Home Headings of UCAV Based on Nash Equilibrium
Article
Licensed
Unlicensed Requires Authentication

Headings of UCAV Based on Nash Equilibrium

  • Li Dai EMAIL logo and Zheng Xie
Published/Copyright: June 29, 2018
Become an author with De Gruyter Brill

Abstract

Given n vertices in a plane and UCAV going through each vertex once and only once and then coming back, the objective is to find the direction (heading) of motion in each vertex to minimize the smooth path of bounded curvature. This paper studies the headings of UCAV. First, the optimal headings for two vertices were given. On this basis, an n-player two-strategy game theoretic model was established. In addition, in order to obtain the mixed Nash equilibrium efficiently, n linear equations were set up. The simulation results demonstrated that the headings given in this paper are effective.

References

[1] Papadimitriou C. The Euclidean traveling salesman problem is NP-complete. Theor. Comp. Sci. 1977, 4(3): 237–244.10.1016/0304-3975(77)90012-3Search in Google Scholar

[2] Garey M R, Graham R L, Johnson D S. Some NP-complete geometric problems. Proc. 8th Annu. ACM Symp. Theory Comp., 1976: 10–22.10.1145/800113.803626Search in Google Scholar

[3] Ny J L, Feron E, Frazzoli E. On the Dubins traveling salesman problem. IEEE Transactions on Autonatic Control, 2012, 57: 265–270.10.1109/TAC.2011.2166311Search in Google Scholar

[4] Dubins L E. On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and Tangents. American Journal of Mathematics, 1957, 79: 497–516.10.2307/2372560Search in Google Scholar

[5] Shkel A M, Lumelsky V. Classification of the Dubins set. Robotics and Automonous Systems, 2001, 34: 179–202.10.1016/S0921-8890(00)00127-5Search in Google Scholar

[6] Dai L, Xie Z. On the length of dubins path with any initial and terminal configurations. Pure and Applied Mathematics Journal, 2015, 4: 248–254.10.11648/j.pamj.20150406.14Search in Google Scholar

[7] Savla K, Frazzoli E, Bullo F. Traveling salesman problems for the Dubins vehicle. IEEE Transections on Automatic Control, 2008, 53: 1378–1391.10.1109/TAC.2008.925814Search in Google Scholar

[8] Kim H S, Cheong O. The cost of bounded curvature. Computational Geometry: Theory and Applications, 2013, 46: 648–672.10.1016/j.comgeo.2012.10.008Search in Google Scholar

[9] Dixon W. Optimal adaptive sontrol and differential games by reinforcement learning principles. Journal of Guidance, Control, and Dynamics, 2014, 37(3): 1048–1049.10.2514/1.G000173Search in Google Scholar

[10] Gu D. A game theory approach to target tracking in sensor networks. IEEE Transactions Systems, Man and Cybernetics, Part B: Cybernetices, 2011, 41(1): 2–13.10.1109/TSMCB.2010.2040733Search in Google Scholar PubMed

[11] Duan H, Wei X, Dong Z. Multiple UCVAs cooperative air combat simulation platform based on PSO, ACO, and game theory. IEEE Aerospace and Electronic Systems Magazine, 2013, 28(11): 12–19.10.1109/MAES.2013.6678487Search in Google Scholar

[12] Duan H, Pei L, Yuan Y X. A predator-prey particle swarm optimization approach to multiple UCAV air combat modeled by dynamic game theory. IEEE Journal of Automatica Sinica, 2015, 2(1): 11–18.10.1109/JAS.2015.7032901Search in Google Scholar

[13] Wang M, Du Z, Duan H. Study on participant behavior game of electronic products reverse supply chain based on ECP. Journal of Systems Science and Information, 2017, 5(5): 441–434.10.21078/JSSI-2017-411-24Search in Google Scholar

[14] Wu J, Yang H, Cheng Y. Domino effect analysis, assessment and prevention in process industries. Journal of Systems Science and Information, 2015, 3(6): 481–498.10.1515/JSSI-2015-0481Search in Google Scholar

[15] Dai Y, Gao Y. Real-time pricing decision based on leader-follower game smart grid. Journal of Systems Science and Information, 2015, 3(6): 481–498.10.1515/JSSI-2015-0348Search in Google Scholar

[16] Porter R, Nudelman E, Shoham Y. Simple search methods for finding a Nash equilibrium. Games and Economic Behavior, 2008, 63(2): 642–662.10.1016/j.geb.2006.03.015Search in Google Scholar

[17] Chen X, Deng X, Teng S H. Settling the complexity of computing two-player Nash equilibrium. Journal of the ACM, 2009, 56(3): Article No.14.10.1145/1516512.1516516Search in Google Scholar

Received: 2017-05-03
Accepted: 2017-12-07
Published Online: 2018-06-29

© 2018 Walter De Gruyter GmbH, Berlin/Boston

Downloaded on 8.10.2025 from https://www.degruyterbrill.com/document/doi/10.21078/JSSI-2018-269-08/html
Scroll to top button