Toosi University of Technology
Abstract:   (668 Views)
 In the present paper, a class of hybrid, nonlinear and non linearizable dynamic systems is considered. The noted dynamic system is generalized to a multi-agent configuration. The interaction of agents is presented based on graph theory and finally, an interaction tensor defines the multi-agent system in leader-follower consensus in order to design a desirable controller for the noted system. A general undirected, simple and connected graph topology is proposed for the system. Next, a nonlinear controller is designed for the multi-agent system to track a predefined reference trajectory and maintain the formation topology. An optimal controller, based on quasi-Newton optimization method is proposed in order to minimize a nonlinear cost function with indefinite variable sign hessian matrix. The convergence of previous optimization algorithms, namely the Newton optimization algorithm, regarding to variable sign hessian matrices fails. Thus, in the present paper, a quasi-newton optimization method is proposed based on eigenvalue modification to design a controller for the system. Afterward, the controller generalized for the multi-agent system and the performance of the controller is examined in a specific scenario of indefinite, variable hessian matrix problem. Consequently, the innovation of the present paper is proposed by considering the quasi-newton optimization method in order to overcome the disadvantages of traditional optimization methods in the problem of undefined hessian cost function. An example is provided in order to illustrate aforementioned claims and declared propositions.
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Type of Article: Research paper | Subject: Special
Received: 2021/10/31 | Accepted: 2022/08/1 | ePublished ahead of print: 2022/09/13

References
1. [1] L. Mo, H. Ho, Y. Yu, 2020, "Distributed heterogeneous multi-agent networks optimization with nonconvex velocity constraints", Journal of the Franklin Institute, vol. 357, no.11, pp. 7139-7158. [DOI:10.1016/j.jfranklin.2020.05.043]
2. [2] T. F. Coleman, A. Liao, 2021, "An efficient trust region method for unconstrained discrete-time optimal control problems", Computational Optimization and Applications, Vol. 4, no. 8, pp. 47-66. [DOI:10.1007/BF01299158]
3. [3] M. A. El-Shorbagy, A. M. El-Refaey, 2021, "Hybridization of grasshopper optimization algorithm with genetic algorithm for solving system of non-linear equations", IEEE Access, vol. 08, no. 10, pp. 1121-1136.
4. [4] R. S. Dembo, S. C. Eisenstat, T. Steihaug,1982, "Inexact Newton methods", SIAM journal on numerical analysis, vol. 19, pp. 400-408. [DOI:10.1137/0719025]
5. [5] Jorge. Nocedal, Stephen. J. Wright, "Numerical optimization", Springer, Mathematics subject classification, Second edition, 2006.
6. [6] T. F. Coleman, A. Liao, 1995, "An efficient trust region method for unconstrained discrete-time optimal control problems", Computational optimization and applications, vol. 4, pp. 47-66. [DOI:10.1007/BF01299158]
7. [7] S. Sen, S. J. Yakowitz, 1987, "A quasi-Newton differential dynamic programming algorithm for discrete-time optimal control", Automatica, vol. 23, no. 6, pp. 749-752. [DOI:10.1016/0005-1098(87)90031-8]
8. [8] T. Carraro, S. Dorsam, S. Frei, D. Schwartz, 2018, "An adaptive Newton algorithm for optimal control problem with application to optimal electrode design", Journal of Optimization theory and application, vol. 177, pp. 498-534. [DOI:10.1007/s10957-018-1242-4]
9. [9] I. E. Livieris, V. Tampakas, P. Pintelas, 2018, "A descent hybrid conjugate gradient method based on the memoryless BFGS update" Numerical Algorithms, vol. 79, pp. 1169-1185. [DOI:10.1007/s11075-018-0479-1]
10. [10] B. Houska, H. Jaochim Ferreau, M. Diehl, 2011, "An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range", Automatica, vol. 47, no. 10, pp. 2279-2285. [DOI:10.1016/j.automatica.2011.08.020]
11. [11] S. Gros, M. Zanon, R. Quirynen, A. bemporad, M. Diehl, 2016, "From linear to nonlinear MPC: bridging the gap via the real-time iteration", vol. 93, no. 1, pp. 62-80. [DOI:10.1080/00207179.2016.1222553]
12. [12] P. Falugi, D. Q. Mayne, 2014, "Getting robustness against unstructured uncertainty: A Tube-based MPC approach", IEEE transaction on automatic control, vol. 59, no. 5, pp. 1290-1295. [DOI:10.1109/TAC.2013.2287727]
13. [13] E. Nejabat, A. Nikoofard, 2021, "Switched robust model predictive based controller for UAV swarm system" IEEE, 29th Iranian conference of electrical engineering (ICEE), pp. 721-725. [DOI:10.1109/ICEE52715.2021.9544123]
14. [14] Z. Qiu, N, Jiang, 2021, "An ellipsoidal Newton's iteration method of nonlinear structural systems with uncertain but bounded parameters", Computer method in applied mechanics and engineering, vol. 373, no. 501, pp. 788-808. [DOI:10.1016/j.cma.2020.113501]
15. [15] X. Feng, S. Cairano, R. Quirenen, 2020, "Inexact adjoint-based SQP algorithm for real time stochastic nonlinear MPC" IFAC, vol. 53, no. 2, pp. 6529-6535. [DOI:10.1016/j.ifacol.2020.12.068]
16. [16] A. Jodaei, J. Saffar-Ardabili, 2021, "Controller design for containment problem of a class of multi-agent systems with nonlinear identical dynamics and fixed directed graph", Journal of Control, vol. 14, no. 4, pp. 198-209. [DOI:10.52547/joc.14.4.133]
17. [17] D. Xie, S. Xu, Y. Chu, Y. Zou, 2015, "Event-triggered average consensus for multi-agent systems with nonlinear dynamics and switching topology", Journal of the Franklin institute, vol. 352, no. 3, pp. 1080-1098. [DOI:10.1016/j.jfranklin.2014.11.004]
18. [18] D. Yang, W. Ren, X. Liu, W. Chen, 2016, "Decentralized event-triggered consensus for linear multi-agent systems under general directed graphs", Automatica, vol. 69, pp. 242-249. [DOI:10.1016/j.automatica.2016.03.003]
19. [19] Zhizheng. Hou, 2016, "Modeling and formation controller design for multi-quadrotor systems with leader follower configuration", M.Sc. Thesis, Universite de Technologie de Copiegne.
20. [۲۰] محمدرضا همایی‌نژاد، محمد حسین سعیدی مستقیم، فرنود عرب، ۱۴۰۱، "بازشناخت الگوی نیرو‌های یاتاقانی محور چرخان صلب دارای نامیرایی‌های جرمی"، نشریه مهندسی مکانیک امیرکبیر، در حال انتشار.
21. [21] Norman. Biggs, "Algebraic Graph Theory" Cambridge University Press, Second edition, 1993.
22. [22] J. Lofberg, 2004, "YALMIP: A toolbox for modeling and optimization in MATLAB", IEEE International Conference on Robotics and Automation, pp. 284-289.

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